The document discusses different types of forces including contact forces, non-contact forces, frictional forces, and buoyant forces. It defines force as a push or pull that can change the motion of an object. There are two main types of forces - contact forces that act directly between objects in contact, and non-contact forces that act over a distance through force fields. Examples of both types are given. Frictional forces oppose the relative motion of objects in contact and can be useful or disadvantageous depending on the situation. Methods to measure the coefficient of friction are also described.
1. The document discusses static equilibrium of coplanar force systems. It covers drawing free-body diagrams, identifying reaction forces, and applying the three equations of equilibrium.
2. Key steps for solving problems include drawing the free-body diagram, identifying known and reaction forces, and setting the sum of forces and moments equal to zero.
3. Examples show calculating unknown forces and reactions for beams, rods, and pulley systems in static equilibrium. Forces and moments are analyzed to determine the magnitude and direction of reaction forces.
- Newton's laws of motion describe the relationship between an object and the forces acting upon it.
- The 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.
- The 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.
1. Physics is the branch of science that deals with the study of matter, energy, and their interaction. It includes various sub-fields like mechanics, electromagnetism, optics, nuclear physics, atomic physics, geophysics, astrophysics, and thermodynamics.
2. Fundamental physics quantities include length, mass, time, temperature, amount of substance, electric current, and luminous intensity. Derived quantities include speed, acceleration, force, work, power, momentum, and others.
3. Vectors represent physical quantities that have both magnitude and direction, while scalars only have magnitude. Vectors can be added and subtracted using the head-to-tail rule.
Definition of force,types of forces,law of forces,system of forces, moment of a force, couple,moment of a couple,types of moments,features of couple and principle of moments.
1. Energy is the ability to cause change. It exists in various forms including kinetic energy (related to motion) and potential energy (stored energy).
2. Kinetic energy depends on an object's mass and speed, and can be calculated as KE = 1/2mv^2. Potential energy includes gravitational potential energy (GPE), which depends on mass and height/position, calculated as GPE = mgh.
3. The law of conservation of energy states that energy can never be created or destroyed, only transferred or changed from one form to another. Mechanical energy equals the sum of an object's kinetic and potential energies.
Forces can cause objects to deform, speed up, slow down, or change direction. A free-body diagram represents all the forces acting on an object with arrows pointing in the direction of each force. Newton's Second Law states that the acceleration of an object is proportional to the net force acting on it. Newton's Third Law states that for every force there is an equal and opposite reaction force.
Free body diagrams show the relative magnitude and direction of all forces acting upon an object by isolating it from its surroundings. The document provides examples of free body diagrams for the Statue of Liberty, a sitting gorilla, a wooden swing, a bungee jumper's bucket, a traffic light, and the pin at point A of a truss bridge. Forces are shown as vectors with arrows indicating direction and labels providing magnitudes. Diagrams for static systems will sum the vertical and horizontal forces to zero, indicating equilibrium.
1. The document discusses static equilibrium of coplanar force systems. It covers drawing free-body diagrams, identifying reaction forces, and applying the three equations of equilibrium.
2. Key steps for solving problems include drawing the free-body diagram, identifying known and reaction forces, and setting the sum of forces and moments equal to zero.
3. Examples show calculating unknown forces and reactions for beams, rods, and pulley systems in static equilibrium. Forces and moments are analyzed to determine the magnitude and direction of reaction forces.
- Newton's laws of motion describe the relationship between an object and the forces acting upon it.
- The 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.
- The 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.
1. Physics is the branch of science that deals with the study of matter, energy, and their interaction. It includes various sub-fields like mechanics, electromagnetism, optics, nuclear physics, atomic physics, geophysics, astrophysics, and thermodynamics.
2. Fundamental physics quantities include length, mass, time, temperature, amount of substance, electric current, and luminous intensity. Derived quantities include speed, acceleration, force, work, power, momentum, and others.
3. Vectors represent physical quantities that have both magnitude and direction, while scalars only have magnitude. Vectors can be added and subtracted using the head-to-tail rule.
Definition of force,types of forces,law of forces,system of forces, moment of a force, couple,moment of a couple,types of moments,features of couple and principle of moments.
1. Energy is the ability to cause change. It exists in various forms including kinetic energy (related to motion) and potential energy (stored energy).
2. Kinetic energy depends on an object's mass and speed, and can be calculated as KE = 1/2mv^2. Potential energy includes gravitational potential energy (GPE), which depends on mass and height/position, calculated as GPE = mgh.
3. The law of conservation of energy states that energy can never be created or destroyed, only transferred or changed from one form to another. Mechanical energy equals the sum of an object's kinetic and potential energies.
Forces can cause objects to deform, speed up, slow down, or change direction. A free-body diagram represents all the forces acting on an object with arrows pointing in the direction of each force. Newton's Second Law states that the acceleration of an object is proportional to the net force acting on it. Newton's Third Law states that for every force there is an equal and opposite reaction force.
Free body diagrams show the relative magnitude and direction of all forces acting upon an object by isolating it from its surroundings. The document provides examples of free body diagrams for the Statue of Liberty, a sitting gorilla, a wooden swing, a bungee jumper's bucket, a traffic light, and the pin at point A of a truss bridge. Forces are shown as vectors with arrows indicating direction and labels providing magnitudes. Diagrams for static systems will sum the vertical and horizontal forces to zero, indicating equilibrium.
This document discusses moments and their applications. It defines moment as the product of a force and the perpendicular distance to the point of rotation. There are clockwise and anticlockwise moments. Varignon's principle of moments states the algebraic sum of moments about any point equals the moment of the resultant force. Levers are machines that use moments to multiply force. There are three types of simple levers and examples of levers include scissors and pliers. Compound levers use multiple simple levers together. Moments allow machines like levers to provide mechanical advantage.
Concept of Particles and Free Body Diagram
Why FBD diagrams are used during the analysis?
It enables us to check the body for equilibrium.
By considering the FBD, we can clearly define the exact system of forces which we must use in the investigation of any constrained body.
It helps to identify the forces and ensures the correct use of equation of equilibrium.
Note:
Reactions on two contacting bodies are equal and opposite on account of Newton's III Law.
The type of reactions produced depends on the nature of contact between the bodies as well as that of the surfaces.
Sometimes it is necessary to consider internal free bodies such that the contacting surfaces lie within the given body. Such a free body needs to be analyzed when the body is deformable.
Physical Meaning of Equilibrium and its essence in Structural Application
The state of rest (in appropriate inertial frame) of a system particles and/or rigid bodies is called equilibrium.
A particle is said to be in equilibrium if it is in rest. A rigid body is said to be in equilibrium if the constituent particles contained on it are in equilibrium.
The rigid body in equilibrium means the body is stable.
Equilibrium means net force and net moment acting on the body is zero.
Essence in Structural Engineering
To find the unknown parameters such as reaction forces and moments induced by the body.
In Structural Engineering, the major problem is to identify the external reactions, internal forces and stresses on the body which are produced during the loading. For the identification of such parameters, we should assume a body in equilibrium. This assumption provides the necessary equations to determine the unknown parameters.
For the equilibrium body, the number of unknown parameters must be equal to number of available parameters provided by static equilibrium condition.
