Part b1)Mass (kg)Velocity (m/s)Force (N)Acceleration (m/s2)Time to come to rest (s)stopping distance (m)
Lab 4--Part b1)
An object with a mass 'm' is moving with an initial speed 'v'and is acted on by a single force ‘F’ in the opposite direction of its motion. Use Excel to determine how long it will take the object to come to rest and how far the object travels until it stops..
i) If the mass is doubled, what is the effect on the time?, on the stopping distance?
ii) If the initial velocity is doubled, what is the effect on the time?, on the stopping distance
input: mass, initial velocity, force
output: acceleration, time to come to rest, stopping distance
Part b2)Mass (kg)Fx (N)Fy (N)ax (m/s2)ay (m/s2)2000050000100000time (s)vx(m/s)vy(m/s)v(m/s)x(m)y(m)d (m)00.511.522.533.544.555.566.577.588.599.510
Lab 4--Part b2)
A rocket ship, with mass m=40,000kg, and engines mounted perpendicularly in the x and y directions, fires both rockets simultaneously. The engine oriented in the x-direction fires for 3s and shuts off. The engine oriented in the y-direction fires for 7s and shuts off. The force from the engine in the x-direction is 50,000N and the force from the engine in the y-direction is 100,000N. Make a scatter plot of the y-position of each particle as a function of the x-position, showing the trajectory of the rocket.
Use Excel to determine the following:
i) While the engines are firing, what is the acceleration of the rocket in the x and y directions?
ii) After 7s, what is the velocity of the rocket in the x and y directions?
iii) After 7s, what is the speed of the rocket?
iv) After 7s, how far has the rocket travelled in the x-direction? How far has it travelled in the y-direction?, After 10 s?
v) After 7s, what is the displacement of the rocket? After 10 s? Is the displacement of the rocket the same as the distance travelled? Explain.
vi) If the mass of the rocket is doubled, what happens to the displacement?
Output: ax, ay, vx, vy, x, y, d
Rocket Trajectory
x
y
Part a1)Mass (kg)Force (N)Acceleration (m/s2)105010100205020100
Lab 4--Part a1)
Use Excel to determine the acceleration for an object with mass 'm' being pulled by a constant,
horizontal force (F) on a flat, frictionless surface.
i) What happens to the acceleration if the magnitude of the force doubles?
ii) What happens to the acceleration if the mass of the object doubles?
iii) What happens to the acceleration if both the mass and the force are doubled?
Input: mass and force
Output: acceleration
Part a2)Mass (kg)Angle (degrees)μkμsf_s(max)f_kF_Wsin(q)Acceleration (m/s2)Accelerating or Stationary?400.20.5450.20.54100.20.54150.20.54200.20.54250.20.54260.20.54270.20.54280.20.54290.20.54300.20.54350.20.54400.20.54450.20.54500.20.510500.20.54900.20.5
Lab 4--Part a2)
Use Excel to determine the acceleration for an object with mass 'm' sliding down a surface inclined at an angle θ (between 0 and 90 degrees) above the horizontal. The surfac.
This document summarizes key concepts from Chapter 4 of Holt Physics about forces and the laws of motion. It discusses the different types of forces, how to draw free-body diagrams, Newton's three laws of motion, mass vs weight, friction, and how to solve problems involving forces. The key points are that forces cause acceleration according to Newton's Second Law, inertia is an object's resistance to changes in motion, and forces always occur in equal pairs according to Newton's Third Law.
The document discusses key concepts in dynamics including different types of forces like normal force and friction. It explains Newton's laws of motion and how they can be applied to solve dynamics problems. Examples are provided on how to use the laws of motion to analyze inclined planes, lifts, tensions in connected objects, and other dynamics scenarios. Key concepts covered in 3 sentences or less include: Newton's laws of motion are introduced to explain how forces cause motion or changes in motion. Different types of forces like normal force, friction, and tension are defined. Examples are given on how to apply Newton's laws to solve dynamics problems involving inclined planes, connected objects, and lifts.
Newton's second law states that an object's acceleration depends on the net force acting on it and its mass. Force equals mass times acceleration. Newton's third law states that for every action there is an equal and opposite reaction. Gravity is a force between any two masses that depends on their masses and the distance between them, as described by the law of universal gravitation. In free fall, the only force acting is gravity, so all objects accelerate at the same rate due to gravity.
1) The document summarizes key concepts from Chapter 4 of a physics textbook, including Newton's laws of motion, forces, friction, and gravitational forces.
2) Newton's laws state that an object at rest stays at rest and an object in motion stays in motion unless acted upon by an unbalanced force, and that acceleration is produced when a net force acts on an object. The third law is that for every action there is an equal and opposite reaction.
3) Other concepts covered include friction, the normal force, gravitational forces, and applications of Newton's laws to inclined planes and tension forces. Examples are provided to illustrate these concepts.
Here are the steps to solve this problem:
a) Since the buckets are at rest, the tension in each cord must balance the weight of the bucket it supports. Therefore, the tension is 3.2 kg * 9.8 m/s2 = 31.36 N
b) Applying Newton's Second Law to each bucket:
Upper bucket: Tension - Weight = Mass * Acceleration
Tension - 3.2 kg * 9.8 m/s2 = 3.2 kg * 1.6 m/s2
Tension = 31.36 N + 3.2 * 1.6 = 35.2 N
Lower bucket: Tension - Weight = Mass * Acceleration
Tension - 3.
This document discusses the concept of forces in physics. It defines a force as a push or pull on an object and explains that forces are vectors that have both magnitude and direction. There are four main forces in nature: gravity, electromagnetism, the strong nuclear force, and the weak nuclear force. Dynamics and statics are introduced as areas of study related to forces and motion. Newton's three laws of motion are outlined. Common ways of measuring mass and examples of force problems are provided, including free body diagrams, friction, inclined planes, and pulleys.
A force is a push or pull that can cause an object to change its motion. There are two types of forces: contact forces that require touching and long-range forces like gravity that act over a distance. Newton's second law states that the acceleration of an object is proportional to the net force acting on it and inversely proportional to its mass. Newton also discovered that the direction of the force is the same as the direction of the acceleration it produces.
The document describes key concepts in physics including energy, force, motion, waves, electricity, and magnetism. Some key points covered include:
- Identifying energy transformations and transfers of heat energy through conduction, convection, and radiation.
- Describing and calculating concepts like velocity, acceleration, Newton's laws of motion, and mechanical advantage of simple machines.
- Investigating light and sound phenomena, static electricity, and the relationship between voltage, current and resistance in electric circuits.
- Relating electricity and magnetism and their common applications.
This document summarizes key concepts from Chapter 4 of Holt Physics about forces and the laws of motion. It discusses the different types of forces, how to draw free-body diagrams, Newton's three laws of motion, mass vs weight, friction, and how to solve problems involving forces. The key points are that forces cause acceleration according to Newton's Second Law, inertia is an object's resistance to changes in motion, and forces always occur in equal pairs according to Newton's Third Law.
The document discusses key concepts in dynamics including different types of forces like normal force and friction. It explains Newton's laws of motion and how they can be applied to solve dynamics problems. Examples are provided on how to use the laws of motion to analyze inclined planes, lifts, tensions in connected objects, and other dynamics scenarios. Key concepts covered in 3 sentences or less include: Newton's laws of motion are introduced to explain how forces cause motion or changes in motion. Different types of forces like normal force, friction, and tension are defined. Examples are given on how to apply Newton's laws to solve dynamics problems involving inclined planes, connected objects, and lifts.
Newton's second law states that an object's acceleration depends on the net force acting on it and its mass. Force equals mass times acceleration. Newton's third law states that for every action there is an equal and opposite reaction. Gravity is a force between any two masses that depends on their masses and the distance between them, as described by the law of universal gravitation. In free fall, the only force acting is gravity, so all objects accelerate at the same rate due to gravity.
1) The document summarizes key concepts from Chapter 4 of a physics textbook, including Newton's laws of motion, forces, friction, and gravitational forces.
2) Newton's laws state that an object at rest stays at rest and an object in motion stays in motion unless acted upon by an unbalanced force, and that acceleration is produced when a net force acts on an object. The third law is that for every action there is an equal and opposite reaction.
