PHYS1101 Physics I.docx
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This document provides instructions for a physics simulation experiment on projectile motion. The objective is to measure the range, time of flight, and angle for cannonball projections under varying angles and to use those measurements to calculate the initial speed. Students are directed to a online simulation and instructed to record data from 5 trials with different angles in a table. They then plot the range versus time of flight cosine of the angle and use the slope of the best fit line to determine the initial speed.
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projectile-motion.ppt
The document discusses vector concepts like displacement, velocity, and force and how to calculate their components in x and y directions. It explains how to use vectors to model projectile motion and calculate quantities like range. It also covers how forces balance in two dimensions, how to find acceleration on an inclined plane, and how to resolve forces into perpendicular components.
projectile-motion.ppt
The document discusses vector concepts like displacement, velocity, and force and how to calculate their components in x and y directions. It also explains how to use vector addition and subtraction to solve problems involving projectile motion and forces in two dimensions, including calculating the acceleration on an inclined plane when given the angle of incline. The objectives cover topics like adding and subtracting vectors, writing vectors in polar and x-y coordinates, and using force vectors to solve two-dimensional equilibrium problems.
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This document discusses the assumptions and equations used to calculate the motion of projectiles. It makes three main assumptions: 1) a projectile is modeled as a particle without regard to its shape or forces, 2) a projectile has no resistance or powered forces except gravity, and 3) air has no effect on its motion. The vertical and horizontal components of a projectile's motion must be considered separately using equations like the SUVAT equations to calculate time of flight, range, and maximum height. Trigonometry is used to determine initial horizontal and vertical velocity components from the angle of projection and initial velocity.
Two Dimensional Motion…, copyright Doug Bradley-Hutchison page.docx
Two Dimensional Motion…, copyright Doug Bradley-Hutchison page - 1 -
The Two-Dimensional Motion of a Projectile
Equipment: air table strobe (furnished by instructor)
meter sticks
Each group will be given a strobe picture of a two-dimensional motion that simulates
the motion of a projectile. By “projectile” it is meant any object thrown or dropped,
which accelerates under the influence of the force of gravity. If the object is given an
initial horizontal component of velocity it will execute a two-dimensional motion. That
is, its path through space will require a specification of two numbers at each point
(vertical and horizontal coordinate) for a complete description. The motions we have
been studying so far , in contrast, have been one-dimensional in that, to describe the
trajectory only one position coordinate need be specified at each point. All
motions take place in three dimensional space, of course, but two and one-dimensional
motions are confined to planes and lines respectively.
The motion depicted is only a simulation of a true projectile as it represents the motion
of a puck sliding over the surface of a tilted air table. The puck is projected up the incline
at an angle so that its velocity has both horizontal and vertical velocity components. A
true projectile is in vertical free fall. The motion studied here will differ from a true
projectile in one respect: the vertical acceleration will be less than g . However, the
essential features of the air table motion are representative of what one would observe for
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An object executing a two dimensional motion as described above, will have two
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this the vertical (or y) velocity, and we can define a corresponding quantity for the
horizontal (or x) coordinate. We call this second quantity the horizontal (or x) velocity.
These quantities are also referred to as components of the overall velocity vector.
Two Dimensional Motion…, copyright Doug Bradley-Hutchison page - 2 -
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Two Dimensional Motion…, copyright Doug Bradley-Hutchison page - 1 -
The Two-Dimensional Motion of a Projectile
Equipment: air table strobe (furnished by instructor)
meter sticks
Each group will be given a strobe picture of a two-dimensional motion that simulates
the motion of a projectile. By “projectile” it is meant any object thrown or dropped,
which accelerates under the influence of the force of gravity. If the object is given an
initial horizontal component of velocity it will execute a two-dimensional motion. That
is, its path through space will require a specification of two numbers at each point
(vertical and horizontal coordinate) for a complete description. The motions we have
been studying so far , in contrast, have been one-dimensional in that, to describe the
trajectory only one position coordinate need be specified at each point. All
motions take place in three dimensional space, of course, but two and one-dimensional
motions are confined to planes and lines respectively.