Force, types of forces and system of forcesKhanSaif2
This presentation covers concept of force and different types of forces as well as different system of forces. I hope this PPT will be helpful for instructors as well as students.
This document discusses levers and moments. It provides examples of levers in the body, such as bones and joints. It explains that the longer the lever, the bigger the force needed to move an object. It also discusses moments and how they are calculated by multiplying force by distance from the pivot. Examples are provided about balancing moments on a seesaw. The document also discusses how counterweights on cranes allow them to lift heavy loads by balancing the moments of the load and counterweight.
This document provides an overview of friction including definitions, types, coefficients, and applications. It defines friction as the resisting force that opposes motion between two surfaces in contact. The document describes static and kinetic friction, the coefficient of friction as the ratio between friction force and normal force, and the angle of friction. It also discusses applications of friction including the angle of repose, ladder friction, wedge friction, and screw friction.
The document discusses heat and phase changes. It defines key terms like heat of fusion and heat of vaporization, which refer to the energy required for a substance to change phases. The document also provides an example heating curve for 1 gram of water and uses equations like q=m*H to calculate energy changes during phase transitions. It gives examples of calculating the heat required to melt ice, condense a gas, and change ice to water over a temperature range.
This document discusses Isaac Newton's three laws of motion and their applications. Newton's first law states that objects at rest stay at rest and objects in motion stay in motion unless acted on by an unbalanced force. Newton's second law establishes that force equals mass times acceleration (F=ma). Newton's third law describes that for every action there is an equal and opposite reaction. Examples are provided to demonstrate these laws, such as how gravity causes apples to fall from trees and how objects with different masses accelerate at the same rate but with different forces due to their mass.
The document discusses the center of gravity (CoG) and stability of objects. It defines CoG as the point where the entire weight of an object can be considered to act. For regular shapes, the CoG is at the geometric center. For irregular objects, methods are described to find the CoG using a plumb line and balance point. An object is stable when its CoG is directly above or within its base, and unstable if the CoG falls outside the base, allowing it to more easily rotate. Features like a low CoG and wide base promote stability.
This document discusses the concepts of uniform circular motion including:
- Uniform circular motion is motion at a constant speed in a circular path.
- Centripetal acceleration is the acceleration directed toward the center of the circle.
- Centripetal force is the force required to cause an object to travel in a circular path and is directed toward the center.
- For an object to remain in a circular orbit, it must travel at a specific orbital speed that depends on the radius of the orbit.
This document defines friction and its types, including static and dynamic friction. It discusses limiting friction force, normal reaction force, and coefficient of friction. It provides the laws of static and dynamic friction. Key concepts covered are that friction opposes motion, static friction is when bodies are at rest while dynamic friction occurs when in motion, and coefficient of friction is the ratio of limiting friction force to normal reaction force.
11. kinetics of particles work energy methodEkeeda
The document provides information about work, kinetic energy, work energy principle, and conservation of energy. It defines key terms like work, kinetic energy, spring force, weight force, friction force, power, and efficiency. It explains:
- Work is the product of force and displacement in the direction of force. Work by various forces can be used to solve kinetics problems.
- Kinetic energy is the energy of motion and is defined as one-half mass times velocity squared.
- The work energy principle states that the total work done by forces on an object equals its change in kinetic energy.
- For conservative forces acting on a particle, the mechanical energy (sum of kinetic and potential energy) is
This document discusses the concept of stability and center of gravity (CoG). It begins by defining stability as an object's ability to return to its original position after being tilted, while instability means an object continues moving past its original position. An object is in equilibrium when stationary. The CoG is the point where all the object's weight seems to be concentrated and where gravitational force acts. For regular shapes, the CoG is at the geometric center. Irregular shapes require finding the CoG experimentally by balancing on different points. Stability depends on CoG position and base size - a lower CoG and wider base increase stability. The document provides various examples and explanations of these concepts.
1) Newton's three laws of motion are described, including the first law of inertia, the second law relating force, mass and acceleration, and the third law of equal and opposite reactions.
2) The first law states that an object at rest stays at rest and an object in motion stays in motion unless acted on by an unbalanced force. Friction is given as an example of a force that can slow objects down.
3) The second law establishes the formula F=ma, where force equals mass times acceleration. Several examples are given to illustrate applications of this law.
This document discusses equilibrium and centre of mass. It defines moment or torque as the turning effect of a force. The moment of a force depends on both the size of the force and the distance from the pivot. An object is in equilibrium when the sum of clockwise moments equals the sum of anticlockwise moments. For an object to be in equilibrium, the forces must balance and the principle of moments must apply. The centre of mass is the point where the entire weight of an object can be considered to act. Several diagrams show how to determine the centre of mass for different objects.
(1) The document discusses moments, which are turning forces that cause an object to rotate rather than push it linearly. Moments depend on the magnitude of the applied force and its distance from the pivot point.
(2) To calculate the moment of a single force, the formula is Moment = Force x Perpendicular Distance from the pivot. When multiple forces are present, their individual moments are summed.
(3) Systems in equilibrium have their clockwise and counter-clockwise moments equal, allowing one to solve for unknown values like reactions at supports. Diagrams are drawn and moments taken to set up and solve equations of equilibrium.
The document summarizes Newton's three laws of motion and other key concepts in mechanics. It discusses Newton's first law of inertia, second law relating force and acceleration, and third law of equal and opposite reaction. It also defines concepts like impulse, momentum, work, energy, and power. Key principles discussed include conservation of linear momentum, mechanical energy, and total energy in a closed system.
This document defines key terms related to moments and forces:
- A moment is the product of a force and its perpendicular distance from the pivot point, and has a direction of either clockwise or counterclockwise.
- The center of gravity is the point where an object's entire weight is considered to act. For regular shapes it is the geometric center, and for irregular shapes it can be found by balancing.
- The plumb line method uses three lines dropped from holes in a lamina to find their intersection point, which is the center of gravity.
- The principle of moments states that the sum of clockwise moments equals the sum of counterclockwise moments about a point, with the total being zero.
The document discusses momentum and its conservation during collisions. It defines impulse as the product of an average force and the time interval over which it acts. The impulse-momentum theorem states that the impulse on an object equals its change in momentum. The conservation of momentum principle states that the total momentum of an isolated system remains constant, even after internal interactions and collisions within the system.
Lesson 2_ effects of forces.pptx about forces and its effectsmadonnasibrahim
Forces can cause objects to change motion, speed, direction or shape. A force is a push or pull that can be measured in Newtons, though forces cannot be seen directly. This document discusses different types of forces including gravity, friction, air resistance, upthrust and how forces affect objects. It provides examples of how pushing and pulling change the motion and shape of objects. An experiment is described to measure the difference between an object's weight in air and water, and how upthrust causes the weight to be less in water.
This document discusses key concepts in fluid mechanics, including:
1) Fluid statics, hydrostatic equilibrium, Archimedes' principle, and buoyancy.
2) Fluid dynamics principles like conservation of mass expressed by the continuity equation, and conservation of energy expressed by Bernoulli's equation.
3) Applications of fluid dynamics concepts like calculating flow rates and velocities using the continuity equation, and calculating velocities using Bernoulli's equation.