3) Other concepts covered include friction, the normal force, gravitational forces, and applications of Newton's laws to inclined planes and tension forces. Examples are provided to illustrate these concepts.
Here are the steps to solve this problem:
a) Since the buckets are at rest, the tension in each cord must balance the weight of the bucket it supports. Therefore, the tension is 3.2 kg * 9.8 m/s2 = 31.36 N
b) Applying Newton's Second Law to each bucket:
Upper bucket: Tension - Weight = Mass * Acceleration
Tension - 3.2 kg * 9.8 m/s2 = 3.2 kg * 1.6 m/s2
Tension = 31.36 N + 3.2 * 1.6 = 35.2 N
Lower bucket: Tension - Weight = Mass * Acceleration
Tension - 3.
This document discusses the concept of forces in physics. It defines a force as a push or pull on an object and explains that forces are vectors that have both magnitude and direction. There are four main forces in nature: gravity, electromagnetism, the strong nuclear force, and the weak nuclear force. Dynamics and statics are introduced as areas of study related to forces and motion. Newton's three laws of motion are outlined. Common ways of measuring mass and examples of force problems are provided, including free body diagrams, friction, inclined planes, and pulleys.
A force is a push or pull that can cause an object to change its motion. There are two types of forces: contact forces that require touching and long-range forces like gravity that act over a distance. Newton's second law states that the acceleration of an object is proportional to the net force acting on it and inversely proportional to its mass. Newton also discovered that the direction of the force is the same as the direction of the acceleration it produces.
The document describes key concepts in physics including energy, force, motion, waves, electricity, and magnetism. Some key points covered include:
- Identifying energy transformations and transfers of heat energy through conduction, convection, and radiation.
- Describing and calculating concepts like velocity, acceleration, Newton's laws of motion, and mechanical advantage of simple machines.
- Investigating light and sound phenomena, static electricity, and the relationship between voltage, current and resistance in electric circuits.
- Relating electricity and magnetism and their common applications.
This document provides an overview of Newton's Laws of Motion, including discussions of weight and normal force, free-body diagrams, tension in cords, incline planes, and several example problems. Key concepts covered are that an object's weight is due to gravitational force, the normal force equals the gravitational force when an object is at rest, and how to draw and analyze free-body diagrams to determine forces and accelerations in various situations. Example problems demonstrate applications of these concepts, such as boxes on tables or inclines being pulled or pushed by various forces.
This document discusses forces and Newton's laws of motion. It begins by asking what causes an object to remain at rest or in motion, and defines force as a vector quantity that can change an object's motion. It then introduces Newton's three laws of motion: 1) An object remains at rest or in uniform motion unless acted upon by an external force, 2) The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass, and 3) For every action there is an equal and opposite reaction. Examples of different types of forces like normal force, friction, and weight are also provided.
A force is any influence that causes an object to change its movement, direction, or shape. Forces can make an object begin moving, change speed or direction of motion, or cause a flexible object to deform. There are two main types of forces: contact forces, which act between objects in direct contact, and non-contact forces, which act over a distance. Contact forces include normal forces, friction, and tension. Non-contact forces include gravitational, electric, and magnetic forces. Newton's laws of motion describe how forces cause motion or changes in motion.
1) Work is defined as a force acting upon an object to cause displacement and is expressed as the product of force and displacement in the direction of force.
2) The work done on a body depends on the magnitude of the force and the displacement through which the body moves in the direction of force.
3) As the angle between the direction of force and motion of the body increases, less work is done along the direction of motion since less of the force is acting in that direction.
This document summarizes key concepts from Chapter 4 of a college physics textbook, including Newton's laws of motion. It discusses concepts like force, mass, inertia, gravity, friction, and how forces cause motion and determine acceleration. Examples are provided to illustrate applying Newton's laws to solve problems involving forces like tension, normal force, gravitational force, and static/kinetic friction. The document also discusses how forces like air resistance impact a falling object's motion.
A force is any interaction that causes a change in the motion of an object. There are several key laws of motion:
1) Newton's First Law states that an object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.
2) Newton's Second Law states that the acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.
3) Newton's Third Law states that for every action, there is an equal and opposite reaction.
The document goes
Horizontal and vertical motion are independent in projectile motion. The horizontal range is maximized when the launch angle is 45 degrees. Uniform circular motion describes objects moving in a circle at constant speed. Centripetal acceleration points toward the center and is required to maintain circular motion. Newton's laws relate forces to motion: the first law states an object in motion stays in motion unless acted on by a net external force, the second law defines acceleration as proportional to net force, and the third law states forces between objects act in equal magnitude but opposite directions.
The document defines different types of forces including contact forces and action-at-a-distance forces. It provides examples of various contact forces like frictional force, tension force, and normal force. Gravity, electricity, and magnetism are given as examples of action-at-a-distance forces. The document also discusses units of force, vectors, mass versus weight, static versus kinetic friction, balanced versus unbalanced forces, and provides practice problems to illustrate these concepts.
5-1 NEWTON’S FIRST AND SECOND LAWS
After reading this module, you should be able to . . .
5.01 Identify that a force is a vector quantity and thus has
both magnitude and direction and also components.
5.02 Given two or more forces acting on the same particle,
add the forces as vectors to get the net force.
5.03 Identify Newton’s first and second laws of motion.
5.04 Identify inertial reference frames.
5.05 Sketch a free-body diagram for an object, showing the
object as a particle and drawing the forces acting on it as
vectors with their tails anchored on the particle.
5.06 Apply the relationship (Newton’s second law) between
the net force on an object, the mass of the object, and the
acceleration produced by the net force.
5.07 Identify that only external forces on an object can cause
the object to accelerate.
5-2 SOME PARTICULAR FORCES
After reading this module, you should be able to . . .
5.08 Determine the magnitude and direction of the gravitational force acting on a body with a given mass, at a location
with a given free-fall acceleration.
5.09 Identify that the weight of a body is the magnitude of the
net force required to prevent the body from falling freely, as
measured from the reference frame of the ground.
5.10 Identify that a scale gives an object’s weight when the
measurement is done in an inertial frame but not in an accelerating frame, where it gives an apparent weight.
5.11 Determine the magnitude and direction of the normal
force on an object when the object is pressed or pulled
onto a surface.
5.12 Identify that the force parallel to the surface is a frictional
the force that appears when the object slides or attempts to
slide along the surface.
5.13 Identify that a tension force is said to pull at both ends of
a cord (or a cord-like object) when the cord is taut. etc...
Welcome to the fascinating world of Work, Energy, and Power! In the realm of physics, these concepts form the cornerstone of understanding how objects interact with each other and how energy is transformed within systems. From the motion of everyday objects to the dynamics of celestial bodies, the principles of work, energy, and power are ubiquitous, shaping the very fabric of the universe.
For more information, visit-www.vavaclasses.com
1) Inertia is the tendency of an object to resist changes in its motion. Mass is a measure of an object's inertia, with more massive objects being harder to accelerate or decelerate.
2) Newton's second law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This relationship can be expressed as F=ma.
3) Newton's third law states that for every action force there is an equal and opposite reaction force. Forces always occur in action-reaction pairs between interacting objects.
Karen Adelan presented on the topic of classical mechanics and energy. Some key points:
- Energy is a conserved quantity that can change forms but is never created or destroyed. It is useful for describing motion when Newton's laws are difficult to apply.
- Kinetic energy is the energy of motion and depends on an object's mass and speed. The work-kinetic energy theorem states that the net work done on an object equals the change in its kinetic energy.
- Potential energy is the energy an object possesses due to its position or state. The work done by a constant force equals the product of force, displacement, and the cosine of the angle between them.
This document provides definitions and concepts related to dynamics and kinematics. It defines dynamics as the study of motion considering the causes that produce it, such as forces and mass, while kinematics is the study of motion in terms of space and time without considering causes. It also defines key concepts like force, mass, Newton's laws of motion. Specifically, it states that Newton's first law is that an object at rest stays at rest or an object in motion stays in motion with constant velocity unless acted upon by a net external force. Newton's second law relates the net force on an object to its acceleration.
1. The document discusses different topics related to work, energy and power including dot product, definitions of work and energy, forms of energy, kinetic energy, work-energy theorem, and potential energy.
2. Key concepts covered are the mathematical definitions of work as the product of force and displacement, and of kinetic energy as one-half mass times velocity squared.
