Changing Velocity
Introduction
In this laboratory you will explore acceleration, the rate at which velocity changes. You will be asked to
design an experiment, so you should read the handout before coming to lab and make some
predictions about how the glider will accelerate on the track.
Textbook Reading
Physics 150: Halliday, Resnick, and Walker: Sections 2-5 and 2-6 (pages 17-21).
Physics 125: Cutnell and Johnson: Sections 2-3 through 2-6 (pages 34-51)
Overview of Laboratory
You will first use velocity-time and distance-time graphs to describe motion at constant velocity and
motion with constantly changing velocity. You will then design an experiment to explore acceleration on
an air track.
Objectives:
·
to observe motion at constant velocity and constant acceleration
·
to measure acceleration from the slope of a velocity-time graph
·
to design an experiment that reveals some of the conditions that determine the acceleration of an object.
Pre-lab Questions
1. Write down an experience you have had in the last 24 hours which could be accurately described by using
the word “acceleration.”
2.
Write the formal physics definition of average acceleration. Hint: if you don't know it, look in your
book.
3.
What is an example of the units for average acceleration?
Physics Laboratory Manual. Jan 1999
Changing Velocity - Page 1 of 10
On the back of this page is a velocity-time graph of the motion of an object.
4.
Find its acceleration over the time period after about 1.05 s when its acceleration is constant by
determining the slope of the straight line that best fits the data. Report the acceleration with units.
5.
What is the acceleration of the object when its velocity is –2 m/s? +2 m/s? 0 m/s?
Write your calculations and results below the graph. Show them to your lab instructor at the beginning of the
lab. Your lab grade will depend on doing these exercises before coming to the lab and on the care you take in
finding the answers.
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Motion of an Air-track Glider on a Horizontal Track
Equipment
·
·
·
Air track with glider
ULI with motion detector
Experiment file ChangingVelocity1
Introduction
Last week you used distance-time graphs to describe motion with constant velocity. You learned how to
determine the velocity from the slope of the graph. This week you’ll explore graphs that show directly
how the velocity changes with time. Start the Logger Pro program and open the file ChangingVelocity1.
Collect some data to make sure that the motion detector “sees” only the glider, and not any other
object, especially your hand.
Practice
1. Using the glider and motion detector, duplicate on the computer the graphs given below as best you can.
Draw your best attempt on top of the given graph. You may find it difficult to match them exactly.
Approximate the shape of the graphs as well as possible.
With each graph, give an explanation of how you performed the experiment, that is, describe how the
glider moved. Then draw the second graph requested.
A. Distance versus time
Describe the motion
Sketch the velocity-time graph
B. Positive velocity versus time
Physics Laboratory Manual. Sept. 1995
Describe the motion
Sketch the distance-time graph
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C. Negative velocity versus
t
i
m
e
D
e
s
c
ribe the motionSketch the distancetime graph
2. Now tilt the air track by placing one thick metal block under the leg of the track closest to the motion
detector. Place the glider at the far end of the track and release it. Observe its motion, but don’t use the
ULI yet. Predict the graphs that the computer will display by following this procedure
Distance-time graph
Velocity-time
At t = 0
(immediately after you released the glider)
Where is the glider?
How fast is it going?
Mark the position on the graph.
Mark the speed on the graph.
At small t
(shortly after you released the glider)
Where is the glider?
Mark the position on the graph.
How fast is it going?
Mark the speed on the graph.
At the end of its motion
(just before it hits the end of the track)
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Where is the glider?
Mark the position on the graph.
How fast is it going?
Mark the speed on the graph.
Now take data and study the distance-time and velocity-time graphs. Draw the results on the axes above,
clearly marking which are the predictions and which are the actual motion. Explain below how you can make
better predictions in the future.
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Investigating the Acceleration of a Glider on a Tilted Air Track
Equipment
·
·
·
·
Air track with bumpers, glider, and weights
Blocks to tilt track
ULI with motion detector
Program ChangingVelocity2
Introduction
If you place a glider on a tilted air track, it will accelerate down the track. How does the acceleration
depend on the properties of the glider and its environment? That is, what can you change that
changes the acceleration? What is the relationship between the manipulated variables and the
resultant variable (the acceleration of the glider)?
Just as important, what parameters can you change
that have no effect at all on the acceleration?
In this part of the laboratory, you will design an experiment to find out.
At the end of the laboratory, your instructor will ask you to use your results to predict the acceleration
of a glider released in a certain way that has a specified mass and is on an air track tilted to a given
angle.
Experiment Planning
Here is a list of conditions that might affect the acceleration of the glider. Feel free to add others.
·
·
·
Initial position of glider on track.
Initial velocity of glider (including +, –, or 0).
Mass of glider.
 Position of detector (upper or lower end of track).
· Angle air track makes with horizontal.
While you are encouraged to explore as many of these parameters as possible, you are required to
test the effect of the mass of the glider, the effect of the initial velocity, and the dependence on the
angle at which the track is tilted.
Experimental Preparation
Open the Logger Pro file ChangingVelocity2.