This document discusses moments and their applications. It defines moment as the product of a force and the perpendicular distance to the point of rotation. There are clockwise and anticlockwise moments. Varignon's principle of moments states the algebraic sum of moments about any point equals the moment of the resultant force. Levers are machines that use moments to multiply force. There are three types of simple levers and examples of levers include scissors and pliers. Compound levers use multiple simple levers together. Moments allow machines like levers to provide mechanical advantage.
Concept of Particles and Free Body Diagram
Why FBD diagrams are used during the analysis?
It enables us to check the body for equilibrium.
By considering the FBD, we can clearly define the exact system of forces which we must use in the investigation of any constrained body.
It helps to identify the forces and ensures the correct use of equation of equilibrium.
Note:
Reactions on two contacting bodies are equal and opposite on account of Newton's III Law.
The type of reactions produced depends on the nature of contact between the bodies as well as that of the surfaces.
Sometimes it is necessary to consider internal free bodies such that the contacting surfaces lie within the given body. Such a free body needs to be analyzed when the body is deformable.
Physical Meaning of Equilibrium and its essence in Structural Application
The state of rest (in appropriate inertial frame) of a system particles and/or rigid bodies is called equilibrium.
A particle is said to be in equilibrium if it is in rest. A rigid body is said to be in equilibrium if the constituent particles contained on it are in equilibrium.
The rigid body in equilibrium means the body is stable.
Equilibrium means net force and net moment acting on the body is zero.
Essence in Structural Engineering
To find the unknown parameters such as reaction forces and moments induced by the body.
In Structural Engineering, the major problem is to identify the external reactions, internal forces and stresses on the body which are produced during the loading. For the identification of such parameters, we should assume a body in equilibrium. This assumption provides the necessary equations to determine the unknown parameters.
For the equilibrium body, the number of unknown parameters must be equal to number of available parameters provided by static equilibrium condition.
Force, types of forces and system of forcesKhanSaif2
This presentation covers concept of force and different types of forces as well as different system of forces. I hope this PPT will be helpful for instructors as well as students.
This document discusses levers and moments. It provides examples of levers in the body, such as bones and joints. It explains that the longer the lever, the bigger the force needed to move an object. It also discusses moments and how they are calculated by multiplying force by distance from the pivot. Examples are provided about balancing moments on a seesaw. The document also discusses how counterweights on cranes allow them to lift heavy loads by balancing the moments of the load and counterweight.
This document provides an overview of friction including definitions, types, coefficients, and applications. It defines friction as the resisting force that opposes motion between two surfaces in contact. The document describes static and kinetic friction, the coefficient of friction as the ratio between friction force and normal force, and the angle of friction. It also discusses applications of friction including the angle of repose, ladder friction, wedge friction, and screw friction.
The document discusses heat and phase changes. It defines key terms like heat of fusion and heat of vaporization, which refer to the energy required for a substance to change phases. The document also provides an example heating curve for 1 gram of water and uses equations like q=m*H to calculate energy changes during phase transitions. It gives examples of calculating the heat required to melt ice, condense a gas, and change ice to water over a temperature range.
This document discusses Isaac Newton's three laws of motion and their applications. Newton's first law states that objects at rest stay at rest and objects in motion stay in motion unless acted on by an unbalanced force. Newton's second law establishes that force equals mass times acceleration (F=ma). Newton's third law describes that for every action there is an equal and opposite reaction. Examples are provided to demonstrate these laws, such as how gravity causes apples to fall from trees and how objects with different masses accelerate at the same rate but with different forces due to their mass.
The document discusses the center of gravity (CoG) and stability of objects. It defines CoG as the point where the entire weight of an object can be considered to act. For regular shapes, the CoG is at the geometric center. For irregular objects, methods are described to find the CoG using a plumb line and balance point. An object is stable when its CoG is directly above or within its base, and unstable if the CoG falls outside the base, allowing it to more easily rotate. Features like a low CoG and wide base promote stability.
This document discusses the concepts of uniform circular motion including:
- Uniform circular motion is motion at a constant speed in a circular path.
- Centripetal acceleration is the acceleration directed toward the center of the circle.
- Centripetal force is the force required to cause an object to travel in a circular path and is directed toward the center.
- For an object to remain in a circular orbit, it must travel at a specific orbital speed that depends on the radius of the orbit.
This document defines friction and its types, including static and dynamic friction. It discusses limiting friction force, normal reaction force, and coefficient of friction. It provides the laws of static and dynamic friction. Key concepts covered are that friction opposes motion, static friction is when bodies are at rest while dynamic friction occurs when in motion, and coefficient of friction is the ratio of limiting friction force to normal reaction force.
11. kinetics of particles work energy methodEkeeda
The document provides information about work, kinetic energy, work energy principle, and conservation of energy. It defines key terms like work, kinetic energy, spring force, weight force, friction force, power, and efficiency. It explains:
- Work is the product of force and displacement in the direction of force. Work by various forces can be used to solve kinetics problems.
- Kinetic energy is the energy of motion and is defined as one-half mass times velocity squared.
- The work energy principle states that the total work done by forces on an object equals its change in kinetic energy.
- For conservative forces acting on a particle, the mechanical energy (sum of kinetic and potential energy) is
This document discusses the concept of stability and center of gravity (CoG). It begins by defining stability as an object's ability to return to its original position after being tilted, while instability means an object continues moving past its original position. An object is in equilibrium when stationary. The CoG is the point where all the object's weight seems to be concentrated and where gravitational force acts. For regular shapes, the CoG is at the geometric center. Irregular shapes require finding the CoG experimentally by balancing on different points. Stability depends on CoG position and base size - a lower CoG and wider base increase stability. The document provides various examples and explanations of these concepts.
1) Newton's three laws of motion are described, including the first law of inertia, the second law relating force, mass and acceleration, and the third law of equal and opposite reactions.
2) The first law states that an object at rest stays at rest and an object in motion stays in motion unless acted on by an unbalanced force. Friction is given as an example of a force that can slow objects down.
3) The second law establishes the formula F=ma, where force equals mass times acceleration. Several examples are given to illustrate applications of this law.
This document discusses equilibrium and centre of mass. It defines moment or torque as the turning effect of a force. The moment of a force depends on both the size of the force and the distance from the pivot. An object is in equilibrium when the sum of clockwise moments equals the sum of anticlockwise moments. For an object to be in equilibrium, the forces must balance and the principle of moments must apply. The centre of mass is the point where the entire weight of an object can be considered to act. Several diagrams show how to determine the centre of mass for different objects.
(1) The document discusses moments, which are turning forces that cause an object to rotate rather than push it linearly. Moments depend on the magnitude of the applied force and its distance from the pivot point.
(2) To calculate the moment of a single force, the formula is Moment = Force x Perpendicular Distance from the pivot. When multiple forces are present, their individual moments are summed.
(3) Systems in equilibrium have their clockwise and counter-clockwise moments equal, allowing one to solve for unknown values like reactions at supports. Diagrams are drawn and moments taken to set up and solve equations of equilibrium.
The document summarizes Newton's three laws of motion and other key concepts in mechanics. It discusses Newton's first law of inertia, second law relating force and acceleration, and third law of equal and opposite reaction. It also defines concepts like impulse, momentum, work, energy, and power. Key principles discussed include conservation of linear momentum, mechanical energy, and total energy in a closed system.
