Your challenge for this laboratory period will be to design and execute two experiments that will demonstrate that the acceleration due to gravity is a constant and to determine that constant. You will be expected to pay particular attention to the problems of accuracy and precision. The following information is presented to give you some guidance, on possible alternatives, but part of your grade will be based on your experimental design.

The acceleration due to gravity, g, can be determined experimentally using a simple pendulum. The pendulum consists of a small massive bob suspended by a string of length l. When the amplitude of oscillation is sufficiently small (q _ 10º), the period of oscillation, T, is given by T = 2p

The period T is the time required for one complete oscillation. By measuring the time t required for N oscillation, one can calculate the period. T 

The period T is the time required for one complete oscillation. By measuring the time t required for N oscillation, one can calculate the period.   T = t/N  Therefore you can find the period a couple of different ways, depending on how you wish to do it. You can use a hand timer to measure several oscillations & then divide the time by the number of oscillations (remember to starting counting at 0 not 1 if you use this method). Or you can set up the photoelectric gates to time the period of one oscillation.  If you use this method, make sure the secondary gate is unplugged from the primary. Put the primary on "pendulum". Adjust the sensor & pendulum so that the pendulum bob, not the string will pass through the photoelectric eye area. Bring the pendulum bob to an angle . Release the bob. Allow the bob to swing over & back twice. The timer will turn on as the bob swings through it the first time. It will ignore the swing on the way back, & turn off when the bob goes back through. Therefore it does not matter where in the swing the sensor is placed. Reset the primary & repeat as many times as you feel necessary to get a reliable average.

You might vary the length l of the simple pendulum ten times. Record l and the corresponding value of T.

A. Plot a graph of T2 vs l using your data set, and calculate the slope of

the graph. From the slope, calculate g.

B. Calculate the average value of g, denoted by using your individual

computed values of g. 

How does compare with the value of g calculated from part A? (% difference) Account for this difference. Why should g from part A be more accurate than from part B? What is the std deviation of the g's calculated? Would changing the weight on the bottom of the pendulum make any difference? Why or why not?

Now consider an air track that is slightly elevated at one end. Measure the height difference h between two points on the air track, along with the corresponding horizontal distance d between these two points.

The angle of elevation q is then given by q = tan-1 ().

You might let the cart accelerate from rest through a distance s (between the photo gates) down the air track. Using the fact that the acceleration is given by a = g sin q, one can measure s and the corresponding time t taken to move through the distance s. By using one-dimensional kinematics, with v0 = 0,


From this equation one can determine g. g = 

Compare all the g's. (% difference & % error's)

Points to be woven into your conclusion section narrative:

What is gravity?

What does gravity have to do with a pendulum? elevated air track?

What is the theoretical value of g?

Is this value the same the world over?

Would you expect the value of g in Gary, IN to be higer or lower than that?

Did your g vary in the direction you would have predicted?

Last Updated: 4 Aug 2000
Comments: Laboratory Supervisor
Copyright 1999, The Trustees of Indiana University