The motion depicted is only a simulation of a true projectile as it represents the motion
of a puck sliding over the surface of a tilted air table. The puck is projected up the incline
at an angle so that its velocity has both horizontal and vertical velocity components. A
true projectile is in vertical free fall. The motion studied here will differ from a true
projectile in one respect: the vertical acceleration will be less than g . However, the
essential features of the air table motion are representative of what one would observe for
a true projectile.
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An object executing a two dimensional motion as described above, will have two
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moves, projected onto the ground. The vertical trajectory is a shadow projected onto a
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Lab 3: Newton’s Second Law of Motion
Introduction
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where Σ F represents a net force acting on an object, m is the mass of the object moving
under the influence of Σ F, and a is the acceleration of that object. The bold letters in
the equation represent vector quantities.
In this lab you will try to validate this law by applying Eq. 1 to the almost frictionless
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(tension in the string) acts upon it. This motion (to be exact the velocity of the moving
object) will be recorded automatically by a motion sensor. The experimental set up
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gF
a
m M
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Because the motion of the car is not frictionless, to get better results it is necessary to
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diagram) Newton’s Second Law is written as follows for each of the moving objects
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and
1 1– gT F ma (6)
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involved in our experiment we will solve the problem by putting the object in two
different situations in which the friction acts in opposite directions respectively while
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and
2 2gT F ma (8)
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We are able to eliminate the force of kinetic friction on the final result, by calculating
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1 2
2
ave
slope slope
a
(9)
Combing the equations (5) – (8) we derive the equation to calculate the value of
gravitational acceleration:
avea M mg
m
(10)
3
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cart with reflector connected to a variable mass hanging over the pulley; motion
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Experiment 11
Simple Harmonic Motion
Questions
How are swinging pendulums and masses on springs related? Why are these types of
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equations? Again, how do you compare two numbers, which have errors?
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due at the end of the period. The explanation of the equations used, the introduction and the
conclusion are not necessary this week. The discussion section can be as little as three sentences
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The force of gravity can be omitted from this analysis because it only serves to move the
equilibrium position and doesn’t affect the oscillations. Acceleration is the second time-
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To solve: we make an educated guess:
Here A and w are constants yet to be determined. At t = 0 this solution gives x(t=0) = A,
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solve the (differential) equation? A second time-derivative gives:
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chosen if w2 = k / m. To understand w, consider the first derivative of the solution:
−kx = ma
a = −
k
m
⎛
⎝
⎜⎜⎜⎜
⎞
⎠
⎟⎟⎟⎟
x
d 2x
dt 2
= −
k
m
x x(t) = A cos(ωt)
d 2x(t)
dt 2
= −Aω2 cos(ωt) = −ω2x(t)
James Gering
Florida Institute of Technology
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Lab 3: Newton’s Second Law of Motion
Introduction
Newton’s Second law of motion can be summarized by the following equation:
Σ F = m a (1)
where Σ F represents a net force acting on an object, m is the mass of the object moving
under the influence of Σ F, and a is the acceleration of that object. The bold letters in
the equation represent vector quantities.
In this lab you will try to validate this law by applying Eq. 1 to the almost frictionless
motion of a car moving along a horizontal aluminum track when a constant force T
(tension in the string) acts upon it. This motion (to be exact the velocity of the moving
object) will be recorded automatically by a motion sensor. The experimental set up
for a car moving away from the motion sensor is depicted below.
If we consider the frictionless motion of the cart in the positive x-direction chosen in
the diagram, then Newton’s Second Law can be written for each of the objects as
follows:
T Ma (2)
and
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From this system of equations we can get the acceleration of the system:
2
gF
a
m M
(4)
Because the motion of the car is not frictionless, to get better results it is necessary to
include the force of kinetic friction fk experienced by the moving car in the analysis.