This document defines key terms related to moments and forces:
- A moment is the product of a force and its perpendicular distance from the pivot point, and has a direction of either clockwise or counterclockwise.
- The center of gravity is the point where an object's entire weight is considered to act. For regular shapes it is the geometric center, and for irregular shapes it can be found by balancing.
- The plumb line method uses three lines dropped from holes in a lamina to find their intersection point, which is the center of gravity.
- The principle of moments states that the sum of clockwise moments equals the sum of counterclockwise moments about a point, with the total being zero.
The document discusses momentum and its conservation during collisions. It defines impulse as the product of an average force and the time interval over which it acts. The impulse-momentum theorem states that the impulse on an object equals its change in momentum. The conservation of momentum principle states that the total momentum of an isolated system remains constant, even after internal interactions and collisions within the system.
Lesson 2_ effects of forces.pptx about forces and its effectsmadonnasibrahim
Forces can cause objects to change motion, speed, direction or shape. A force is a push or pull that can be measured in Newtons, though forces cannot be seen directly. This document discusses different types of forces including gravity, friction, air resistance, upthrust and how forces affect objects. It provides examples of how pushing and pulling change the motion and shape of objects. An experiment is described to measure the difference between an object's weight in air and water, and how upthrust causes the weight to be less in water.
This document discusses key concepts in fluid mechanics, including:
1) Fluid statics, hydrostatic equilibrium, Archimedes' principle, and buoyancy.
2) Fluid dynamics principles like conservation of mass expressed by the continuity equation, and conservation of energy expressed by Bernoulli's equation.
3) Applications of fluid dynamics concepts like calculating flow rates and velocities using the continuity equation, and calculating velocities using Bernoulli's equation.
Forces can push or pull on objects and change their motion. A force is measured in Newtons. The net force on an object determines its acceleration according to F=ma. Newton's three laws describe how forces interact: 1) objects in motion stay in motion unless a force acts; 2) F=ma; 3) for every action there is an equal and opposite reaction. Centripetal force provides the inward pull that causes objects to travel in circular paths. Stability depends on the location of an object's center of mass relative to its base.
Forces can push or pull on objects and change their motion. A force is measured in Newtons. The net force on an object determines its acceleration according to F=ma. Newton's three laws describe how forces interact: 1) objects in motion stay in motion unless a force acts, 2) F=ma, and 3) for every action there is an equal and opposite reaction. Centripetal force provides the inward force needed for circular motion. Levers, moments, and fulcrums can be used to make work easier by reducing the needed force. The location of an object's center of mass determines its stability.
The document provides information about forces and work. It defines force as a push or pull and discusses different types of forces including gravitational, frictional, electrostatic, and magnetic forces. It also defines work as the product of the applied force and the distance moved, and power as the rate at which work is done. Methods for reducing friction like lubricants and ball bearings are presented. Examples of calculating work, power, and solving physics problems involving forces are also included.
This document provides an introduction to engineering mechanics from Baba Farid College of Engineering and Technology. It includes:
1) Biographical information about the instructor Parvinkal Singh Mann, who has worked in engineering education for many years and published over 20 research papers.
2) An overview of engineering mechanics, which involves the study of forces and their effects on bodies at rest (statics) and in motion (dynamics), and how it relates to other fields like kinematics and kinetics.
3) Definitions of key terms in mechanics like force, pressure, mass, weight, density, and others, and explanations of the differences between concepts like mass and weight.
Here are the answers:
1. Work = Force x Distance
= 50N x 10m
= 500 Joules
2. Work = Force x Distance
= Weight x Height
= 45 kg x 9.8 m/s^2 x 1.2m
= 546.4 Joules
3. Total Force = Tom's Force + Jerry's Force = 50N + 70N = 120N
Work = Total Force x Distance
= 120N x 4m
= 480 Joules
1) Force is an external agent that can change the motion or position of an object, and has both magnitude and direction. Forces can be balanced or unbalanced. Balanced forces do not change the motion of an object, while unbalanced forces do.
2) Graphs can represent motion, including distance-time graphs for objects with uniform or non-uniform speed, and velocity-time graphs for objects with uniform or non-uniform acceleration. Equations relate displacement, velocity, acceleration, and time for accelerated motion.
3) Newton's Three Laws of Motion describe how forces affect the motion of objects: an object at rest stays
The document describes various concepts related to forces including:
1) Different types of forces such as magnetic, weight, tension, contact, and friction forces.
2) The effects of forces including changing an object's motion, speed, direction, shape, and putting a stationary object into motion.
3) The relationship between net force, mass, and acceleration given by F=ma.
4) How to calculate weight, distinguish it from mass, and how it depends on gravitational strength.
This document provides information about force and pressure in physics for class 8. It discusses that force has magnitude and direction, is represented by an arrow, and does not affect the mass of an object. It also explains the turning effect of force, called moment, which depends on the force and perpendicular distance from the pivot point. Further, it defines pressure as the force per unit area and discusses how liquid pressure increases with depth due to the weight of the liquid above. Archimedes' principle of upthrust or buoyancy is also summarized.
This document provides an introduction to work, energy and power. It defines work as the product of force and displacement in the direction of force. Positive work is when force and displacement are in the same direction, while negative work is when they are in opposite directions. Kinetic energy is defined as half the mass times the velocity squared. The work-energy theorem states that work done equals the change in kinetic energy. Potential energy is the energy an object has due to its position or state. The conservation of mechanical energy principle applies to systems where only conservative forces act. It states the total mechanical energy of the system, which is the sum of kinetic and potential energy, remains constant. An example is provided of calculating work and energy for a
This document discusses key concepts relating to forces in physics. It defines a force as a push or pull and notes they can be measured in newtons. Balanced forces cause no acceleration while unbalanced forces produce changes in motion. Friction and air resistance are examples of contact forces. Hooke's law states the extension of a spring is proportional to the applied load. Newton's second law relates force, mass and acceleration using the equation F=ma.
This document discusses key concepts relating to forces in physics. It defines a force as a push or pull and notes they can be measured in newtons. Balanced forces will not cause a change in motion, while unbalanced forces will. Friction and air resistance are examples of contact forces. Hooke's law states the extension of a spring is proportional to the applied force. Newton's second law relates force, mass and acceleration using the equation F=ma.
Sehs 4.3– biomechanics ii (4.3.3, force, com)strowe
The document discusses the fundamentals of biomechanics, including forces and levers. It defines a force as a push or pull that acts on an object, and can be quantified by both magnitude and direction. Forces can be contact forces, which require touching the object, or long-range forces like gravity that act without contact. Levers are rigid bars that rotate around a fulcrum, and there are three classes of levers that differ based on the relative positions of the fulcrum, effort, and resistance. The center of mass of an object can change based on factors like body position, external loads, and age or sex, and affects an object's stability.
This document contains information about an introductory fluid mechanics course, including:
- The lecturer's name and contact information, as well as consultation hours for the lecturer and another professor.
- An outline of topics to be covered, including fluid motion, thermal physics, electricity, and revision.
- A brief overview of fluid properties like density, pressure, compressibility of gases, liquids and solids.