Measuring acceleration Before coming to the lab you found the slope of a printed velocity-time
graph. The computer can find the best straight-line fit to the velocity-time data.
a.
Use the mouse to select the region of the data on the v-t graph that you want to analyze.
b.
Click on the curve fit icon:
Physics Laboratory Manual. Sept. 1995
or select Curve fit from the Analyze menu. You will see a menu box.
Introduction to the Physics Laboratory - Page 6 of 8
c.
d.
In the box at the lower left select linear. Click on Try Fit. A thin straight line will appear on the graph
and numeric values of the slope and intercept will be written in the box under the graph. If you are not
satisfied with the fit, you can select a different range of data and try again.
When you are satisfied with the fit, click on OK. A “floating box” will appear on the original graph that
shows the parameters of the fit: m, the slope, is the acceleration; b, the intercept, is the velocity at t = 0;
St. Dev. Slope measures the uncertainty in the acceleration. If this measure doesn’t appear, double-click
on the floating box and click on the box for “Std. Dev. of Slope.”
Varying mass You should have four chrome-plated steel cylinders that fit over the pins on the skirts
of the glider. Always put them on in pairs, either one or two on each pin.
Tilting the track You will find aluminum blocks of various thicknesses on the table. Use them to
raise the end of the track closer to the motion detector. You can use them either individually or stack
them up.
The sine of the tilt angle of the track can be found by
dividing the height of the blocks, H, by the distance
between the legs of the air track, L. Note that this
distance is measured along the track, not the table.
Then, sin θ = H/L.
Making a Measurement
Select one glider mass and track tilt. Decide how your team will collect data, and whether you will
simply release the glider from rest or give it a push uphill or downhill. Then try it. Analyze the data
as displayed on the velocity-time graph as outlined on the previous page to find the acceleration.
Reporting Your Results
Dependence of acceleration on mass
Description of procedure used:
Results (be sure to use appropriate units for each measured quantity):
Glider mass
(kg)
Tilt of track
sin θ
θ
Acceleration (including uncertainty)
(m/s2)
Conclusions (Does the acceleration depend on mass?):
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Dependence of acceleration on initial velocity
Description of procedure used:
Results (be sure to use appropriate units for each measured quantity):
Glider mass
(kg)
Tilt of track
sin θ
θ
Initial velocity
Acceleration (including uncertainty)
(m/s)
(m/s2)
Conclusions (Does the acceleration depend on the initial velocity? Within your uncertainties, is the
acceleration of the glider up the track the same as it is down the track? Attach printed velocity-time
graphs to support your conclusions.):
Dependence of acceleration on tilt of track
Description of procedure used:
Results (be sure to use appropriate units for each measured quantity):
Glider mass
(kg)
Tilt of track
sin θ
Physics Laboratory Manual. Sept. 1995
θ
Initial Velocity
(m/s)
Acceleration (including uncertainty)
(m/s2)
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Use the program Graphical Analysis for Windows to plot your results. Include error bars on acceleration.
Decide whether you should plot the acceleration as a function of θ or sin θ. One goal is to find the
acceleration that the glider would have if the track were vertical (θ = 90o), so plan your graph to be able to
answer that question.
Describe, according to your experimental data, how the acceleration of the glider depends on the mass of the
glider and its initial velocity and the tilt of the track.
What acceleration would the glider have under the conditions (mass, initial position, initial velocity, etc.)
given you by your instructor if the track were tilted at 90o?
Describe any additional experiments in this format on your own paper.
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Name_____________________________
Lab Section ____
Velocity-time graphs
Answer the following questions in the spaces provided
1.
a) How do you move to create a horizontal line in
the positive part of the v-t graph?
b) Draw the motion diagram for your motion.
2.
a) How do you move to create a straight line v-t
graph that slopes up from zero?
b) Draw the motion diagram for your motion.
3.
a) How do you move to create a straight-line v-t
graph that slopes down to zero?
b) Draw the motion diagram for your motion.
4.
The v-t graph of an object is shown. Find the total
change in position (displacement) of the object. Show your
work.
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Displacement = _________ m
5.
This v-t graph shows the motion of two objects.
a) Is one faster than the other? If so, which one?
Does it depend on the time? If so, which one,
when?
b) What does the intersection mean?
c) Does either A or B reverse direction? Explain.
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Sketch a velocity-time graph and a motion diagram corresponding to each of the following descriptions of the
motion of an object.
6.
The object moves away from the origin at a constant
velocity.
Motion diagram:
7.
The object is standing still.
Motion diagram:
8.
The object moves with a steady (constant) velocity
toward the origin for 10 seconds and then stands still for 10
seconds.
Motion diagram:
9.
The object moves with a steady velocity away from
the origin for 10 seconds, then reverses direction and moves
at the same speed toward the origin for 10 seconds.
Motion diagram:
10. Draw the velocity-time graphs for three objects. All have
accelerations of –0.50 m/s2.
One has an initial velocity of +2.0 m/s, the second has an initial
velocity of 0 m/s, the third has an initial velocity of –2.0 m/s.
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