3. The work-energy theorem states that the work done on an object equals its change in kinetic energy, or the work equals the final kinetic energy minus the initial kinetic energy.
The document discusses tension formula, rotational motion, torque, rotational kinetic energy, elasticity, plasticity, Hooke's law, and simple pendulums. It provides formulas for calculating tension, rotational kinematics, torque, rotational kinetic energy, elastic modulus, Hooke's law, and the period of a simple pendulum. It also includes example problems and solutions for some of the formulas.
The document discusses key concepts in mechanics including:
1. Free body diagrams show only the external forces acting on an object and are useful for solving dynamics problems.
2. Newton's Second Law states that acceleration is proportional to net force and inversely proportional to mass.
3. Impulse is the product of force and time and equals change in momentum, affecting how objects move after collisions or other impacts.
The document discusses work, energy, and the work-energy principle as an alternative way to analyze motion compared to using forces and Newton's laws. It defines key terms like work, kinetic energy, and systems. The work-energy principle states that the net work done on an object equals its change in kinetic energy (Wnet = ΔKE). This allows reexpressing Newton's second law in terms of energy rather than forces. Examples show how to calculate work, kinetic energy, and use the work-energy principle to solve motion problems.
Engineering Mechanics covers various topics in mechanics including:
1. Relativistic mechanics deals with mechanics compatible with special and general relativity.
2. Quantum mechanics provides a mathematical description of energy, matter, and their interactions at nanoscopic scales.
3. Mechanics of deformable bodies deals with how forces are distributed in solid bodies and the resulting stresses and deformations.
This document discusses the kinetics of particles and Newton's laws of motion. It explains that the two main factors affecting an object's motion are the forces acting on it and its mass. Newton's second law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The equation F=ma expresses this relationship, where F is the net force, m is the mass, and a is the acceleration. The document also provides examples demonstrating applications of Newton's laws to problems involving blocks connected by cords and pulleys.
Write a 5-7 page paper describing the historical development of info.docxherbertwilson5999
Healthcare informatics has evolved over time with different types of systems emerging to manage health information. Properly handling personal health data requires ethical expertise. Today's integrated delivery systems rely on informatics to coordinate complex care across settings while protecting privacy.
Write a 5 paragraph essay related to the healthcare fieldthree.docxherbertwilson5999
Write a 5 paragraph essay related to the healthcare field/three major points are required
Use a variety of sentences
Use transitional words
Use in-text citations to avoid plagiarism
Remember to hand it in with a cover and a reference page
.
More Related Content
Similar to Part b1)Mass (kg)Velocity (ms)Force (N)Acceleration (ms2)Time to.docx
This document provides an overview of Newton's Laws of Motion, including discussions of weight and normal force, free-body diagrams, tension in cords, incline planes, and several example problems. Key concepts covered are that an object's weight is due to gravitational force, the normal force equals the gravitational force when an object is at rest, and how to draw and analyze free-body diagrams to determine forces and accelerations in various situations. Example problems demonstrate applications of these concepts, such as boxes on tables or inclines being pulled or pushed by various forces.
This document discusses forces and Newton's laws of motion. It begins by asking what causes an object to remain at rest or in motion, and defines force as a vector quantity that can change an object's motion. It then introduces Newton's three laws of motion: 1) An object remains at rest or in uniform motion unless acted upon by an external force, 2) The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass, and 3) For every action there is an equal and opposite reaction. Examples of different types of forces like normal force, friction, and weight are also provided.
A force is any influence that causes an object to change its movement, direction, or shape. Forces can make an object begin moving, change speed or direction of motion, or cause a flexible object to deform. There are two main types of forces: contact forces, which act between objects in direct contact, and non-contact forces, which act over a distance. Contact forces include normal forces, friction, and tension. Non-contact forces include gravitational, electric, and magnetic forces. Newton's laws of motion describe how forces cause motion or changes in motion.
1) Work is defined as a force acting upon an object to cause displacement and is expressed as the product of force and displacement in the direction of force.
2) The work done on a body depends on the magnitude of the force and the displacement through which the body moves in the direction of force.
3) As the angle between the direction of force and motion of the body increases, less work is done along the direction of motion since less of the force is acting in that direction.
This document summarizes key concepts from Chapter 4 of a college physics textbook, including Newton's laws of motion. It discusses concepts like force, mass, inertia, gravity, friction, and how forces cause motion and determine acceleration. Examples are provided to illustrate applying Newton's laws to solve problems involving forces like tension, normal force, gravitational force, and static/kinetic friction. The document also discusses how forces like air resistance impact a falling object's motion.
A force is any interaction that causes a change in the motion of an object. There are several key laws of motion:
1) Newton's First Law states that an object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.
2) Newton's Second Law states that the acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.
3) Newton's Third Law states that for every action, there is an equal and opposite reaction.
The document goes
Horizontal and vertical motion are independent in projectile motion. The horizontal range is maximized when the launch angle is 45 degrees. Uniform circular motion describes objects moving in a circle at constant speed. Centripetal acceleration points toward the center and is required to maintain circular motion. Newton's laws relate forces to motion: the first law states an object in motion stays in motion unless acted on by a net external force, the second law defines acceleration as proportional to net force, and the third law states forces between objects act in equal magnitude but opposite directions.
The document defines different types of forces including contact forces and action-at-a-distance forces. It provides examples of various contact forces like frictional force, tension force, and normal force. Gravity, electricity, and magnetism are given as examples of action-at-a-distance forces. The document also discusses units of force, vectors, mass versus weight, static versus kinetic friction, balanced versus unbalanced forces, and provides practice problems to illustrate these concepts.
5-1 NEWTON’S FIRST AND SECOND LAWS
After reading this module, you should be able to . . .
5.01 Identify that a force is a vector quantity and thus has
both magnitude and direction and also components.
5.02 Given two or more forces acting on the same particle,
add the forces as vectors to get the net force.
5.03 Identify Newton’s first and second laws of motion.
5.04 Identify inertial reference frames.
5.05 Sketch a free-body diagram for an object, showing the
object as a particle and drawing the forces acting on it as
vectors with their tails anchored on the particle.
5.06 Apply the relationship (Newton’s second law) between
the net force on an object, the mass of the object, and the
acceleration produced by the net force.
5.07 Identify that only external forces on an object can cause
the object to accelerate.
5-2 SOME PARTICULAR FORCES
After reading this module, you should be able to . . .
5.08 Determine the magnitude and direction of the gravitational force acting on a body with a given mass, at a location
with a given free-fall acceleration.
5.09 Identify that the weight of a body is the magnitude of the
net force required to prevent the body from falling freely, as
measured from the reference frame of the ground.
5.10 Identify that a scale gives an object’s weight when the
measurement is done in an inertial frame but not in an accelerating frame, where it gives an apparent weight.
5.11 Determine the magnitude and direction of the normal
force on an object when the object is pressed or pulled
onto a surface.
5.12 Identify that the force parallel to the surface is a frictional
the force that appears when the object slides or attempts to
slide along the surface.
5.13 Identify that a tension force is said to pull at both ends of
a cord (or a cord-like object) when the cord is taut. etc...
Welcome to the fascinating world of Work, Energy, and Power! In the realm of physics, these concepts form the cornerstone of understanding how objects interact with each other and how energy is transformed within systems. From the motion of everyday objects to the dynamics of celestial bodies, the principles of work, energy, and power are ubiquitous, shaping the very fabric of the universe.
For more information, visit-www.vavaclasses.com
1) Inertia is the tendency of an object to resist changes in its motion. Mass is a measure of an object's inertia, with more massive objects being harder to accelerate or decelerate.
2) Newton's second law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This relationship can be expressed as F=ma.
3) Newton's third law states that for every action force there is an equal and opposite reaction force. Forces always occur in action-reaction pairs between interacting objects.
Karen Adelan presented on the topic of classical mechanics and energy. Some key points:
- Energy is a conserved quantity that can change forms but is never created or destroyed. It is useful for describing motion when Newton's laws are difficult to apply.
- Kinetic energy is the energy of motion and depends on an object's mass and speed. The work-kinetic energy theorem states that the net work done on an object equals the change in its kinetic energy.