- Explanations of concepts like hydrostatic equilibrium, Pascal's law, Archimedes' principle, buoyancy, and the continuity equation.
- Examples of calculating pressure, buoyant force, and applying conservation of mass.
The bottles did not move because of inertia - their mass resists changes in motion. It is a real demonstration of inertia. To pull it off:
- The bottles are glued to the table, so they cannot slide when pushed.
- The person pushes on the table, not directly on the bottles, so the bottles feel less force than what appears.
- Quick camera cuts and angles are used to hide that the bottles are fixed in place. It's an illusion that fools the eye through clever filming.
So in summary, it uses inertia and camera tricks to create the illusion that the bottles are resisting the push through their own inertia alone.
This document defines force and gravity. It explains that force is a push or pull that can cause an object to change its motion or speed. There are different types of forces including contact forces like friction and non-contact forces like magnetic and gravitational forces. Gravity is the force of attraction between all objects with mass and the Earth. The center of gravity is the point where all of an object's weight can be considered to be concentrated. An object's stability depends on whether its line of gravity falls within the base of support.
This document provides definitions and explanations of basic biomechanical concepts including:
- Mass is the quantity of matter an object contains and is measured in kilograms. Weight is the force exerted on a surface due to gravity and is measured in kilograms-force.
- A force can produce movement or deformation and is measured in Newtons. Newton's laws of motion describe how objects interact under various forces.
- The centre of gravity is the point where total mass of an object is considered to be concentrated. An object's stability depends on the position of its centre of gravity relative to its base of support.
- Forces can be analyzed using graphical methods like the parallelogram and triangle methods
This document provides an overview of key concepts in strength of materials including:
- Stress is defined as the internal resisting force induced per unit area when an external force is applied. The two basic types of stress are normal stress and shear stress.
- Strain is the ratio of deformation to original dimension when a body undergoes stress. The main types of strain are longitudinal, lateral, normal, tensile, compressive, and shear.
- Hooke's law states that within the elastic limit, stress is directly proportional to strain for a material. When stress is applied and removed, elastic materials will return to their original state.
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
it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
This document provides an overview of wound healing, its functions, stages, mechanisms, factors affecting it, and complications.
A wound is a break in the integrity of the skin or tissues, which may be associated with disruption of the structure and function.
Healing is the body’s response to injury in an attempt to restore normal structure and functions.
Healing can occur in two ways: Regeneration and Repair
There are 4 phases of wound healing: hemostasis, inflammation, proliferation, and remodeling. This document also describes the mechanism of wound healing. Factors that affect healing include infection, uncontrolled diabetes, poor nutrition, age, anemia, the presence of foreign bodies, etc.
Complications of wound healing like infection, hyperpigmentation of scar, contractures, and keloid formation.
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.
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.
Leveraging Generative AI to Drive Nonprofit InnovationTechSoup
In this webinar, participants learned how to utilize Generative AI to streamline operations and elevate member engagement. Amazon Web Service experts provided a customer specific use cases and dived into low/no-code tools that are quick and easy to deploy through Amazon Web Service (AWS.)
This presentation was provided by Steph Pollock of The American Psychological Association’s Journals Program, and Damita Snow, of The American Society of Civil Engineers (ASCE), for the initial session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session One: 'Setting Expectations: a DEIA Primer,' was held June 6, 2024.
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...PECB
Denis is a dynamic and results-driven Chief Information Officer (CIO) with a distinguished career spanning information systems analysis and technical project management. With a proven track record of spearheading the design and delivery of cutting-edge Information Management solutions, he has consistently elevated business operations, streamlined reporting functions, and maximized process efficiency.
Certified as an ISO/IEC 27001: Information Security Management Systems (ISMS) Lead Implementer, Data Protection Officer, and Cyber Risks Analyst, Denis brings a heightened focus on data security, privacy, and cyber resilience to every endeavor.
His expertise extends across a diverse spectrum of reporting, database, and web development applications, underpinned by an exceptional grasp of data storage and virtualization technologies. His proficiency in application testing, database administration, and data cleansing ensures seamless execution of complex projects.
What sets Denis apart is his comprehensive understanding of Business and Systems Analysis technologies, honed through involvement in all phases of the Software Development Lifecycle (SDLC). From meticulous requirements gathering to precise analysis, innovative design, rigorous development, thorough testing, and successful implementation, he has consistently delivered exceptional results.
Throughout his career, he has taken on multifaceted roles, from leading technical project management teams to owning solutions that drive operational excellence. His conscientious and proactive approach is unwavering, whether he is working independently or collaboratively within a team. His ability to connect with colleagues on a personal level underscores his commitment to fostering a harmonious and productive workplace environment.
Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
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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.
This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
Main Java[All of the Base Concepts}.docxadhitya5119
This is part 1 of my Java Learning Journey. This Contains Custom methods, classes, constructors, packages, multithreading , try- catch block, finally block and more.
2. RECAP (FORCES)
FORCE Is defined based on what it can cause bodies to do, it may cause a
body’s length to increase or decrease. IT CAN CAUSE A BODY’S REST
POSITION TO CHANGE OR IF IN MOTION TO CHANGE IT DIRECTION
hence
FORCE is defined as a push or a pull that can change a bodies
state of rest or uniform motion in a straight line.
3. TYPES OF FORCES
•THERE ARE TWO TYPES OF FORCES. THESE ARE
CONTACT FORCE / LOCAL FORCE
NON – CONTACT / NON – LOCAL / FORCE FIELDS
4. CONTACT FORCE
•They are forces that are experienced by bodies when they
are in direct contact with the source of the force.
•EXAMPLES
Upthrust
Frictional force
Tension force
Surface tension
Forces exerted on a ball when kicked
Viscous force (fluid resistance)
5. NON –CONTACT FORCE
•They are forces that are experienced by bodies that may or
may not be in direct contact with the source of the force.
•EXAMPLES
Magnetic force
Gravitational force
Electric Force
Nuclear force
NB: CONTACT FORCE ARE CALLED LOCAL FORCE BECAUSE THE SOURCE OF THE FORCE MUST BE IN THE
AREA(LOCALITY) OF THE OBJECT.
6. FRICTIONAL FORCE•It is the tangential force that acts on surfaces in contact and which opposes
their relative motion. It is experienced by solid bodies in contact.
•USES / ADVANTAGES OF FRICTIONAL FORCES
It makes body in motion to stop
It is use for sharpening cutlasses
It makes walking possible
It enables us light fire
It makes writing possible
It enables a screw or a nail to remain in place after being screwed into
position.
7. •DISADVANTAGES OF FRICTIONAL
It makes the sole of shoes wear and tear
It produces heat when 2 solid bodies in contact makes relative motion
It reduces the efficiency of a machine
•HOW WE WILL REDUCE FRICTION
Greasing solid surfaces in contact
Introducing impurities between surfaces reduces friction
By introducing spherical metallic balls in between two metals moving
over each other has in ball bearings or race reduces friction.
8. BALL RACE OR BEARING & LABELLING
Spherical body
Metal run
Metal
9. TWO TYPES OF FRICTION
•THESE ARE:
1) STATIC – These opposes motion of bodies when they are stationary
2) DYNAMIC - These opposes motion of bodies already in motion
Static friction is always bigger than they the dynamic frictional force
10. NORMAL FORCE OR REACTION
It is the component of a supported force that is perpendicular to
the supporting surface.
