# University of California, San Diego Physics 11 - Survey of Physics

 H. E. Smith Fall 2004

 Physics 11 - Lab 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.

### 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 (similar to Problem 4-35 in Serway & Jewett): 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 free-body diagram of: (a) the student, (b) the scales, (c) the elevator
• What is the acceleration in each case? (Remember, acceleration is a vector.) Express your answer both in m/s2 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.

1. Carefully weigh each team member in the SERF Foyer, outside the elevator, and record your results.
2. Enter the elevator and confirm that the scale records the same "rest" value for the first of your team members.
3. With one of your team acting as subject and one acting as recorder, take the elevator to the 3rd or 4th 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.)
4. Repeat the measurements as the elevator descends to the ground floor.
5. 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.

1. 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.)
2. With the elevator stopped, confirm that the ball drop gives the correct value of g.
3. 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.
4. 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

Gene Smith