Acceleration
kinematics
friction
Important terms to remember
displacement
velocity
controls
variables
acceleration
magnitude
Prior to lab: Draw a diagram that illustrates what you know or remember about motion, what
impacts motion and what forces are involved in the process of something moving. Label your
drawing in your lab notebook and describe what is happening in the diagram using the important
terms listed in the table above.
Introduction
In the previous Kinematics experiment the focus was on position and velocity. A complete
description of motion requires specifying position, velocity, and acceleration. The focus of this
experiment is on acceleration. The purpose of this experiment is to study the acceleration of cart
on a tilted track, the deceleration of a cart due to friction, and the acceleration of a fan-powered
cart.
The equation of physics that describes the displacement of an object moving with constant
acceleration is given by:
xt   x 0  v 0 t  1 at 2
2
(1)
The equation of physics that describes the velocity of an object moving with constant
acceleration is given by:
vt   v 0  at
(2)
Objectives




To practice making precise measurements with the motion sensor.
To explore how various motions are represented on an acceleration-time graph.
To discover the relationship between position, velocity, and acceleration graphs.
To present results related to experiments on motion to classmates by using visuals to describe
the mathematic formulas related to motion.
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Flat Airtrack
To begin with you will repeat the measurements you did last week of the cart on the airtrack,
now also recording the acceleration versus time graph.
1. Following the procedure from last week, set-up the motion sensor to record the displacement
and velocity of the cart on a flat airtrack. Keep working on the alignment of your system until
the velocity versus time curve is very smooth.
Prediction 1. After giving the cart a push on a level airtrack, what do you expect the acceleration
versus time curve will look like? Sketch a picture in your notebook. Does this drawing have a
connection to what you drew in your pre-lab reflection? If so, how? If not, what are some
differences?
2. Open an “acceleration versus time graph” and again record the motion of the cart traveling in
one direction down the level airtrack. Print both the velocity and acceleration graphs and tape
them in your notebook. Describe how the equation for velocity relates to these graphs.
Create a drawing next to the graph that shows your understanding of the motion of the cart
on the ramp in relation to what you observe on the motion graph.
Question 1. What was the approximate value of the cart’s acceleration? Given that we can define
acceleration as the rate of change of the velocity, explain how your velocity and acceleration
graphs indicate the same value for the acceleration.
Prediction 2. Before proceeding to the next section, PREDICT what a graph would look like for
position versus time if a cart was allowed to move downhill on its own due to gravitational pull.
Record this prediction in your notebook.
Downhill Airtrack
Design an experiment for a cart moving under constant, acceleration (hint: gravity is constant).
Sketch you experimental setup and describe your initial conditions. Will you give the cart an
initial push? How might your push affect the outcome of your experiment? You will again
measure the motion of the cart, creating position, velocity, and acceleration graphs.
1. Apply a linear curve fit to the velocity graph and a quadratic curve fit to the position graph.
Print all three graphs (position, velocity, and acceleration vs. time) and tape them into your
notebook.
Question 2. Are your displacement and velocity graphs consistent with equations (1) and (2)?
Write the equations for the displacement and velocity using the parameters from your curve fit.
For example, your velocity equation might look something like:


vt   0.05 m s  0.25 m s 2 t
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(3)
2. Apply equation 3 to an actual diagram by scetching a motion diagram in your lab notebook
that describes your motion equation. Include your experimental parameters on your diagram.
3. Measure h and L for your set-up (see picture above). Calculate the theoretical acceleration as
a = g sin   g tan  = g h/L
(4)
Question 3. Compare the theoretical acceleration to the experimental values of a you derived
from i) the curve fit to your displacement graph, ii) the curve fir the your velocity graph, and iii)
directly from your acceleration graph. Calculate the percent discrepancy for each of these. Why
is it important to calculate the theoretical acceleration and make this comparison? Would you
expect any one of these values to be more accurate than the others?
Prediction 3. If instead of starting the cart from rest, how would you expect the velocity and
acceleration curves to change if you gave the cart and initial push downhill? Make two side by
side velocity vs. time sketches and two side by side acceleration vs. time sketches in your lab
notebook, one for a cart with an initial push downhill and the other without at push. How does
this impact the mathematical formula that accompanies each scenario?
4. Again record the motion of the cart down the airtrack, this time giving the cart an initial
gentle push downhill. Sketch the resultant graphs in your lab book and compare to your
prediction.
Uphill Airtrack
We will now measure the motion of the airtrack as it moves up the airtrack.
1. Remove the wooden block and place it under the opposite end of the airtrack. The airtrack
should now rise up away from the motion sensor.
Prediction 4. Based on your previous measurements, what will be the approximate magnitude
and direction of the carts acceleration if it is given a push up the slope? Again, make two side by
side velocity vs. time sketches and two side by side acceleration vs. time sketches in your lab
notebook, one for a cart with an initial push uphill and the other without at push. How does this
impact the mathematical formula that accompanies each scenario?
Prediction 5. Sketch your prediction for the velocity versus time graph if you were to give the
cart a gentle push up the track and observe it until it come back down to the bottom.
2. Again realign the motion sensor. Start with the air off, and then turn the air back on and
ensure that the velocity curves are smooth.
3. Record the motion of the cart after giving it a gentle push up the slope. Record the motion
until the cart comes back down to the bottom of the airtrack. Curve fit both the displacement
and velocity curves as before. Print out both graphs and tape them into your notebook.
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Question 4. How does the value of acceleration you obtain from your graphs compare to your
prediction? Is the value roughly the same as in the downhill experiment? Any important
differences?
Question 5. Does the velocity graph match your prediction? Explain? What happens on the
velocity curve when the cart reaches the top of the airtrack and starts back downhill? What
happens on the acceleration graph at this point? Explain.
Question 6. Create a chart to compare the scenarios, diagrams, graphs and equations – how are
they similar? Different? Where do the important terms fit into this comparison?
Question 7. What are some APPLICATIONS of these ideas to REAL WORLD examples?
Describe a scenario of activities in real life that would mirror the scenarios found in this
laboratory exercise.
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