Acceleration Due to Gravity
Acceleration is the rate of change of velocity. A moving object that
speeds up or slows down is said to be accelerating. Acceleration is caused
by a force, and forces are defined by the acceleration they create.
Acceleration is a key concept in understanding force, work, and energy.
One particular example of acceleration is the acceleration created by
the force of gravity. As gravity pulls on a falling object the object gains
velocity at a constant rate. In a vacuum, without the interference of air
resistance, all objects gain velocity at the same rate. This rate, known as the
acceleration due to gravity, is used to calculate the gravitational potential
energy of an object: P.E. = mgh, where g is the acceleration due to gravity.
The purpose of this lab is to determine the acceleration due to gravity by
collecting data on the time it takes an object to fall several distances and
then using an Excel spreadsheet to analyze the data.
PROCEDURE
Set up a table clamp and pole assembly as illustrated by your
instructor.
The computer will be used with an interface to collect data about the
time of fall.
Place the steel ball in the sensor assembly and tighten the thumbscrew
to hold the ball in place. You will need to push the outside part of the clamp
by hand before you tighten the thumbscrew.
Measure the distance from the bottom of the ball to the touch pad and
record in the data table.
Click the “start” button to activate the sensor.
Make sure the touch pad is directly under the ball, and then use the
thumbscrew to release the ball and let it strike the sensor. The digital
window should record the time of fall to 4 decimal places. Record the time
in the data table. Click “stop”.
Lower the top clamp approximately 5-6 centimeters and repeat the
procedure.
Perform 10 trials, lowering the clamp each time approximately 5-6
cm.
DATA
distance (m)
time (sec)
ANALYSIS
The theoretical relationship between distance and the time squared is
as follows:
d = ½ g t2
This relationship is equivalent to the linear relationship y = m x + b
where m is the slope of a graph representing the relationship between
y (d) and x (t2).
Prepare a spreadsheet showing (1) data table (2) a linear graph of the
relationship between d and t2 (3) a display of the formula for the graph (4) a
display of the value of g (g = 2*m) (5) a display of the per cent error, using
the following formula:
% error = (your observed value – accepted value) x 100
accepted value
The accepted value for g is 9.8 m/sec2.