HORIZONTAL SURFACE
11. •EXAMPLES
Determine the reaction exerted on a surface when a 20 kg body
is placed on the surface. Assume horizontal.
SOLUTION
Reaction = 𝑚 × 𝑔
= 20 × 10
= 200 𝑁
12. INCLINED SURFACE
𝑚𝑔𝑐𝑜𝑠 𝜃 causes the body to remain on the surface
𝑚𝑔𝑠𝑖𝑛 𝜃 causes the body to pulled down the surface
13. •EXAMPLES
A 10 kg mass rest on a surface at 10° to the horizontal. Calculate
i. The force that presses the body unto the plane
ii. The force that tries to pull the body down along the surface
iii. The reaction
14. 1) 𝑚𝑔𝑐𝑜𝑠 𝜃 = 10 × 10 cos 10 = 98.48 𝑁
2) 𝑚𝑔𝑠𝑖𝑛 𝜃 = 10 × 10 sin 10 = 17.36 𝑁
3) 𝑅 = 𝑚𝑔𝑐𝑜𝑠 𝜃 = 10 × 10 cos 10 = 98.48 𝑁
LIMITING STATIC FRICTION
This is the minimum force required to move a body at rest. The
force is described as dynamic limiting frictional force when it is
the minimum force that must be applied on a moving body to make
the body move at a constant velocity.
15. •Coefficient of Static Friction
It is defined as the
𝐥𝐢𝐦𝐢𝐭𝐢𝐧𝐠 𝐬𝐭𝐚𝐭𝐢𝐜 𝐟𝐫𝐢𝐜𝐭𝐢𝐨𝐧𝐚𝐥 𝐟𝐨𝐫𝐜𝐞
The normal force or reaction
.
𝜇 =
𝐹𝑥
𝑅
or 𝐹𝑥 = 𝜇 × 𝑅
Example
A 15 kg body is on a horizontal surface which has a coefficient of
friction of 0.25. Calculate
i) The normal force
ii) The limiting static frictional force
16. • Solution
i. The normal force = 𝑚 × 𝑔 = 15 × 10 = 150 𝑁
ii. The limiting static frictional force = 𝐹𝑥 = 𝜇𝑅 = 0.25 × 150 = 37.5 𝑁
EXAMPLE
A 100 kg body is on a plane inclined 30 ° to the horizontal, if the frictional force on
the body is 50.0 N, calculate the
i. The normal force
ii. The coefficient of friction
17. •Solution
i. The normal force = 𝑚𝑔𝑐𝑜𝑠 𝜃 = 100 × 10 cos 30 = 866.03 𝑁
ii. The coefficient of friction 𝜇 =
𝐹𝑥
𝑅
=
50 𝑁
866.03
= 0.058 𝑁
RESULTANT FORCE – This is the difference between the total force in the
direction of motion and the total force opposite the direction of motion
𝑹 𝒇 =Total force in the direction of motion – total force opposite the direction
of motion
Or it can also be determined by mass × acceleration = 𝒎 × 𝒂 = 𝒎𝒂
18. EXAMPLE
A 20 kg body on a horizontal surfaces is pulled to the right with a force of
100N. Determine.
i. The frictional force
ii. The resultant force
iii. The acceleration 𝑇𝑎𝑘𝑒 𝜇 = 0.2
19. • SOLUTION
• I. Frictional force , 𝐹𝑥 = 𝜇 × 𝑅 , 𝑅 = 𝑚𝑔 = 20 × 10 = 200 𝑁
𝐹𝑥 = 0.2 × 200 = 40.0 𝑁
II. Resultant force , 𝑅𝑓 =Total force in the direction of motion – total force opposite the
direction of motion = 100 − 40 = 𝟔𝟎 𝑵
20. III. Acceleration
𝑹 𝒇 = 𝒎𝒂𝒔𝒔 × 𝒂𝒄𝒄𝒆𝒍𝒆𝒓𝒂𝒕𝒊𝒐𝒏
60 = 20 × 𝑎
∴ 𝑎 =
60
20
= 𝟑 𝒎𝒔−𝟐
Home work 1
A 100 kg toy car is pulled up a plane inclined 30 ° to the horizontal with a force of
1000 N. Given that the 𝐹𝑥 coefficient of the force is 0.25,
Calculate
i. 𝐹𝑥 force ii. Total force down along the plane iii. The resultant force
iii. The acceleration of the body act along the plane
21.
22. • SOLUTION
i. FRICTIONAL FORCE, 𝐹𝑥 = 𝜇 × 𝑟 , 𝑟 = 𝑚𝑔𝑐𝑜𝑠 𝜃
𝐹𝑥 = 𝜇 × 𝑚𝑔𝑐𝑜𝑠 𝜃 = 0.25 × 100 COS 30 = 𝟐𝟏𝟔. 𝟓 𝑵
ii. TOTAL FORCE DOWN ALONG THE PLANE = 𝑚𝑔𝑠𝑖𝑛 𝜃 + 𝐹𝑥 = 100 × 10 𝑠𝑖𝑛30 + 216.5
= 716.5 𝑁
iii. RESULTANT FORCE, 𝑅𝑓 = 𝑡𝑜𝑡𝑎𝑙 𝑓𝑜𝑟𝑐𝑒 𝑖𝑛 𝑡ℎ𝑒 𝑑𝑖𝑟𝑒𝑐𝑡𝑖𝑜𝑛 𝑜𝑓 𝑡ℎ𝑒 𝑚𝑜𝑡𝑖𝑜𝑛 −
𝑡𝑜𝑡𝑎𝑙 𝑓𝑜𝑟𝑐𝑒 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑡ℎ𝑒 𝑑𝑖𝑟𝑒𝑐𝑡𝑖𝑜𝑛 𝑜𝑓 𝑚𝑜𝑡𝑖𝑜𝑛 = 1000 − 716.5 = 𝟐𝟖𝟑. 𝟓𝑵
iv. ACCELERATION =
𝑅𝑒𝑠𝑢𝑙𝑡𝑎𝑛𝑡 𝑓𝑜𝑟𝑐𝑒
𝑚𝑎𝑠𝑠
=
283.5
100
= 2.835 𝑚𝑠−2
23. Question
A 200 kg body rest on a surface inclined 25 ° to the horizontal. If this body
is pulled down along the plane with a force of 100 N. Calculate
i. 𝐹𝑥 force ii. Total force in the direction of motion iii. The
resultant force iii. The acceleration of the body act along the plane
[Take 𝜇 𝑎𝑠 0.3]
24.