- Potential energy is the energy an object possesses due to its position or state. The work done by a constant force equals the product of force, displacement, and the cosine of the angle between them.
This document provides definitions and concepts related to dynamics and kinematics. It defines dynamics as the study of motion considering the causes that produce it, such as forces and mass, while kinematics is the study of motion in terms of space and time without considering causes. It also defines key concepts like force, mass, Newton's laws of motion. Specifically, it states that Newton's first law is that an object at rest stays at rest or an object in motion stays in motion with constant velocity unless acted upon by a net external force. Newton's second law relates the net force on an object to its acceleration.
1. The document discusses different topics related to work, energy and power including dot product, definitions of work and energy, forms of energy, kinetic energy, work-energy theorem, and potential energy.
2. Key concepts covered are the mathematical definitions of work as the product of force and displacement, and of kinetic energy as one-half mass times velocity squared.
3. The work-energy theorem states that the work done on an object equals its change in kinetic energy, or the work equals the final kinetic energy minus the initial kinetic energy.
The document discusses tension formula, rotational motion, torque, rotational kinetic energy, elasticity, plasticity, Hooke's law, and simple pendulums. It provides formulas for calculating tension, rotational kinematics, torque, rotational kinetic energy, elastic modulus, Hooke's law, and the period of a simple pendulum. It also includes example problems and solutions for some of the formulas.
The document discusses key concepts in mechanics including:
1. Free body diagrams show only the external forces acting on an object and are useful for solving dynamics problems.
2. Newton's Second Law states that acceleration is proportional to net force and inversely proportional to mass.
3. Impulse is the product of force and time and equals change in momentum, affecting how objects move after collisions or other impacts.
The document discusses work, energy, and the work-energy principle as an alternative way to analyze motion compared to using forces and Newton's laws. It defines key terms like work, kinetic energy, and systems. The work-energy principle states that the net work done on an object equals its change in kinetic energy (Wnet = ΔKE). This allows reexpressing Newton's second law in terms of energy rather than forces. Examples show how to calculate work, kinetic energy, and use the work-energy principle to solve motion problems.
Engineering Mechanics covers various topics in mechanics including:
1. Relativistic mechanics deals with mechanics compatible with special and general relativity.
2. Quantum mechanics provides a mathematical description of energy, matter, and their interactions at nanoscopic scales.
3. Mechanics of deformable bodies deals with how forces are distributed in solid bodies and the resulting stresses and deformations.
This document discusses the kinetics of particles and Newton's laws of motion. It explains that the two main factors affecting an object's motion are the forces acting on it and its mass. Newton's second law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The equation F=ma expresses this relationship, where F is the net force, m is the mass, and a is the acceleration. The document also provides examples demonstrating applications of Newton's laws to problems involving blocks connected by cords and pulleys.
Write a 5-7 page paper describing the historical development of info.docxherbertwilson5999
Healthcare informatics has evolved over time with different types of systems emerging to manage health information. Properly handling personal health data requires ethical expertise. Today's integrated delivery systems rely on informatics to coordinate complex care across settings while protecting privacy.
Write a 5 paragraph essay related to the healthcare fieldthree.docxherbertwilson5999
Write a 5 paragraph essay related to the healthcare field/three major points are required
Use a variety of sentences
Use transitional words
Use in-text citations to avoid plagiarism
Remember to hand it in with a cover and a reference page
.
Write at least a six-page paper, in which youIdentify the.docxherbertwilson5999
Write at least a six-page paper, in which you:
Identify the two LDCs (from the provided list), which you will compare and assess. Explain why you chose these two countries. (Congo and Philippines)
Analyze the features that the LDCs have in common using at least five of the following nine factors (clearly label the five factors using headings):
Geography.
Extractive institutions.
Governmental corruption.
Internal or external conflicts.
Shaky financial systems.
Unfair judicial systems.
Ethnic, racial, or tribal disparities.
Lack or misuse of natural resources.
Closed (statist) economies.
Use at least seven credible sources. Wikipedia, encyclopedias, dictionaries, and blogs do not qualify as reputable academic source work at the college level. Do not use sources that are older than seven years.
.
Write a 2 page paper analyzing the fact pattern scenario below. Plea.docxherbertwilson5999
Write a 2 page paper analyzing the fact pattern scenario below. Please use your own state law. Your analysis should include application of the topics covered during the past 7 weeks. For example, search and seizure, search warrant, execution of warrant, exclusionary rule, Miranda rights, and the right against self incrimination.
Make sure all citations are in APA or Blue book format.
Please see the attached grading rubric below. This grading rubric will be used to grade this assignment.
Leila is a police officer. She is out of uniform and knocked on Dan's front door of his house and asked if she could enter to enforce a warrant she had. The warrant was a search warrant issued by a magistrate at the Lawrence District Court. His name is Mark McCale, a retired police officer for the state police department in Lawrence. The warrant indicated that "the first floor of Dan's house will be searched for a gun used in connection with a robbery and some jewelry, which was stolen." While looking in Dan's house, Officer Leila smelled what she thought to be gun powder emanating from the second floor. Officer Leila immediately walked upstairs and found a gun at the tops of the stairs. She went to confiscate the gun and while doing so noticed a note attached to the gun with an address on it. Later that afternoon police officers went to the address of the house listed on the note of the gun. Jewelry was found at this address and collected by the police officers. The address was a known address for stolen jewelry to be pawned. While at Dan's house, Dan told Officer Leila that, "I do not know what you are here for, because I did not rob Terri Grubb's jewelry store." Officer Leila asked Dan to go to the police station and Dan agreed. As they walked into the police station, Magistrate McCale yelled, "is that the person who robbed Terri Grubb's jewelry store?!" Dan replied, "I told Officer Leila already, I did not rob Terri Grubb's jewelry store."
Supporting Materials
Week 8 Assignment Grading Rubric.docx
(14 KB)
.
Write a 2 page paper analyzing the fact pattern scenario below. .docxherbertwilson5999
Write a 2 page paper analyzing the fact pattern scenario below. Please use your own state law. Your analysis should include application of the topics covered during the past 7 weeks. For example, search and seizure, search warrant, execution of warrant, exclusionary rule, Miranda rights, and the right against self incrimination.
Make sure all citations are in APA or Blue book format.
Please see the attached grading rubric below. This grading rubric will be used to grade this assignment.
Leila is a police officer. She is out of uniform and knocked on Dan's front door of his house and asked is should could enter to enforce a warrant she had. The warrant was a search warrant issued by a magistrate at the Lawrence District Court. His name is Mark McCale, a retired police officer for the state police department in Lawrence. The warrant indicated that "the first floor of Dan's house will be searched for a gun used in connection with a robbery and some jewelry, which was stolen." While looking in Dan's house, Officer Leila smelled what she thought to be gun powder emanating from the second floor. Officer Leila immediately walked upstairs and found a gun at the tops of the stairs. She went to confiscate the gun and while doing so noticed a note attached to the gun with an address on it. Later that afternoon police officers went to the address of the house listed on the note of the gun. A bunch of jewelry was found at this address and collected by the police officers. The address was a known address for stolen jewelry to be pawned. While at Dan's house, Dan told Officer Leila that, "I do not know what you are here for, because I did not rob the Terri Grubb's jewelry store." Officer Leila asked Dan to go to the police station and Dan agreed. As they walked into the police station, Magistrate McCale yelled, "is that the person who robbed Terri Grubb's jewelry store?!" Dan replied, "I told Officer Leila already, I did not rob the Terri Grubb's jewelry store."
.
Write a 100-word response in Spanish that addresses both of .docxherbertwilson5999
Write a
100
-word response in
Spanish
that addresses both of the following questions:
1.
What are some of the distinctive characteristics that make Costa Rica a haven for naturalists and environmentalists?
2.
What are some of the steps that the government, private sector and individuals are doing to maintain the balance between man and nature?
.
Write a Request for Proposal (approx. 3 - 4 pages in a word doc.docxherbertwilson5999
The document provides guidance on creating a Request for Proposal (RFP) that is approximately 3-4 pages. It lists 9 key elements that should be included in an effective RFP: 1) a clear statement of work with deliverables, 2) a timeline for proposal submission, 3) how questions will be handled, 4) information for vendors to develop a cost proposal, 5) a project timeline and milestones, 6) the type of contract, 7) evaluation criteria, 8) an outline and format for proposals, and 9) a scheduled award date. Submitters are asked to write an RFP that incorporates these elements and submit the PMP template for Section 8.