When the cart is moving away from the motion detector (positive x-direction in the
diagram) Newton’s Second Law is written as follows for each of the moving objects
m and M:
1 1– kT f Ma (5)
and
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Since it is quite difficult to assess quantitatively the magnitude of kinetic friction
involved in our experiment we will solve the problem by putting the object in two
different situations in which the friction acts in opposite directions respectively while
the tension in the string remains the same.
When the cart M is forced to move towards the motion detector (negative x-direction
in the diagram), the corresponding Newton’s Second Law equations will change as
follows:
2 2kT f Ma (7)
and
2 2gT F ma (8)
Note that in equations 5, 6, 7, and 8 the direction of acceleration represented by vector
a has been chosen in the same direction as the direction of motion.
We are able to eliminate the force of kinetic friction on the final result, by calculating
the mean acceleration from these two runs:
1 2
2
ave
slope slope
a
(9)
Combing the equations (5) – (8) we derive the equation to calculate the value of
gravitational acceleration:
avea M mg
m
(10)
3
Equipment
Horizontal dynamics track with smart pulley and safety stopper on one end; collision
cart with reflector connected to a variable mass hanging over the pulley; motion
detector connected to the Science Workshop interface recording the velocity of the
moving cart.
Procedure:
a) Weigh the cart (M) and the small mass (m) hanger.
b) Open the experiment file “New ...
Chapter 3
This document summarizes key concepts about two-dimensional motion and vectors:
1) It introduces scalars, which have magnitude but no direction, and vectors, which have both magnitude and direction.
2) It describes methods for adding vectors graphically by drawing them as arrows and finding the resultant, or using trigonometry.
3) It explains projectile motion as objects moving under gravity with both horizontal and vertical components of motion that can be analyzed separately using kinematic equations.
International Journal of Engineering Research and Development (IJERD)
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yahoo journals, bing journals, International Journal of Engineering Research and Development, google journals, hard copy of journal
Ch#4 MOTION IN 2 DIMENSIONS
The document discusses projectile motion, which is two-dimensional motion under constant acceleration. Projectiles follow a parabolic trajectory due to gravity acting downward. The horizontal and vertical motions can be analyzed separately, with the horizontal motion having constant velocity and the vertical following equations for constant acceleration. Key aspects include calculating the maximum height, range, and landing location of a projectile given initial velocity and angle.
ADAPTIVE TREADMILL CONTROL BY HUMAN WILL
The document describes a new adaptive treadmill control strategy that allows the treadmill speed to be controlled by the user's intended walking speed. It analyzes the center of pressure formula and simulation results to identify the ratio of reaction forces yF and zF (denoted as ,y zR ) as a key index related to intended walking speed. An experiment is conducted where subjects walk on a treadmill while viewing a virtual reality shopping scene. Force plate data is used to model the relationship between ,y zR and treadmill velocity V, and least squares regression is used to calibrate the model. The results show the treadmill speed can be smoothly controlled to match the user's intended speed.
11 - 3 Experiment 11 Simple Harmonic Motio.docx
11 - 3
Experiment 11
Simple Harmonic Motion
Questions
How are swinging pendulums and masses on springs related? Why are these types of
problems so important in Physics? What is a spring’s force constant and how can you measure
it? What is linear regression? How do you use graphs to ascertain physical meaning from
equations? Again, how do you compare two numbers, which have errors?
Note: This week all students must write a very brief lab report during the lab period. It is
due at the end of the period. The explanation of the equations used, the introduction and the
conclusion are not necessary this week. The discussion section can be as little as three sentences
commenting on whether the two measurements of the spring constant are equivalent given the
propagated errors. This mini-lab report will be graded out of 50 points
Concept
When an object (of mass m) is suspended from the end of a spring, the spring will stretch
a distance x and the mass will come to equilibrium when the tension F in the spring balances the
weight of the body, when F = - kx = mg. This is known as Hooke's Law. k is the force constant
of the spring, and its units are Newtons / meter. This is the basis for Part 1.
