Acceleration Down an Incline
There is a well-known story that Galileo dropped two objects of different
weights from the Leaning Tower of Pisa in order to show that all objects
accelerate toward the Earth at the same rate, regardless of their weight
as long as air resistance is negligible. Historians, however, are quite
certain that Galileo never performed such an experiment.
Galileo’s experiments with acceleration involved rolling balls down an inclined plane. He did this out
of necessity because of his inability to make precise measurements of the short time intervals
needed for measuring the acceleration of objects in free fall. The inclined plane’s angle could be
adjusted until the time for the ball to roll to the end was long enough for even the crude timemeasuring devices of his day to produce useful results.
In this exercise, you will examine acceleration by measuring the time needed for an object to roll
various distances down an inclined plane – much like Galileo did around 400 years ago.
Gathered Data:
 Speed is the distance an object travels per unit of time. Speed can be expressed as
kilometers per hour (km/hr), meters per second (m/s), and so on. In most cases, objects
don’t travel at a constant speed. Therefore, the average speed is used to describe the
motion.
d
s
t
s = speed, t = time, and d = distance

Acceleration is the rate at which an object’s speed changes. Acceleration can be
expressed as meters per second per second (m/s/s or m/s2). Forces such as gravity, air
resistance, and friction can cause an object to decelerate (decrease speed over time).
Other forces can cause and object to accelerate (increase speed over time). If the car does
not encounter these forces and travels at a constant speed, then it is not changing speed
and there is no acceleration or deceleration.
a = acceleration, v = change in velocity or speed, and t = time
v
a
t
v = final velocity or speed – initial velocity or speed
1
Purpose:
1. Examine the acceleration of an object rolling down an inclined plane
2. Determine the shape of a “Distance vs Time” graph for an accelerating object
3. Determine the mathematical relationship between the distance and time an object travels
while it is accelerating
Materials:
inclined plane, “Hot Wheels” car, track, stopwatch, meter stick or measuring tape
(Note: marbles may be used if toys cars and track are unavailable)
Hypothesis:
What will be the average speed of a marble rolling down a 20cm tall ramp and traveling 5m?
Will the marble continually accelerate as it travels the 5m? Or will it decelerate?
Vf= a*t when Vi = 0
d = ½ at2 when Vi = 0
Where Vf is the final velocity of the object after falling for time, t, the acceleration is a and d is the
distance the object has fallen. The average velocity (of any object) is just
Va= d / t
In this experiment, you will be able to calculate the average velocity, Va. The final velocity, Vf,
will be twice as large (2Va)
Procedure:
1.
2.
3.
4.
5.
6.
7.
Measure and mark from one end of the inclined plane the distances indicated in the data
table.
Place your inclined plane on something (a book?) so that one end is slightly elevated. Be sure
to support the track so that it does not bow.
Use the stopwatch to determine how much time is needed for the car (marble) to roll each
indicated distance down the incline. Record this time in the data table.
Perform two time trials for each distance and average them.
Use MS Excel to make a graph of “Distance vs Time.”
Use the MS Excel “Add Trendline” function to draw and calculate the best-fit curve to your
data points. Place this on your graph.
Answer the questions at the end of this activity.
2
Distance, meters
Average
Time,
seconds
Time, seconds
Trial 1
Trial 2
Acceleration
Trial 3
0.10
0.30
0.50
0.70
0.90
1.20
1.60
2.00
2.30
Questions:
1.
How does a “Distance vs Time” graph of accelerated motion compare with a “distance vs
time” graph of non-accelerated motion (constant velocity)?
2. How can you tell by looking at a “Distance vs Time” graph whether or not the object has
constant or changing speed?
3. What does the shape of your graph and the “best-fit” equation tell us about the
mathematical relationship between distance and time for a uniformly accelerating object?
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4. When looking at his data, Galileo discovered that an object would travel 4 times as far (2 2)
in twice the time, 9 times as far (32) in triple the time, 16 times as far in (42) in quadruple
the time, etc...
Use your graph to find the
time to travel 0.40 m ____
time to travel 0.60 m ____
time to travel 0.80 m ____
time to travel 1.00 m ____
time to travel 1.20 m ____
time to travel 1.60 m ____
time to travel 2.00 m ____
time to
time to
time to
time to
time to
travel
travel
travel
travel
travel
0.90 m ____
1.35 m ____
1.53 m ____
1.80 m ____
2.07 m ____
….
time to
time to
time to
time to
time to
time to
time to
travel
travel
travel
travel
travel
travel
travel
0.10 m ____
0.15 m ____
0.20 m ____
0.25 m ____
0.30 m ____
0.40 m ____
0.50 m ____
ratio
ratio
ratio
ratio
ratio
ratio
ratio
= ____
= ____
= ____
= ____
= ____
= ____
= ____
time to
time to
time to
time to
time to
travel
travel
travel
travel
travel
0.10 m ____
0.15 m ____
0.17 m ____
0.20 m ____
0.23 m ____
ratio
ratio
ratio
ratio
ratio
= ____
= ____
= ____
= ____
= ____
5. Do your results seem to agree with Galileo’s discovery? _____ Why/Why not?
6. What could you do in order to experimentally test whether or not all objects accelerate at
the same rate, regardless of their weight?
7. How do you think the angle of incline affects this experiment?
8. What should happen to the time values in your data table if the incline is made steeper?
9. What should happen to the ratios in question #4 if the incline is made steeper?
10. List possible sources of error in this lab.
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1. Look at your hypothesis. Address each question as whether your guesses were
true or false and how close you were.
2. Draw a diagram showing the exact path of each trial. Be detailed as to the exact
points the ball might have curved in its path.
3. Did your ball travel at a constant speed? How do you know?
4. How could you change the experiment to make the ball decelerate faster?
5. How could you change the experiment to make the ball accelerate faster?
b.
c.
d.
e.
f.
g.
h.
6. How could you change the experiment to make the ball not accelerate or
decelerate for an entire 5m?
7.
Is the acceleration in Part 1 constant? What about the velocity?
Why was Galileo unable to accurately directly measure the velocity of falling
bodies?
How would Aristotle explain wood burning? A rock falling?
Can you prove mathematically that Vf = 2Va?
How is it possible to determine g, the rate of acceleration due to gravity for a
freely falling object, by rolling balls down an inclined plane? Hint: at what angle
does g=a?
How does the mass of an object effect it’s rate of acceleration during freefall?
What are the sources of error in your experiment?
1.
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