Write a 5 paragraph essay related to Physical Therapy Assistant th.docxherbertwilson5999
Write a 5 paragraph essay related to Physical Therapy Assistant /three major points are required
Use a variety of sentences
Use transitional words
Use in-text citations to avoid plagiarism
Include a cover and a reference page
Minimal of three sources
.
Write a 5 page paper with at-least three images that represent.docxherbertwilson5999
Write a 5 page paper with at-least three images that represent the African American Visual Arts Movement (discuss artists, art, historical information . Give background information, characteristics and style. Analyze each work of art. Do not forget to list at-least three sources used to assist in writing paper, APA format guidelines. Place appropriate captions under each image.
Fragments of African American Art
Contemporary Art
Surrealism
Realism
OR
After reviewing the videos below and researching , write a two page paper on the
challenges of
African American VISUAL Artists
and other professional minority visual artists through out history and up to the present day
. Use a minimum of 5 references that will assist you in writing your paper.
https://www.youtube.com/watch?v=u8kg8xzJNt8
.
Write a 5 paragraph essay related to the healthcare fieldthree maj.docxherbertwilson5999
Write a 5 paragraph essay related to the healthcare field/three major points are required
Use a variety of sentences
Use transitional words
Use in-text citations to avoid plagiarism
Remember to hand it in with a cover and a reference page
.
Write at least Ten sentences on your discussion. Compare and con.docxherbertwilson5999
Write at least Ten sentences on your discussion.
Compare and contrast the California economy of the Great Depression and the California economy of World War II. Which industries were prevalent during the war and why was California's location/geography so important?
.
Write at least a three-page analysis using the case study on pages.docxherbertwilson5999
This document provides instructions and examples for students to write posts discussing similarities and differences between the current COVID-19 pandemic and past pandemics like the 1918 influenza pandemic and 2009 H1N1 pandemic. Students are asked to write three original posts making comparisons and commenting on five other student posts. The examples provided compare transmission methods and case numbers between COVID-19 and H1N1. References must be included. The document also provides questions for students to respond to in writing assignments on global leadership and managing corporations internationally while considering cultural differences.
Write at least a six-page paper, in which you Identify th.docxherbertwilson5999
Write at least a six-page paper, in which you:
Identify the two LDCs (from the list above), which you will compare and assess. Explain why you chose these two countries.
Analyze the features that the LDCs have in common using
at least five of the following nine factors
(clearly label the five factors using headings):
geography
extractive institutions
governmental corruption
internal or external conflicts
shaky financial systems
unfair judicial systems
ethnic, racial or tribal disparities
lack or misuse of natural resources
closed (statist) economies
Use
at least seven credible sources
. Wikipedia, encyclopedias, dictionaries, blogs and other material that does not qualify as reputable academic source work at the college level. Do not use sources that are older than seven years.
.
Write at least a paragraph for each.1) What is your understand.docxherbertwilson5999
Write at least a paragraph for each.
1) What is your understanding of how a 401(k) plan works? What are the advantages/disadvantages for an employer/employee?
2) What three major types of benefits do contributions to Social Security pay for?
3) What are the employee benefits required by law?
*Use APA format please! and cite accordingly!
.
Write at least 500 words analyzing a subject you find in this .docxherbertwilson5999
Write at least 500 words analyzing a subject you find in this
article
related to a threat to confidentiality, integrity, or availability of data. Use an example from the news.
Include at least one quote from 3 articles, place them in quotation marks and cite in-line (as all work copied from another should be handled).
Cite your sources in a reference list at the end. Do not copy without providing proper attribution (quotation marks and in-line citations). Write in essay format not in bulleted, numbered or other list format
.
Write at least 750 words paper on Why is vulnerability assessme.docxherbertwilson5999
Write at least 750 words paper on “Why is vulnerability assessment critical for data security?” And also prepare twelve minutes or more presentations on this topic by adding notes under each slide. with a separate reference list of at least 3 academically appropriate sources. Provide appropriate attribution. It is important that you use your own words, that you cite your sources, that you comply with the instructions regarding the length of your post. Do not use spinbot or other word replacement software. It usually results in nonsense and is not a good way to learn anything.
.
Write As if You Are Writing in Your Journal (1st Person)Your T.docxherbertwilson5999
**Write As if You Are Writing in Your Journal (1st Person)
Your Thoughts And Intentions.
What challenges do you face (i.e., bad habits, weaknesses, etc.) that you need to address to move forward as a leader? How can you begin to address them? (Be sure to make personal application and make it practical).
.
Write an original, Scholarly Paper, addressing a topic relevant to t.docxherbertwilson5999
Write an original, Scholarly Paper, addressing a topic relevant to the course. A scholarly paper should demonstrate a standard of critical thinking at levels of analysis, evaluation, and synthesis. Be sure to use and cite references that meet the standard for scholarship.
.
Write an observation essay that explains the unique significance.docxherbertwilson5999
Write an
observation essay
that explains the unique significance of a particular person or place within a larger community. Describe the person or place through vivid description, narration, dialogue and sensory details. Help others outside of your community understand why the person or place is important to the community.
Assignment
Observation
, as the CEL describes it, requires writers to "study their subjects and learn something by seeing them in a particular way" (93). Observation essays do more than just report facts: they also "find the hidden meaning, the significant issues, and the important aspects of a particular subject" (93).
Your purpose in this Observation Essay is to
convey the significance of a particular person or place in your community through details that show how the subject "fits" within the community's priorities and values
. Your descriptions and details should make it easy for someone unfamiliar with your community to understand why the person or place you chose is relevant and significant to the community.
*Note: although this essay is intended to be based in recent, firsthand observations, you may write from recent memories instead if you are restricted in travel and mobility during the COVID pandemic. If you are writing from memories, try to recreate scenes and descriptions as though you are seeing them again for the first time.
In order to achieve this purpose, you need to:
Observe and Take field notes. Begin with observing the person or place and writing down notes about what you see, hear, and sense. Plan to observe this person or place 2-3 times. In your notes, record specific actions that you notice, dialogue you overhear, interactions you have with other people, and any important details about the scene that might help you SHOW its significance through vivid detail and narration.
Describe the person or place through actions, details, and dialogue that offer
insight
into why this person or place has unique
significance
as an important part of the community.
Explain context and background that shows how the person or place matters within the larger community. Context might include history, factual information, anecdotes, geographical information, or other details that help an audience understand the person or place as part of something bigger than themselves/itself.
Follow a carefully planned organizational structure that gives priority to specific details, themes, and values. Your final draft should be organized to show the significance of the person or place and should not simply list details in the order you observed them.
Offer a strong introduction that hooks readers with vivid details or action and focuses attention on the significance of the subject. Provide a strong conclusion that
As you look back over your observations and notes, remember that your essay should do more than simply relate details without any larger significance. Your observation of the person or place should .
Write an introduction in APA format in about 2 pages to describe.docxherbertwilson5999
Write an introduction in APA format in about 2 pages to describe any bank organization – its background etc. Then explain how data science and big data is useful for the back.
Also explain the IT team dynamics in the organization I.e. all the positions that are in the IT team of the bank developers, project managers etc.
Also explain how the company uses the agile model in the workflow for the data science projects.
Explain what is structured and unstructured data. What the sources of structured and unstructured data in a bank and what are the sources of these data.
Please provide at least 3-4 in text citation and references.
.
Beyond Degrees - Empowering the Workforce in the Context of Skills-First.pptxEduSkills OECD
Iván Bornacelly, Policy Analyst at the OECD Centre for Skills, OECD, presents at the webinar 'Tackling job market gaps with a skills-first approach' on 12 June 2024
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
How to Manage Your Lost Opportunities in Odoo 17 CRMCeline George
Odoo 17 CRM allows us to track why we lose sales opportunities with "Lost Reasons." This helps analyze our sales process and identify areas for improvement. Here's how to configure lost reasons in Odoo 17 CRM
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UPRAHUL
This Dissertation explores the particular circumstances of Mirzapur, a region located in the
core of India. Mirzapur, with its varied terrains and abundant biodiversity, offers an optimal
environment for investigating the changes in vegetation cover dynamics. Our study utilizes
advanced technologies such as GIS (Geographic Information Systems) and Remote sensing to
analyze the transformations that have taken place over the course of a decade.
