University of California, San Diego
Physics 11  Survey of Physics

Physics 11  Lab Exercise #2

Laboratory Exercise #2
The Equivalence Principle: Acceleration vs
Gravity
Einstein's General Theory of Relativity states that "a suitably chosen
acceleration" is indistinguishable from a gravitational field. In this
laboratory experiment we will investigate the relationship between
gravitational force & accelerationn and other accelerations using an
elevator, a bathroom scale, and a simple experiment to measure g.
Prelab Homework (6 pts)
You are to hand in your homework to your TA at the beginning of the
lab. Keep a duplicate for your own use during the lab and submit it
with your lab report.
Work the following problem:
A student weighs herself on a scale in an elevator, measuring a weight of
490 Newtons. Shortly after the elevator begins moving upward, the student
notes that the scale reads 588N, and, as the elevator reaches the desired
floor, the scale reads 392N.
Draw a freebody diagram of: (a) the student, (b) the scales,
(c) the elevator
What is the acceleration in each case?
Express your answer both in m/s^{2} and in
terms of g's, relative to the acceleration of gravity.
Estimate the reading on the scale (a) as the elevator starts back
downward, and (b) shortly before it returns to the ground floor.
During the initial upward acceleration, the student drops a steel ball
from a height of 2m. How long does it take to hit the floor of the
elevator? What is the effective acceleration of the ball?
In terms of General Relativity, what would be equivalent accelerations
out in intergalactic space?
The scale you will be using will read in lbs and kg; what is wrong
here? What reading would the scale give if the student were to
attempt to measure her weight on the moon.
Lab Procedure
You will be issued a bathroom scale, a ball drop timer (similar to the one
used to measure g in lecture) and an elevator
(Well, we will use the elevators in the SERF building). Please be
considerate of those wishing to use the elevators for more pedestrian
purposes, such as getting to their offices. It should be possible
for at least two lab teams to use each elevator simultaneously.
Part 1: Weight and Acceleration
In this part you will use the scale in the elevator to calculate the value
of the acceleration as the elevator ascends and descends.
 Carefully weigh each team member in the SERF Foyer, outside the
elevator, and record your results.
 Enter the elevator and confirm that the scale records the same
"rest" value for the first of your team members.
 With one of your team acting as subject and one acting as recorder,
take the elevator to the 3^{rd} or 4^{th} floor.
Record the reading on the scale as the elevator accelerates upward and
as it decelerates at the chosen floor. (You should have a couple of
seconds when the scale reading is stable. Be certain to wait until
it stabilizes and be certain that the subject is still.)
 Repeat the measurements as the elevator descends to the ground floor.
 Repeat the measurements at least three times for each subject and
use each team member as subject.
Part 2: Acceleration and Gravity
You will use the ball drop apparatus to measure the effective value of the
gravitational acceleration g in the accelerating elevator.
 Set up the ball drop apparatus following the TAs instruction. The
apparatus consists of a pair of contacts, which may be used to hold
the steel ball, mounted about 2m above the elevator floor. The
contacts are connected to a timer, which in turn is connected to a pad
on the elevator floor.
 Place the steel ball between the contacts and hold them closed with
the drop pad directly beneath.
 Press RESET on the timer when the contacts are closed around
the ball.
 When the ball is released, the contacts start the timer which stops
when the ball hits the drop pad (IF the ball hits the drop pad...; try
to be careful not to let the ball drop through the crack at the door.)
 With the elevator stopped, confirm that the ball drop gives the
correct value of g.
 Now perform the experiment during the upward acceleration phase as the
elevator rises; you may want to use the scale to tell you when you
have fairly constant acceleration.
 Perform the experiment at least 3 times  or as many times as
necessary to get a consistent time.
Lab Report (14 pts)
You will, of course, perform the experiment with your lab partners,
and you may jointly calculate the results, but the report should be
your work alone, in your own words. Lab reports that are overly
similar will be penalized and may receive no credit. Reports for Monday
labs are due at the Tuesday lecture 1 week following the date of the
experiment; Wednesday & Thursday reports are due in lecture the following
Thursday.
Include the copy of your homework in your lab report.
Describe the steps that you took to perform the experiment.
(Suggestions for improving the expt are welcome!)
Part 1:
Calculate the acceleration of the elevator in each of the four cases
for each subject.
(Regardless of the units on the scale, perform your calculations
in appropriate metric units.) Estimate your errors and discuss
possible sources of systematic errors.
Does the resulting acceleration depend upon the mass or other
characteristics of the subject?
Part 2:
Use the results of the ball drop to calculate the effective acceleration
of gravity as the elevator ascends.
Compare the results of this calculation with the results of Part 1.
Discuss sources of error that might produce different results.
Is there any way that you can tell from the ball drop experiment
whether the experiment was performed in a pure gravitational field, in an
accelerating elevator, or as was the case here, in an accelerating elevator
in a gravitational field? Discuss this question in terms of Einstein's
Equivalence Principle
Last
modified: Sat., 30 Sept. 2006