Falling Masses Activity
Hypothesis: You will be plotting a graph of distance fallen vs. time for a falling object. Thinking
about what the slope of such a graph represents and what happens to that quantity as the object falls
(and thinking about the reading you have been doing in the textbook and on physicsclassroom.com),
sketch the shape of the graph you expect to get:
d
t
Materials:
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a dollar bill
length measuring device(s) (calibrated straight edge, meter stick, tape measure, etc., as long as
it measures in metric units or you are willing to convert)
towel (optional)
stopwatch (the one on your cell phone is just fine)
3 spheres of various sizes (marbles, bouncy balls, sports balls, etc.); try to use two of the same
size but different masses
Procedure:
1) Measure the length (longer dimension) of a dollar bill in centimeters. Record it on the Data/Results page
provided.
2) You need a partner for this step. Hold the dollar bill the long way vertical so that it hangs between your
partner’s thumb and forefinger with his/her fingers positioned at the halfway mark. Without telling your
partner when you will do it, drop the dollar bill. See if your partner can close his/her fingers in time to
catch the bill. (Most people can’t react quickly enough.)
3) Using kinematics equations, calculate the time it takes for half the dollar bill’s length to pass between
your partner’s fingers. This is an approximation of human reaction time. (what units should the distance be
in?)
SAFETY: For the next part, you will be dropping objects from various heights. Make certain
everyone around you knows what is going on so no one steps into the path of a falling object and
gets hurt. Inform your parents about this experiment so they can make suggestions that will keep
you (and their floors) safe.
4) Drop the smallest of your spheres (marble, bouncy ball, tennis ball, etc.) from rest from each of the given
heights and measure the time to fall. Get a partner to help you, especially with the larger heights. Put a
folded towel down where the sphere will hit so the floor does not get damaged and, if using a fragile
object (such as a glass marble), the sphere will not get break. Alternatively, perform the experiment
outside in a grassy area. Use a stopwatch to time how long it takes to hit the ground. This will be Trial
1. Do it again. This time will be Trial 2. Repeat a third time. Average the three trials. There are 4
blank rows in your data table. Pick 4 additional heights of your choosing – larger is better.
5) Repeat step 4 with
a) another sphere of approximately the same size but different mass
b) a large sports ball, such as a soccer ball or a basketball (not a bowling ball – you’ll hurt
yourself or others).
6) For each object, complete the remaining columns on the data chart. There is no need to show work for
those calculations.
Data/Results:
Length of dollar bill: ___________
Calculation for human reaction time (show work here):
Object: ______________
Distance
Fallen (m)
Time to Fall (s)
Trial 1
2.00
1.80
1.60
1.40
1.20
0.80
0.40
0.20
0
Trial 2
Trial 3
2 x (Distance
Fallen) (m)
Average
(Average
Time)2 (s2)
Object: ______________
Distance
Fallen (m)
Time to Fall (s)
Trial 1
2.00
1.80
1.60
1.40
1.20
0.80
0.40
0.20
0
Trial 2
Trial 3
2 x (Distance
Fallen) (m)
Average
(Average
Time)2 (s2)
Object: ______________
Distance
Fallen (m)
Time to Fall (s)
Trial 1
2.00
1.80
1.60
1.40
1.20
0.80
0.40
0.20
0
Trial 2
Trial 3
2 x (Distance
Fallen) (m)
Average
(Average
Time)2 (s2)
Graphs: (graph paper is provided in this packet)
Before plotting any graphs, carefully read the “Expectations for Graphing” part of the Summer Assignment.
You will plot 4 separate graphs, as listed below, on 4 separate pieces of graph paper. Make sure the title of
each graph indicates the object used for that data set.
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Plot Distance Fallen vs. Average Time for the first object only.
Plot 2 (Distance Fallen) vs. (Average Time)2 for the first object.
Plot 2 (Distance Fallen) vs. (Average Time)2 for the second object.
Plot 2 (Distance Fallen) vs. (Average Time)2 for the third object.
Analysis: (answer on these pages)
1) What shape was the distance vs. time graph for the first object? Does it match your hypothesized
graph? If not, YOU MAY NOT CHANGE YOUR HYPOTHESIS. Instead, explain what you have
learned.
2) What does the slope of a distance vs. time graph represent?
3) So, why is it natural to expect this particular shape for distance vs. time for this situation? (What was
happening to the marble’s motion as it fell?)
4) The equation of motion that applies to uniform acceleration is: d = vot + ½ at2
Since you dropped all the objects from rest, vo = 0 m/s. Crossing out the vot term and multiplying both sides
by 2 yields: 2d = at2. Notice that the remaining graphs you plotted had 2d on the vertical axis and t2 on the
horizontal axis and, if all went well, you should have gotten very good straight-line trends when you plotted
these three graphs. (If you didn’t, then maybe it’s time to go back and do the experiment again . . . .) The
general algebraic equation for a straight line is y = mx + b. Fitting the rearranged kinematics equation to this
form shows:
2d = at2
it might help if it is written so: (2d) = (a)(t2)
y = mx + b
y = m x+b
So, what does the slope of your 2d vs. t2 graph represent?
5) Assuming the dropped objects were in free-fall, what is the expected value for the slope of the graph?
6) If you have not already done so, calculate the slope of each 2d vs. t2 graph. Show your work on the
graph. (If your pattern is not a good straight line, find the best straight line that goes through the pattern
of plotted points and use that.) (Or again, maybe you should re-do the experiment . . . .)
Object
Slope
7) What challenges did you have to overcome in performing this experiment? What difficulties did you
encounter, based on the size of the object?
8) When measuring the starting height of each object, what part of the object did you measure to (center,
top, bottom, random)? Upon reflection, was that the best choice? If so, what mistake might another
student have made? If not, how would you change it to better correspond to the distance the object fell?
9) When trying to establish a pattern, how many data points do you think are necessary? 3? 5? More?
Why are you told to take data for 8 different heights in this experiment?
10) Which is easier – measuring long times or short times? How does human reaction time play a role in
this? Which data points do you have the most confidence in?
11) Why are multiple trials done for the same height?
12) For each object, calculate the percent discrepancy, using your answer to Analysis number 5 as the
accepted value and your slope as the observed. Show your work in the space below.
% discrepancy = |observed – accepted| x 100
accepted
13) Evaluate your results. Do you feel, within experimental error, this experiment showed objects in
freefall? For some, not others? What factors were present that you could not control and how did they
affect each object?