The complex relationship between human activities and the environment has been the focus
of extensive research and worry. As the global community grapples with swift urbanization,
population expansion, and economic progress, the effects on natural ecosystems are becoming
more evident. A crucial element of this impact is the alteration of vegetation cover, which plays a
significant role in maintaining the ecological equilibrium of our planet.Land serves as the foundation for all human activities and provides the necessary materials for
these activities. As the most crucial natural resource, its utilization by humans results in different
'Land uses,' which are determined by both human activities and the physical characteristics of the
land.
The utilization of land is impacted by human needs and environmental factors. In countries
like India, rapid population growth and the emphasis on extensive resource exploitation can lead
to significant land degradation, adversely affecting the region's land cover.
Therefore, human intervention has significantly influenced land use patterns over many
centuries, evolving its structure over time and space. In the present era, these changes have
accelerated due to factors such as agriculture and urbanization. Information regarding land use and
cover is essential for various planning and management tasks related to the Earth's surface,
providing crucial environmental data for scientific, resource management, policy purposes, and
diverse human activities.
Accurate understanding of land use and cover is imperative for the development planning
of any area. Consequently, a wide range of professionals, including earth system scientists, land
and water managers, and urban planners, are interested in obtaining data on land use and cover
changes, conversion trends, and other related patterns. The spatial dimensions of land use and
cover support policymakers and scientists in making well-informed decisions, as alterations in
these patterns indicate shifts in economic and social conditions. Monitoring such changes with the
help of Advanced technologies like Remote Sensing and Geographic Information Systems is
crucial for coordinated efforts across different administrative levels. Advanced technologies like
Remote Sensing and Geographic Information Systems
9
Changes in vegetation cover refer to variations in the distribution, composition, and overall
structure of plant communities across different temporal and spatial scales. These changes can
occur natural.
A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.
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How to Make a Field Mandatory in Odoo 17Celine George
In Odoo, making a field required can be done through both Python code and XML views. When you set the required attribute to True in Python code, it makes the field required across all views where it's used. Conversely, when you set the required attribute in XML views, it makes the field required only in the context of that particular view.
Reimagining Your Library Space: How to Increase the Vibes in Your Library No ...Diana Rendina
Librarians are leading the way in creating future-ready citizens – now we need to update our spaces to match. In this session, attendees will get inspiration for transforming their library spaces. You’ll learn how to survey students and patrons, create a focus group, and use design thinking to brainstorm ideas for your space. We’ll discuss budget friendly ways to change your space as well as how to find funding. No matter where you’re at, you’ll find ideas for reimagining your space in this session.
Part b1)Mass (kg)Velocity (ms)Force (N)Acceleration (ms2)Time to.docx
1. Part b1)Mass (kg)Velocity (m/s)Force (N)Acceleration
(m/s2)Time to come to rest (s)stopping distance (m)
Lab 4--Part b1)
An object with a mass 'm' is moving with an initial speed 'v'and
is acted on by a single force ‘F’ in the opposite direction of its
motion. Use Excel to determine how long it will take the object
to come to rest and how far the object travels until it stops..
i) If the mass is doubled, what is the effect on the time?, on the
stopping distance?
ii) If the initial velocity is doubled, what is the effect on the
time?, on the stopping distance
input: mass, initial velocity, force
output: acceleration, time to come to rest, stopping distance
Part b2)Mass (kg)Fx (N)Fy (N)ax (m/s2)ay
(m/s2)2000050000100000time
(s)vx(m/s)vy(m/s)v(m/s)x(m)y(m)d
(m)00.511.522.533.544.555.566.577.588.599.510
Lab 4--Part b2)
A rocket ship, with mass m=40,000kg, and engines mounted
perpendicularly in the x and y directions, fires both rockets
simultaneously. The engine oriented in the x-direction fires for
3s and shuts off. The engine oriented in the y-direction fires
for 7s and shuts off. The force from the engine in the x-
direction is 50,000N and the force from the engine in the y-
2. direction is 100,000N. Make a scatter plot of the y-position of
each particle as a function of the x-position, showing the
trajectory of the rocket.
Use Excel to determine the following:
i) While the engines are firing, what is the acceleration of the
rocket in the x and y directions?
ii) After 7s, what is the velocity of the rocket in the x and y
directions?
iii) After 7s, what is the speed of the rocket?
iv) After 7s, how far has the rocket travelled in the x-direction?
How far has it travelled in the y-direction?, After 10 s?
v) After 7s, what is the displacement of the rocket? After 10 s?
Is the displacement of the rocket the same as the distance
travelled? Explain.
vi) If the mass of the rocket is doubled, what happens to the
displacement?
Output: ax, ay, vx, vy, x, y, d
Rocket Trajectory
x
y
Part a1)Mass (kg)Force (N)Acceleration
(m/s2)105010100205020100
3. Lab 4--Part a1)
Use Excel to determine the acceleration for an object with mass
'm' being pulled by a constant,
horizontal force (F) on a flat, frictionless surface.
i) What happens to the acceleration if the magnitude of the
force doubles?
ii) What happens to the acceleration if the mass of the object
doubles?
iii) What happens to the acceleration if both the mass and the
force are doubled?
Input: mass and force
Output: acceleration
Part a2)Mass (kg)Angle
(degrees)μkμsf_s(max)f_kF_Wsin(q)Acceleration
(m/s2)Accelerating or
Stationary?400.20.5450.20.54100.20.54150.20.54200.20.54250.
20.54260.20.54270.20.54280.20.54290.20.54300.20.54350.20.5
4400.20.54450.20.54500.20.510500.20.54900.20.5
Lab 4--Part a2)
Use Excel to determine the acceleration for an object with mass
'm' sliding down a surface inclined at an angle θ (between 0 and
90 degrees) above the horizontal. The surface has a coefficient
of kinetic friction μk and a coefficient of static friction μs.
4. Note 1: Within the calculation, before taking sine or cosine, the
angle must be converted to radians.
Use the built in function 'RADIANS' for this purpose
Note 2: the coefficient of static friction must be overcome in
order for the object to start sliding. Therefore, you must
determine if the force pulling the object down the incline is
greater than the force of static friction. If it is, the acceleration
can be determined. Otherwise, the object will remain stationary
and the acceleration reading will be erroenous.
Use the built in function 'IF' for this purpose.
If the object is accelerating, have the IF command output
"Accelerating".
If the object is not accelearting, have the IF command output
"Stationary".
Once it has been determined that the object is accelerating,
determine the magnitude of the acceleration.
Create a scatter chart of acceleration versus angle of incline for
angles from 0 to 50 degrees.
i) Does the mass of the object affect the acceleration? Explain.
ii) What happens when θ=90 degrees? Is the acceleration
affected by the coefficients of friction?
Input: m, θ, μk, μs
Output: Accelerating or Stationary?, magnitude of the
5. acceleration
acceleration versus angle of incline
0 5 10 15 20 25 26 27 28 29 30 35 40
45 50
angle (degrees)
acceleration (m/s^2)
Part a3)Mass (kg)Weight (N)Acceleration (m/s2)Scale Reading
(N)
Lab 4--Part a3)
An object, with mass m=100kg, is sitting on a scale in an
elevator. Use Excel to determine the reading on the scale (in
Newtons) for the following 4 situations:
i) elevator accelerating upward at +3 m/s2
ii) elevator moving at constant speed
iii) elevator accelerating downward at -3 m/s2
iv) elevator accelerating downward at -9.8 m/s2
Input: acceleration of the elevator
Output: Reading on the scale
6. Lab 4—Newton’s Second Law of Motion
Background
Newton’s Second Law of Motion
Newton‟s Second Law of Motion relates the total force on an
object to the resultant acceleration.
Mathematically, it can be expressed as
where m is the „mass‟ or „inertial mass‟ of the object and a is
the acceleration.
On the left hand side of this equation, the forces are being
added together, using Σ. Thus, if there
is more than one force acting on an object, it is the resulting
sum that determines the
acceleration. On the right hand side of the equation, is the
effect of the force: a net force results
in an acceleration that is proportional to an objects mass.