25. • SOLUTION
i. FRICTIONAL FORCE, 𝐹𝑥 = 0.3 × 𝑟 , 𝑟 = 𝑚𝑔𝑐𝑜𝑠 𝜃
𝐹𝑥 = 𝜇 × 𝑚𝑔𝑐𝑜𝑠 𝜃 = 0.3 × 2000 COS 25 = 𝟓𝟒𝟑. 𝟕𝟖𝑵
ii. TOTAL FORCE IN THE DIRECTION OF MOTION= 𝑚𝑔𝑠𝑖𝑛 𝜃 + 𝐹𝑑 = 200 × 10 𝑠𝑖𝑛25 + 100
= 𝟗𝟒𝟓. 𝟐𝟒 𝑵
iii. RESULTANT FORCE, 𝑅𝑓 = 𝑡𝑜𝑡𝑎𝑙 𝑓𝑜𝑟𝑐𝑒 𝑖𝑛 𝑡ℎ𝑒 𝑑𝑖𝑟𝑒𝑐𝑡𝑖𝑜𝑛 𝑜𝑓 𝑡ℎ𝑒 𝑚𝑜𝑡𝑖𝑜𝑛 −
𝑡𝑜𝑡𝑎𝑙 𝑓𝑜𝑟𝑐𝑒 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑡ℎ𝑒 𝑑𝑖𝑟𝑒𝑐𝑡𝑖𝑜𝑛 𝑜𝑓 𝑚𝑜𝑡𝑖𝑜𝑛 = 945. 24 − 543.78 = 𝟒𝟎𝟏. 𝟒𝟔𝑵
iv. ACCELERATION =
𝑅𝑒𝑠𝑢𝑙𝑡𝑎𝑛𝑡 𝑓𝑜𝑟𝑐𝑒
𝑚𝑎𝑠𝑠
=
401.46
200
= 𝟐. 𝟎𝟎𝟕 𝒎𝒔−𝟐
26. MEASUREMENT OF COEFFICIENT OF 𝐹𝑥
The test body is placed on a horizontal table that has a pulley fixed to one end of a thread that
is passing over a pulley attached to a scale pan. Masses are gently placed on the scale pan
until the test body just begins to move.
Weigh the mass on the scale pan and record it as 𝑀𝑠. WEIGH THE TEST BODY AND RECORD THE MASS
AS 𝑀
THEORY
WHEN THE BODY JUST BEGINS TO MOVE 𝑀𝑠 𝑔 = 𝑇
BUT 𝑇 = 𝑓𝑠 HENCE 𝐹𝑥 = 𝑚 𝑠 𝑔 REACTION 𝑅 = 𝑀𝑔
∴ COEFFICIENT OF FRICTION 𝜇 =
𝐹𝑥
𝑅
=
𝑀𝑠 𝑔
𝑀𝑔
=
𝑀𝑠
𝑀
27.
28. TO DETERMINE 𝜇 USING INCLINED PLANE
• The test body is placed on a plain. One end of the plane is gradually raised until the body
just begins to move.
• The angle of inclination 𝜃 at this instant is measured with a protector. 𝛍 = 𝐭𝐚𝐧 𝛉
29. When a body just begins to move 𝐹𝑥 =
𝑚𝑔 sin 𝜃
But 𝐹𝑥 = 𝜇𝑅
𝑅 = 𝑚𝑔𝑐𝑜𝑠𝜃
𝜇𝑚𝑔𝑐𝑜𝑠 𝜃 = 𝑚𝑔𝑠𝑖𝑛 𝜃
𝝁 =
𝑚𝑔𝑠𝑖𝑛 𝜃
𝑚𝑔𝑐𝑜𝑠 𝜃
=
sin 𝜃
cos 𝜃
= 𝐭𝐚𝐧 𝜽
30. ARCHIMEDES PRINCIPLE
• A body in a fluid apart from experiencing its own weight also experiences a vertically
directed upward force that tends to reduce the weight of the body.
• Hence, bodies in fluid weigh less. UPTHRUST OR BUOYANT FORCE is the vertically directed
force experienced by bodies in fluid.
• The volume of fluid displaced = the volume of the part of solid or body immerse in
fluid
• The weight of the fluid displaced = the volume of solid immersed × density of fluid ×
gravity
• The weight of fluid displaced = UPTHRUST.
• The apparent loss in weight of bodies is the UPTHRUST
31. QUESTIONS
• A piece of wood has a mass of 200 g. When placed in 𝐻2 𝑂 with 50 𝑐𝑚3 of the wood in
𝐻2 𝑂 , there is a loss in mass. Calculate
• Volume of 𝐻2 𝑂 displaced
• Mass of 𝐻2 𝑂 displaced
• The upthrust on the wood
• Find the apparent loss in mass of the wood.
32. SOLUTION
1. Volume of 𝐻2 𝑂 displaced = 50 𝑐𝑚3
2. Mass of 𝐻2 𝑂 displaced = Density × Vol. of the 𝐻2 𝑂 = 1 × 50 = 50 g
3. The upthrust on the wood =
50
1000
= 0.050 × 10 𝑚/𝑠 = 0.5 𝑁
4. Apparent loss in mass of the wood = Mass in air – mass in fluid = 200 − 50 = 150 𝑔
33. A 20 𝑐𝑚3
balloon is left in air of density 0.0014 𝑔/𝑐𝑚3
. Calculate the mass of air displaced and hence, the
upthrust.
Answer
Density =
𝑀𝑎𝑠𝑠
𝑉𝑜𝑙𝑢𝑚𝑒
Mass = Density × Volume = 0.0014 × 20 = 0.028 g
Upthrust =
0.028𝑔
1000
= 0.000028 × 10 = 𝟎. 𝟎𝟎𝟎𝟐𝟖 𝑵
Archimedes Principle
When a body is fully or partially immersed in a fluid, it experiences an upthrust equal to the weight of fluid
displaced.
NB: The upthrust reduces the weight.
34. FLOATATION
•Law of Floatation
A floating body displaces its own weight of fluid in the fluid in which its floates.
During Floatation
• The volume of fluid displaced = the volume of the body immersed.
• Mass of fluid displaced = Mass of the body
• Upthrust = weight of body
35.
36. METHOD
• 1. Fill an overflow can with 𝐻2 𝑂 upto the spout level
• 2. Weigh an empty beaker with an electric balance to record the mass 𝑀1
• 3. Place the beaker below the spout
• 4. Place the test tube in the 𝐻2 𝑂 and add lead shots to the tube for the tube to float upright.
• 5. Weight the beaker with the overflow 𝐻2 𝑂 and record the mass 𝑀2
• 6. Evaluate the mass of the overflow 𝐻2 𝑂 AS 𝑊 = 𝑀2 − 𝑀1
• 7. Remove the test tube with the leadshots from the 𝐻2 𝑂, weigh and record the mass as 𝑀
37. OBSERVATION AND CONCLUSION
• It is found that 𝑀 = 𝑚𝑔 indicating that mass of the test tube/ body is equal to the mass of
overflow water
• Weight of body = 𝑚𝑔
• Upthrust = mass of fluid × g = 𝐴ℎ 𝜌 𝑓𝑙𝑢𝑖𝑑 𝑔
• 𝐴 = 𝐶𝑟𝑜𝑠𝑠 𝑠𝑒𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝑎𝑟𝑒𝑎, ℎ = ℎ𝑒𝑖𝑔ℎ𝑡 , 𝜌 = 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 𝐴ℎ = 𝑉𝑜𝑙𝑢𝑚𝑒
𝑚𝑔 = 𝐴ℎ𝜌𝑔
𝑚 = 𝐴ℎ𝜌(𝑑𝑒𝑛𝑠𝑖𝑡𝑦)
𝑚 = 𝑉𝜌
38. QUESTIONS
• A test tube has a mass of 15 g, a cross sectional area of 1.5 𝑐𝑚2
. The test tube floats
in the liquid of 𝜌 = 0.8 𝑔/𝑐𝑚3. Calculate the depth of immersion of the test tube.
