PHY105L: Investigation on the Acceleration due to Gravity
Introduction:
The purpose of this investigation is to measure the acceleration due to gravity g in the laboratory. An object is in free fall
if only the force of gravity is acting on it. Since the atmosphere is a fluid, there is always some amount of atmospheric
drag present when an object falls through the air. Since we will be measuring the position of the falling object with a
paper tape there will also be some tape drag of the paper over the timing mechanism. These two drag forces act opposite
the direction of the force of gravity and, thus, reduce the actual acceleration the object experiences to a value slightly less
than that of free fall.
To, at least partially account for the effect of drag forces, the acceleration of masses of similar cross-sectional area will be
measured as they fall. The requirement for similar cross-sectional areas in the falling masses is an attempt to keep the
drag forces to a constant value for the different masses since the aerodynamic drag forces depend on cross-sectional area
as well as other factors. We will assume that the tape drag is a constant for all the masses as well.
If the net drag forces FDrag are the same for the different falling masses m then the measured
1
acceleration a is related to the acceleration of free fall g by a   FDrag     g . See the
m
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derivation of this relation to the right. Thus if a is graphed as a function of
then a straight
m
line will result whose slope is negative the net drag force and whose y-intercept is the
acceleration due to gravity.
FDrag
F Net mg  FDrag
and
F Net ma
a  g 
To accomplish the purpose of ascertaining the value of the acceleration due to gravity g, the
acceleration of various falling masses of similar cross-sectional area will be plotted against the
reciprocal of the mass and g will be given by the value of the y-intercept.
FDrag
m
mg
Measurements:
1. Using the paper tape, measure accurately and record the position as a function of time of each of the masses
assigned to you as they fall from the timing mechanism.
Analysis:
1. Plot the position versus time for each of your assigned masses. If the acceleration is constant, as expected, then
the shape of x vs. t will be parabolic following x(t )  xi  vi  t 
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a  t 2 . Determine the acceleration of each of
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your falling masses using the quadratic coefficient of the best fit parabolic trend line. Record the acceleration of
each mass in cm/s2. Also, calculate the average velocity of each of your falling masses using your accelerations
and the displacement of each mass assuming that the initial velocity is zero. Finally, record the acceleration and
average velocity of each mass in the Class Lab Results Data Table at the front of the laboratory.
2. Create a properly formatted graph of a vs.
1
for all the data in the Class Lab Results Data Table. Determine the
m
value of the acceleration of gravity g and the magnitude of the net drag force from the trend line coefficients.
Compare your value of g to the accepted value using a percent difference. Discuss how well the class data
constrains the value of g. In other words, is the class data so linear that there is very little uncertainty in the
values of the y-intercept, or is the class data noisy enough to allow a range of values for the y-intercept?
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3. Discuss the drag force. What is its mass equivalence (i.e. what mass would have the same weight as the net drag
force)? How does this mass equivalence of the net drag force compare to the masses used in the investigation? Is
the magnitude of the net drag force a reasonable value? Why? What are the dominant sources of the net drag
force?
Optional advanced analysis question:
If the net drag force is dominated by aerodynamic drag as the masses fall through the air and if the velocity is not too
large, then the empirical relation for that force is FDrag 
1
cd v 2 A where ρ is the density of air (1.2041 kg/m3), v is the
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particle’s average velocity, A is the cross-sectional area of the falling masses and cd is called the Drag Coefficient and is
dimensionless. For many objects falling through air at not too large a velocity the value of cd is around 1. Using the
average velocity of the class data in m/s and a value for A of 1.81×10-3 m2, calculate cd. If your calculated value for cd is
very different from 1 then aerodynamic drag is not the dominant component of the net drag force. Discuss the
significance of your calculated value of cd as it relates to the dominant source of the net drag force.
Structure of the Report:
Your report should include a sketch and a short description of the experiment, a discussion of the theory presented in the
introduction on this handout, yours and the class’s data, the graphs, answers to the analysis questions and this handout.
Data
Graphs
Title Page
(Names, Date)
Discussion of Analysis
points 1 to 3.
5.
&
This handout.
Introduction
 Purpose.
 Method of attaining the
purpose.
 Description of the apparatus.
 Discussion of the theory with
equations.
1, 2
3
4
5
6
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