For two dimensional problems, the vector equation above can be
rewritten as two scalar
equations
7. where now the forces are accelerations are scalar quantities.
In the SI system, we use the following units for mass and
acceleration: [m] = kg, [a] = m/s
2
.
From Newton‟s Second Law, therefore, the units for a force are
[F] = (kg•m/s
2
). In honor of
Isaac Newton, we call a (kg•m/s
2
) a newton (N) and express forces in newtons.
Gravitation
With gravity, every particle in the universe with mass attracts
every other particle with mass.
This was first postulated by Isaac Newton, and it later became
known as Newton‟s Law of
Universal Gravitation:
Every particle of matter in the universe attracts every other
particle with a force that is directly
proportional to the product of the masses of the particles and
inversely proportional to the square
of the distance between them
8. Mathematically, this can be expressed as
2
21
r
mGm
where m1 and m2 are the objects gravitational masses
r is the distance between the center of masses
G is Newton‟s gravitational constant, 2211 /1067.6 kgmNG
For any object with mass „m‟ near the surface of the Earth, we
can write
gmm
r
Gm
r
mGm
F
E
E
9. 21
where
rE is the radius of the Earth
mE is the mass of the Earth
Since mE and rE are known quantities, they can be combined
with „G‟, leading to
Since we call the local force of gravity on an object due to the
earth the object‟s weight, we can
write
Normal Force
The normal force arises from two solid objects in direct contact
and it is always a push. An
object resting on a surface is supported by a normal force and a
surface has a normal force
exerted on it by an object it supports. The normal force is
called „normal‟ because it‟s always
perpendicular to or normal to a surface.
10. For an object resting on a scale for example, the reading on the
scale is the normal force exerted
by the object, on the scale. In other words, the scale reads how
hard the object is pushing on it
(the normal force).
Kinetic and Static Friction
Frictional forces act to resist the motion of objects. The contact
force between two bodies can
often be represented by the normal force + frictional force. The
normal force acts perpendicular
to surface and the frictional force acts parallel. The normal and
frictional forces are thus always
perpendicular
Frictional force can be categorized as either „kinetic‟ or
„static‟. The kinetic friction force (fk )
acts when a body slides over a surface. Its magnitude increases
as the normal force increases. In
many cases the magnitude of the kinetic friction force can be
expressed (approximately) as
11. where µk is the coefficient of kinetic friction and „n‟ is the
magnitude of the normal force
The coefficient of kinetic friction is a unit-less quantity
between 0 and 1 and characterizes how
„slippery‟ the interface between two materials is. µk is smaller
(closer to 0) for more „slippery‟
surfaces and larger (closer to 1) for less „slippery‟ surfaces.
The static friction force( fs ) acts when there is no relative
motion between two surfaces. And
like the force of kinetic friction, its magnitude also increases as
the normal force increases. In
order to move a body, the static friction force must be overcome
first, and then the force of
kinetic friction acts.
fs is a variable force, meaning it can take on a range of values,
and can be expressed
(approximately) as
where µs is the coefficient of static friction and „n‟ is the
magnitude of the normal force.
12. As with the coefficient of kinetic friction, the coefficient of
static friction is a unit-less quantity
between 0 and 1 and characterizes how „slippery‟ the interface
between two materials is. The
Note that after fs is overcome, fk is less (since μk<μs). So,
once an object breaks loose
(overcomes static friction), it slides more easily.
Inclined plane with friction:
Newton‟s Second Law is a useful tool to analyze an object
sliding down an incline. For an
object with a mass „m‟ sliding down a surface inclined at an
angle θ above the horizontal,
we can draw a free body diagram and coordinate system, like
the one below
θ
m
with the x-axis oriented parallel to the surface and the y-axis
oriented perpendicular.
Assuming the object is already sliding, we can apply Newton‟s
13. Second Law to the „x‟ and „y‟
directions separately to find the acceleration is the x-direction
(down the incline).
y-direction
x-direction
cossincossin
cossinsin
sinsin
kk
kkW
x
kWfWxx
ggg
m
mgmg
m
14. nF
a
nFFFmaF
As mentioned above, the object will not slide until the force of
static friction is first overcome.
Applying the same analysis, this requires that
Thus, when this condition is met, the force of gravity acting
down the incline is greater than the
force of static friction, and the object begins to slide.
θ
Ff
Fgx
15. Fgy
Fg
x
y
n
This laboratory exercise is divided into a part (a) and a part(b).
At your instructor’s
discretion, you may be required to work each part together or
separately.
Part a1)
Apply Newton‟s Second Law directly to determine the
acceleration of an object, given a mass
and a net force. Use Excel to calculate the acceleration for any
force and mass entered by the
user. Since there is only one force acting, Newton‟s Second
Law reduces to .
Part a2)
Using Excel and the equations above, analyze an object on an
inclined plane. First, determine if
the component of the gravitational force acting down the plane
is enough to overcome the static
16. frictional force. To do so, use the IF command
IF(logical_test, value_if_true, value_if_false)
For the logical test, use
For the value if true, type “Stationary”
For the value if false, type “Accelerating”
Allow the user to input the mass, angle, and coefficients of
friction and have Excel determine if
the object is accelerating, and if so, what the magnitude of the
acceleration is.
To do so, you will need to have Excel convert from degrees to
radians using the function
RADIANS. Note that this expression can be inserted directly
into a mathematical statement. So,
for example, to calculate the cosine of an angle initially given
in degrees, we can convert it to
radians and calculate the cosine in a single step:
=COS(RADIANS(angle))
Part a3)
Using Excel and the equations above, determine the apparent
weight of an object under
acceleration. In this case, we are considering an object resting
17. on a scale in an elevator. If we
consider the object alone, there are two forces acting on it: the
force of gravity and the normal
force from the scale.
Object
n
From Newton‟s third law of motion, the normal force from the
scale on the object is equal and
opposite to the normal force from the object on the scale. Since
the scale reads the normal force
from the object, we can solve for the normal force exerted on
the object and know the reading on
the scale.
Applying Newton‟s second law to the object, we have
∑
Note: when applying this equation, g is +9.8 m/s
2
18. (not -9.8m/s
2
) and „a‟ is negative if the
elevator is accelerating downward and positive if it‟s
accelerating upwards.
Allow the user to input the acceleration of the elevator and have
Excel determine the reading on
the scale.
Part b1)
Using Excel and the equations above, determine how long it
takes an object to come to rest if it‟s
acted on by a force in the opposite direction of its velocity.
From Newton‟s Second Law, we can solve for the acceleration
„a‟ of an object with mass „m‟,
affected by a single force „F‟
Recall that for an object under constant acceleration, its
velocity as a function of time is
where vi is the initial velocity. Thus, using the two equations
above, we can solve for the
stopping time „ts‟ where v = 0.
19. Note: when using this equation, vi and F must be in opposite
directions (opposite signs) or the
object will never come to rest. From the stopping time, the
stopping distance can be calculated
from the formula:
Fg
Part b2)
Using Excel and the equations above, determine the
displacement of an object acted on by forces
in both the „x‟ and „y‟ directions. As mentioned above, we can
apply Newton‟s second law to
determine the accelerations in the „x‟ and „y‟ directions
separately
Once we know the accelerations in the „x‟ and „y‟ directions,
we can apply our kinematic
equations to solve for the velocity and displacement as a
20. function of time.
and
with similar equations for „y‟.
Recall though that the kinematic equations are only valid when
the acceleration is constantThe
acceleration is constant for „x‟, from 0 to 3 secondsbut for „x‟,
at t=3s, the acceleration changes
(to zero). Thus from 3s to 10s, the displacement in the x-
direction is
where vi is the speed in the x-direction after 3 seconds. The
total displacement in the x-direction
is the displacement from 0s to 3s plus the displacement from 3s
to 10s. The acceleration in the y-
direction is constant from 0s to 7s and then is zero from 7s to
10s.
Deliverables
See the syllabus for due date information. Place all your work
inside the Week 4 Lab
Template. Be sure to follow all instructions carefully.
Save your ONE Excel file using the filename format
"lastname_firstinitial_week4lab".
21. For example, if you are Albert Einstein and you are submitting
your Week 4 lab, the
filename should be "einstein_a_week4lab". Submit your
assignment to the Lab4
dropbox located on the silver tab at the top of this page.