SOLUTION
𝑀 = 15 𝑔 𝐴 = 1.5 𝑐𝑚2 𝜌 = 0.8 𝑔/𝑐𝑚3
𝑀 = 𝐴ℎ𝜌
15 = 1.5 × ℎ × 0.8
ℎ =
15
1.2
= 12.5 𝑐𝑚
39. QUESTION
• A piece of wood floats in a liquid of relative density(RD) = 1.02 if the mass of the
wood is 25 kg and the volume of wood above the liquid is 0.0071 𝑚3. Calculate the
total volume of the wood
SOLUTION
41. QUESTIONS
• A 200g wood float in 𝐻2 𝑂. If the top part of the wood is just above covered water. What
is the size length of the wood
SOLUTION
𝑀 = 𝑉𝜌
200 = 𝑉 × 1
𝑉 = 200 𝑐𝑚3
But 𝐿3 = 𝑉
𝐿3 = 200
𝐿 = 5.85 𝑐𝑚
42. HYDROMETER
• This is an instrument used to measure relative density or consist off a uniform glass tube
containing lead shots. In another form of the instrument a uniform stem is mounted on a
large bulb that has lead shots in it as shown in the diagram below
44. WEIGHTLESSNESS – MOTION IN A LIFT
When a lift accelerates downwards occupants feel lighter, however they feel heavier
when it accelerates upwards. These changes can be explained by considering the
resultant force, which acts on the occupants as a combination of two forces that are
acting. These are:
i. Force of gravity on weight
ii. The force needed to accelerate or decelerate the lift
45. WEIGHTLESSNESS – MOTION IN A LIFT
If the lift accelerates downwards with an acceleration of 𝑎ms−2
then 𝑾 = 𝒎𝒈 − 𝒎𝒂. If
the lift accelerates upwards with acceleration of 𝑎ms−2
then 𝑾 = 𝒎𝒈 + 𝒎𝒂 which
implies that the weight appears to be increased and occupants appear to be decreased.
As the lift increases its downwards acceleration, the apparent weight will be less and
less until eventually becomes zero. If the acceleration of the lift increases beyond 10
𝑚/𝑠2 then the person inside will fly. Spacemen experience weightlessness when the
acceleration of their spacecraft is greater than or equal to acceleration due to
gravity.
46. QUESTION
• Calculate the force with which the feet of a passenger passes downwards on the floor of an
elevator accelerating upwards of 4 × 10−3
𝑚𝑠−2
if the passenger’s weight is 60 𝑁.
SOLUTION
Weight of passenger = 60 N
But weight of passenger = 𝐦𝐚𝐬𝐬 𝐨𝐟 𝐦𝐚𝐧 × 𝐚𝐜𝐜𝐞𝐥𝐞𝐫𝐚𝐭𝐢𝐨𝐧 𝐝𝐮𝐞 𝐭𝐨 𝐠𝐫𝐚𝐯𝐢𝐭𝐲
Mass of passenger =
𝐰𝐞𝐢𝐠𝐡𝐭 𝐨𝐟 𝐩𝐚𝐬𝐬𝐞𝐧𝐠𝐞𝐫
𝐚𝐜𝐜𝐞𝐥𝐞𝐫𝐚𝐭𝐢𝐨𝐧 𝐝𝐮𝐞 𝐭𝐨 𝐠𝐫𝐚𝐯𝐢𝐭𝐲
I.E 𝒎 =
𝑾
𝒈
=
𝟔𝟎
𝟏𝟎
= 𝟔 𝒌𝒈.
Let 𝑊𝑎 be the apparent weight of the passenger
⇒ 𝑊𝑎 = 𝑚𝑔 + 𝑚𝑎
⇒ 𝑊𝑎 = 6 × 10 + 6 × (4 × 10−3
)
⇒ 𝑊𝑎 = 𝟔𝟎. 𝟎𝟐𝟒 𝑁
47. QUESTION
• A man of mass 70 kg is standing in a lift. What force does the floor of the lift exert on the man if
the lift is
i. moving with a uniform velocity?
ii. accelerating at 3 𝑚𝑠−2 upwards?
iii. Accelerating at 3 𝑚𝑠−2
downwards? (Take 𝑔 = 10 𝑚𝑠−2
)
48. SOLUTION
R is the normal reaction from the floor on the man
i)
Since the lift is moving with a uniform velocity, the resultant force is zero: 𝑅 = 𝑚𝑔 = 70 × 10 =
700 𝑁
R
mg
a
Since the lift is accelerating upwards
Equation of motion: 𝑅 − 𝑚𝑔 = 𝑚𝑎
⇒ 𝑅 = 𝑚𝑔 + 𝑚𝑎 = 𝑚 𝑔 + 𝑎 = 70 10 + 3 = 70 × 13 = 𝟗𝟏𝟎 𝑵
49. ii)
Since the lift is accelerating downwards
Equation of motion: 𝑚𝑔 − 𝑅 = 𝑚𝑎
⇒ 𝑅 = 𝑚𝑔 − 𝑚𝑎 = 𝑚 𝑔 − 𝑎 = 70 10 − 3 = 70 × 7 = 𝟒𝟗𝟎 𝑵
50. CONNECTED BODIES
Two particles connected by a light inextensible string passing over a fixed light smooth
frictionless pulley are called connected bodies. The tension in the string is the same
throughout its length so the body is acted upon by the same tension. Problems concerned
with connected bodies usually involve finding the acceleration of the system and the
tension in the string.
54. PULLEY SYSTEM
Because the direction 𝑚1 𝑔 is greater than the 𝑚2
𝑚1 > 𝑚2
For 𝒎 𝟏
𝑚1 𝑎 = 𝑚1 𝑔 − 𝑇 − (1)
For 𝒎 𝟐
𝑚2 𝑎 = 𝑇 − 𝑚2 𝑔 − 2
Eqn (1) + eqn(2)
𝑚1 𝑎 + 𝑚2 𝑎 = 𝑚1 𝑔 − 𝑚2 𝑔
𝑎 𝑚1 + 𝑚2 = 𝑚1 𝑔 − 𝑚2 𝑔
𝒂 =
𝒎 𝟏 𝒈
𝒎 𝟏 + 𝒎 𝟐
−
𝒎 𝟐 𝒈
𝒎 𝟏 + 𝒎 𝟐
55. A thread is passed over a pulley. 10 kg mass and 8 kg mass are suspended at the ends of
the ropes. Draw the arrangement and indicate the body force diagram on the masses.
Evaluate
1. The acceleration of either masses
2. The tension in the tie
Solution
For 𝒎 𝟏
10𝑎 = 100 − 𝑇 − (1)
For 𝒎 𝟐
8𝑎 = 𝑇 − 80 − 2
Eqn (1) + eqn(2)
18𝑎 = 20
𝑎 =
20
18
=
10
9
= 1.11 𝑚/𝑠2
Substitute a into eqn 1
𝑻 = 𝟖𝟖. 𝟗 𝑵