Free Fall
position
constant
Important terms to remember
displacement
velocity
linear
quadratic
acceleration
discrepancy
Introduction
The purpose of this experiment is to study the motion of objects undergoing constant
acceleration, and to measure the acceleration due to gravity, g. You will use two different
methods to measure g, and determine whether your documented experimental errors can account
for the discrepancy between your value and the accepted value of g = 9.8 m/s2. You will also
study an object in free fall when air resistance can not be neglected.
It was Galileo who first hypothesized, then demonstrated, that all objects are accelerated toward
the earth by the force of gravity at the same rate, independent of their mass. An object
accelerating towards earth is said to be in free fall. In our everyday experience objects will
experience other forces in addition to gravity, such as air resistance, which normally causes
heavier objects to fall faster. In today’s lab we will measure the net acceleration of an object and
compare it to the acceleration caused by the gravitational force alone.
The acceleration of an object in free fall can be described quite simply as:
a
(1)
g
a = g = 9.8 m/s2 (towards the earth)
0
How does the velocity of such an object evolve with time?
Acceleration is the rate of change of velocity, so the velocity
must be increasing at a constant rate.
v
(2)
v0
v = v0 + gt
0
Since velocity is the rate of change of position, the position vs.
time graph will have a constantly increasing slope. Therefore,
instead of a straight line the graph will be quadratic.
(3)
t
t
y
y = y0 + v0t + ½gt2
y0
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0
t
Objectives



To determine the magnitude of the acceleration of a falling object under the influence of the
gravitational force of the Earth.
To discover how air resistance affects the motion of falling objects.
To learn to estimate measurement errors and determine whether known errors can account
for the discrepancy between theory and experiment.
Crude method of determining g
Our first method to determine g will make use of the relation between displacement and time for
an object undergoing constant acceleration. You will release a ball from rest so v0 = 0, and we
will assume that the initial position is at the origin so y0 = 0. Therefore from equation (3) the
relation between the displacement and time to fall is y = ½gt2.
1. Drop a ball from a height of 2 m and measure the time it takes for the ball to reach the
ground. Repeat five times and then calculate the average value tav..
2. Now calculate the acceleration, g = 2y/t2. Use y = 2m, and your value of tav.
Question 1. Does your value of g agree with the accepted value of 9.8 m/s2? Was this an
accurate method for determining g?
Motion Sensor
In this part of the lab we will use the motion sensor to record the position, velocity, and
acceleration of a rubber ball as it drops to the ground. As you did last week you will determine
the acceleration by curve fitting the position and velocity curves and directly from the
acceleration graph.
1. Connect the motion sensor to the Science Workshop interface box. Turn on the Science
Workshop box before turning on the computer. Attach the motion sensor to a rod and clamp
it to the table so it over hangs the table’s edge, is directed down toward the floor, and is about
1.5 meters above the floor. If you are having trouble recording several bounces, lower the
motion sensor or turn it around over the table and let the ball bounce off the tabletop.
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2. Open Data Studio and select motion sensor by double clicking on the motion sensor icon.
Change the trigger rate of the motion sensor to 40 Hz.
3. Open up a position vs. time graph by double clicking the graph icon and selecting position.
4. Check to see that the motion sensor is working properly by placing your hand in front of the
sensor, turning on data collection, and moving your hand down and up. Verify that the graph
is consistent with the motion of your hand.
5. Hold the ball directly under the sensor, begin data collection, and release the ball from rest.
The ball should strike the floor, bounce back up toward the motion sensor, and strike the
floor a second time. Stop data collection. You will analyze the motion of the ball between
the first and second bounces, when it was in freefall.
6. The recorded position versus time graph should have a parabolic shape. Use the software to
perform a quadratic curve fit.
Question 2. Compare this equation to your kinematic equation (3), and give a physical
interpretation of each constant. Find the acceleration of gravity from this and compare to the
accepted value of 9.80 m/s2.
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Question 3. Look at the graph of velocity versus time for the selected data. Explain (in terms of
the motion of the ball) the regions of the curve where the velocity is negative, positive, and
where it is zero. What does the slope of this graph represent?
7. Perform a linear fit to obtain the slope. Find the acceleration of gravity from this.
8. Look at the graph of acceleration versus time for the selected data.
acceleration over the same region.
Find the mean
9. Repeat steps 3-6 at least 5 more times. In Excel create a table similar to the one shown
below. Compare your average value for g with the accepted value by calculating the percent
discrepancy. Also calculate the standard deviation of each set of accelerations you measured.
Use the Excel formula =STDEV (…).
Trial
Acceleration (m/s2)
(position graph)
% discrepancy
Acceleration (m/s2)
(velocity graph)
% discrepancy
Acceleration (m/s2)
% discrepancy
(Acceleration graph)
1
2
3
4
5
6
Average
Std. Dev
10. Print out one representative curve of position vs time, velocity vs time, and acceleration vs
time and include them in your lab book.
Question 4. The standard deviation is a measure of the uncertainty in your measurements of
acceleration. Given this uncertainty, does your experimental value of g agree with the accepted
value of 9.8 m/s2? How does your method of measuring g in this section compare with your
earlier method of measuring g?
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