In Part 2 the object hanging from the spring is allowed to oscillate after being displaced
down from its equilibrium position a distance -x. In this situation, Newton's Second Law gives
for the acceleration of the mass:
Fnet = m a or
The force of gravity can be omitted from this analysis because it only serves to move the
equilibrium position and doesn’t affect the oscillations. Acceleration is the second time-
derivative of x, so this last equation is a differential equation.
To solve: we make an educated guess:
Here A and w are constants yet to be determined. At t = 0 this solution gives x(t=0) = A,
which indicates that A is the initial distance the spring stretches before it oscillates. If friction is
negligible, the mass will continue to oscillate with amplitude A. Now, does this guess actually
solve the (differential) equation? A second time-derivative gives:
Comparing this equation to the original differential equation, the correct solution was
chosen if w2 = k / m. To understand w, consider the first derivative of the solution:
−kx = ma
a = −
k
m
⎛
⎝
⎜⎜⎜⎜
⎞
⎠
⎟⎟⎟⎟
x
d 2x
dt 2
= −
k
m
x x(t) = A cos(ωt)
d 2x(t)
dt 2
= −Aω2 cos(ωt) = −ω2x(t)
James Gering
Florida Institute of Technology
11 - 4
Integrating gives
We assume the object completes one oscillation in a certain period of time, T. This helps
set the limits of integration. Initially, we pull the object a distance A from equilibrium and
release it. So at t = 0 and x = A. (one.
Projectile Motion
The document discusses projectile motion and circular motion. It defines key terms related to projectile motion such as trajectory, angle of projection, horizontal range, time of flight, and velocity of projection. It then derives equations for the trajectory, time of flight, horizontal range, maximum height, and velocity at impact of a projectile. Examples and problems are provided to demonstrate the application of these equations.
Projectile motionchemistory (4)
Nehru Nagar is a residential area made by Siddhant and Saurabh. Their document discusses projectile motion through defining its components, equations of path and motion, time of flight, maximum height, horizontal range, and examples like cannon balls. Projectile motion results from independent horizontal and vertical motions. The path is a parabola defined by equations combining the horizontal and vertical components. Time of flight, maximum height, and horizontal range can be calculated from initial velocity and launch angle.
Linear_Motion-1.pptx
This document provides an overview of mechanical science concepts related to linear motion. It defines key terms like displacement, velocity, acceleration, and discusses displacement-time and velocity-time graphs. Uniform acceleration equations of motion are derived. Gravity is described as causing uniform acceleration. Projectile motion is analyzed by resolving velocities into horizontal and vertical components. Examples demonstrate calculating projectile range and maximum height.
Section1revision
1) Projectile motion involves motion in two dimensions - horizontal and vertical. The horizontal motion is constant while the vertical motion accelerates downward at 9.8 m/s^2.
2) Uniform circular motion requires a centripetal force directed toward the center of rotation to cause centripetal acceleration.
3) Newton's law of universal gravitation describes the gravitational attraction between two objects, proportional to their masses and inversely proportional to the square of the distance between them.
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- 1. PHYS1101 Physics I Answer: Objective: To find the initial speed using the projectile motion simulation Background Knowledge: Projectile motion is the motion of object under the effect of the gravity. Usually we ignore the air resistance in the projectile motion. If the y-axis is perpendicular to the earth surface, the motion along the y-axis is a constant acceleration motion and the x-axis motion is a constant velocity motion. Equations for motions along the y-axis and the x axis are respectively: In this virtual experiment, we measure some physical quantities of projective motions such as the angle, range and flight time and find the initial speed from these physical quantities. Of course, we know the answer already as it is a value, which you choose in the simulation. Thus, the purpose of this exercise is to provide an exercise to show how a physical quantity can be determined from some measured data. Procedure: Go to the Phet website and start the simulation of projectile motion using the weblink: https://phet.colorado.edu/en/simulation/projectile-motion Go to the lab: as shown in the figure. Choose a height of the cannon and an initial speed. Keep these two values fixed throughout the simulation. Adjust the angle of the cannon and then fire the cannon. Measure the range (the x distance travelled ) and time of flight. Record 5 sets of data in the following table. You can use this instrument to measure the time and position along the path Plot a graph of
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