Measure Gravity at Home

1. Materials Needed: A stopwatch app on your phone (or a watch with a second hand), a piece of string, two kind of heavy things (like a coffee mug) to tie to the string, someplace secure to tie the top of the string.

2. Goal: We are going to measure the quantity "g", the acceleration due to the force field of gravity, in your home.

3. Mathematical Background: A pendulum of length L will swing back and forth one time with period T. From these two numbers, we can calculate g like this: g = 4 ² L / T²

4. The FIRST model we will test is that the equation g = 4 ² L / T² gives you a number that agrees with what other people measure on earth.

5. Here are detailed steps on how to make and observation for this FIRST model:

Tie something heavy (coffee cup) on a string (or ribbon or thread or thin wire).

Fasten the other end of the string on something solid: a door frame. take a picture of your setup!

Measure L, the length of your entire pendulum, from the pivot at the top to the CENTER of the heavy thing, in meters. (If you measure it in inches, write down the measurement in inches, and then convert that to meters using wolframalpha.com. If you measured 12 inches, type this in the search bar: "12 inches in meters" and keep track of the length in meters. Or, you can show off how internationally adept you are and measure it directly in meters!

MEASURED length L = __________ inches = _______________ meters

Watch it swing back and forth. You want to measure the PERIOD -- the time for it to go back and forth one time. A nice way to be more accurate is to measure how long it takes to go back and forth 10 times, and then divide that total time by ten, to get the period.

I do this by starting it swinging, and make sure it is going without hitting anything. (Or

The cat hitting it.) Then as it goes "left, right, left, right, left, right..." I count "zero, right,

one, right, two, right, ...nine, right ten) Start the stopwatch when you say "zero" and

stop it when you say "ten". Divide the total time by ten and enter the period here

This will be your OBSERVED period T = __________________

The acceleration due to gravity (g) is given by: g = 4 ² L / T² Notice that the units of this will be an acceleration, in meters per second squared. The 4 ² is necessary to get the physics to work out. If you really want to know, I can show you that derivation. Or, you can trust me. Your choice.

Write down your OBSERVED value of g = _________________

Let's use 9.8 meters/sec² as the ACCEPTED value of g, since that is the generally accepted value for g on the surface of the earth. Calculate the PERCENT DIFFERENCE and put it here:

Percent difference = 100(OBSERVED-ACCEPTED)/(ACCEPTED) = _______________

6. Conclusion for this FIRST observation. This should get you a value of g that is with 10 or 20 percent of the accepted answer.

SECOND MODEL and OBSERVATION: notice that nowhere did we think about the mass of the pendulum. So, repeat the measurement with a larger mass. I usually tie a second coffee cup to the string. MAKE SURE YOU DO NOT CHANGE THE LENGTH! Make the measurement and a conclusion for the SECOND experiment.

7. THIRD experiment: change L to be a lot longer (or shorter) and see if you get the same value of g.

8. Discussion: a brief discussion of what you learned in this lab.