Tutorials: Entering formulas in Excel and creating graphs
For more information on using Excel, please watch the
following tutorials from the Microsoft
Excel 2007 website:
Excel 2007 support/training: http://office.microsoft.com/en-
us/training/CR010047968.aspx
1) “Get to know Excel 2007: Enter formulas”
2) “Charts 1: How to create a chart in Excel 2007”
”
http://office.microsoft.com/en-us/training/CR010047968.aspx
TemplateTime35m/s @ 55°35m/s @ 25°t (s)x (m)y (m)vx
(m/s)vy (m/s)speed (m/s)x (m)y (m)vx (m/s)vy (m/s)speed
(m/s)00.00.00.00.00.250.50.7511.251.51.7522.252.52.7533.253.
53.7544.254.54.7555.255.55.756
x-position vs time
55 degrees 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2
22. 2.25 2.5 2.75 3 3.25 3.5 3.75 4 4.25 4.5 4.75 5
5.25 5.5 5.75 6 0 25 Degrees 0 0.25 0.5
0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 3.25
3.5 3.75 4 4.25 4.5 4.75 5 5.25 5.5 5.75 6 0
Time (s)
Horizontal Position (m)
y-position vs time
55 Degrees 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2
2.25 2.5 2.75 3 3.25 3.5 3.75 4 4.25 4.5 4.75 5
5.25 5.5 5.75 6 0 25 Degrees 0 0.25 0.5
0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 3.25 0
Time (s)
Height (m)
Trajectory
55 Degrees 0 0 25 Degrees 0 0
x-position
y-position
Lab 3
Two identical projectiles are launched from the Earth's surface
Projectile #1 has an intial velocity of 35 m/s and is launched at
an angle of 55 degrees above horizontal.
Projectile #2 also has an initial velocity of 35 m/s and is
launched at an angle of 25 degrees above horizontal.
Assume the ground is perfectly flat and both projectiles are
launched from ground level (y=0m), where x=0m.
Neglecting air resistance, do the following:
i) Determine the x-position and y-position of both projectiles as
a function of time, from t=0s
23. until they hit the ground (y=0m). In each case, include only one
value where y<0.
Note that one projectile will hit the ground before the other, so
one set of values needs to be calculated beyond the
other.
ii) Make a scatter plot of the x-position versus time for each
projectile, on the same graph (started to the right).
Approximately, what is the range of each projectile?
Compare this value with the range equation, R=(vi2•sin2θ)/g
where vi is the inital speed of the projectile,
θ is the launch angle and 'g' is the local gravitational constant
(=9.8m/s2 near Earth's surface).
iii) Make a scatter plot of the y-position versus time for each
projectile on the same graph (started to the right).
Approximately, what is the maximum height of each projectile?
Compare this value with the height equation, h=(vi2•sin2θ)/2g
where vi is the inital speed of the projectile,
θ is the launch angle and 'g' is the local gravitational constant
(=9.8m/s2 near Earth's surface).
How long does it take each projectile to reach it's maximum
height?
24. iv) Make a scatter plot of the y-position of each particle as a
function of the x-position, showing the trajectory of
the projectiles.
Mathematically, how do we describe the shape of this graph?
v) Determine the velocity in the x and y directions, along with
the speed of both projectiles as a function of time,
from t=0s until they hit the ground (y=0m). As with step i), in
each case, include only one value where y<0.
What happens to the velocity in the y-direction when the
projectiles reach their maximum height?
What is true about the velocity in the x-direction for both
projectiles?
What is true about the speed of both projectiles at the instances
when they are launched and when they hit the ground?
Does the launch angle affect the speed of the projectiles when
they hit the ground? Explain.
25. Lab 3—Projectile Motion
Background
For an object undergoing constant acceleration in one
dimension, we developed equations that
describe the position and velocity of the object as a function of
time.
∆ ∆ and ∆
If we assume the object starts at position xi=0 at time ti=0, the
equations can be simplified as
and
where ‘x’ is the final position of the object and ‘v’ is the final
velocity.
Since these equations are true for any direction, they can be
applied to the y-direction in a two-
dimensional motion problem, assuming the acceleration in the
y-direction is also constant. Thus
we have,
and
For an object with an initial speed vi and initial velocity
directed at an angle θ above the +x axis,
the x and y components of the velocity vector are
26. ∙ and ∙
Since the velocity has components in both the x direction and
the y direction, the speed of the
object at any time can be found from the Pythagorean Theorem:
| |
Projectile motion problems are a specific case of two-
dimensional motion problems. Most
projectile problems take place on the Earth’s surface. To solve
the problems in the simplest
terms, we ignore air resistance. Furthermore, we assume the
projectile does not travel far from
the surface. Otherwise, the acceleration in the y-direction
would not be constant. Under these
conditions, the components of the acceleration are constant, and
shown below
and
where ‘g’ is the local gravitational acceleration near the surface
of the Earth.
Inserting these values into our general equations, we have
and
27. Inserting our expressions for the initial velocities, we now have
∙
and
∙
At this point, we will assume our projectile is travelling over a
flat surface. Without this
assumption, we would need to consider whether our projectile
might hit a hill or even a mountain
or land at a higher or lower point. From our equation for y, we
can set y = 0, solve for t. This
will be the time it takes the projectile to hit the ground. If we
plug this expression into the
equation for x, we will have an expression for the horizontal
distance the object travels before it
strikes the ground as a function of the initial speed, launch
angle and local gravitational
acceleration. This is the so called range equation.
0
1
2
→
1 2⁄
g
v
R i
28. Realizing that the expression for t in the equation above is the
time it takes for the projectile to
hit the ground, ½ of this value will be the time it takes to reach
its maximum height. We can
then derive an expression for the maximum height by plugging
the time to reach the maximum
height into our expression for y:
1
2
∙
1 2⁄
→
∙
1
2
→
∙
2
Modeling in Excel
Using the equations above, develop an Excel spreadsheet to
determine the velocity and position
of projectiles as a function of time. To do so, you will need to
29. have Excel convert from degrees
to radians using the function RADIANS. Note that this
expression can be inserted directly into a
mathematical statement. So, for example, to calculate the
cosine of an angle initially given in
degrees, we can convert it to radians and calculate the cosine in
a single step:
=COS(RADIANS(angle))
For all of the steps below, consider two projectiles, both
launched with the same initial speed,
but at different angles.
Projectile #1 has an initial velocity of 35 m/s and is launched at
an angle of 55 degrees above
horizontal.
Projectile #2 also has an initial velocity of 35 m/s and is
launched at an angle of 25 degrees
above horizontal.
Answer the questions in the text box in Excel by typing
complete sentences directly under the
question. Change the color of your text to dark blue to highlight
your answers.
i. Determine the x-position and y-position of both projectiles as
a function of time, from t =
0 s until they hit the ground (y = 0 m). In each case, include
only one value where y < 0.
Note that one projectile will hit the ground before the other, so
one set of values needs to
be calculated beyond the other.
30. ii. Make a scatter plot of x versus t, estimate the range of the
projectile and compare this
value with the range equation shown above.
iii. Make a scatter plot of y versus t, estimate the maximum
height of the projectile and
compare this value with the height equation shown above.
iv. Make a scatter plot of y versus x. This shows the trajectory
of the projectile, or the path
traced out by the projectile, through space.
v. Determine the components of the projectile’s velocity and
speed as a function of time
Again, note that one projectile will hit the ground before the
other, so one set of values
needs to be calculated beyond the other.
Deliverables
See the syllabus for due date information. Place all your work
inside the Week 3 Lab
Template. Be sure to follow all instructions carefully.
Save your ONE Excel file using the filename format
"lastname_firstinitial_week3lab".
For example, if you are Albert Einstein and you are submitting
your Week 3 lab, the
31. filename should be "einstein_a_week3lab". Submit your
assignment to the Lab3
dropbox located on the silver tab at the top of this page.
Tutorials: Entering formulas in Excel and creating graphs
For more information on using Excel, please watch the
following tutorials from the Microsoft
Excel 2007 website:
Excel 2007 support/training: http://office.microsoft.com/en-
us/training/CR010047968.aspx
1) “Get to know Excel 2007: Enter formulas”
2) “Charts 1: How to create a chart in Excel 2007”