Lab Activity: Use of Pendulum to Find g and Mass of Earth

            Purpose:  In this activity, you will determine the acceleration of gravity and the mass of the Earth using a simple pendulum. 

            Background:  A pendulum is a simple device that exhibits periodic motion when the bob is lifted and given potential energy.  Gravity does work on the bob and transforms the potential energy into kinetic energy.  As potential energy and kinetic energy take turns transforming into each other, the resulting motion is of a periodic nature.  The period of a pendulum, which refers to the time it takes to swing back and forth once (a full swing), is related to the length of the pendulum and the acceleration of gravity (this assumes a ‘small angle’):

                                          Period = T = 2p(L / g)^{1/ 2}

(Why do you suppose the factor of 2p comes up? We will eventually derive this.)

            Materials:       

Stop watch or video (phone, camera)

endulum

Meter stick                  Your brain

            Procedure:

            You and your lab partners need to determine an accurate way of determining the acceleration of gravity, from which you will also calculate a value of the mass of the Earth!  You will need to do this using a pendulum, which you know something about because of your last experiment in determining a pendulum’s properties.  Decide what the best measurements and methods are, as well as how to minimize any potential errors.  Then, write down your step-by-step procedure, and clearly and neatly present your data.

            Analysis (answer in complete sentences):

1.      Based on your measurements, determine the acceleration of gravity, g.  Show your calculation.

2.      Using your result in (1), calculate the percent error relative to the accepted g = 9.81 m/s².  Recall that %-error = {[your value – accepted value] / [accepted value]} x 100.

3.      Explain, in your own words, why the period of a pendulum is independent of the mass of the bob.

4.      What should the period of your pendulum be if you performed this experiment on the moon (gravity is about 1/6 that of the Earth)?  What about on Jupiter (gravity is about 20 times that on Earth)?  Is this a direct or inverse relationship between T and g?

5.      What are the main sources of error in this particular activity?  How did your group try to minimize those errors? 

6.   Explain what a Foucault pendulum is used for.  You may need to look this one up.

7.   How long would you need to make a pendulum in order for it to have a period of 1.0  

     second?  Show your calculation.

8.  From your value of g, determine the mass of the earth!  Show your calculation.  Other

     useful information may include the radius of the earth and G. 

G = 6.67 x 10^-11 Nm²/kg² and R_E = 6.4 x 10⁶ m.

*Note that by knowing the size (radius) of other moons and planets, you could take a pendulum, measure the period, and determine their masses, too.  Sensitive measurements of a pendulum’s period anywhere on earth also allows us to determine small difference in g, which tells us something about how the radius changes as well as densities of the earth at those locations.