Cycle II Regents Physics

John Dewey High School

Mr. Klimetz

T = 2 x pi x sqrt(L/g)

where T is period (s), pi is a constant (3.14), L is pendulum length (m), and g is local gravitational acceleration (m/sexp2).

By reorganizing the variables in the above equation to isolate g we obtain

g = 4 x piexp2 x L/Texp2

thereby permitting us to determine local gravitational acceleration (g) directly merely by precisely measuring a pendulum's period of swing (T) in seconds and its length (L) in meters from the pivot to the center of mass of the suspended pendulum bob.

(1)

(2)

Brass spherical pendulum bob

Ring stand

Nylon fishing line

Meter stick

Stopwatch

Three-position horizontal cord clamp

C-clamp

1. Place the ring stand so that the upright is close to the edge of the lab table.

2. Securely affix the base of the ring stand to the lab table with the c-clamp.

3. Attach the three-position horizontal cord clamp to the upright of the ring stand,

approximately 3 cm from the top.

4. Thread a 1.3 m length of fishing line through a pendulum and attach by knotting the

protruding end of the line. Remove any excess line with scissors.

5. Firmly attach the pendulum line to the outermost fitting on the three-position horizontal

cord clamp and suspend the bob.

6. Set the pendulum to the lengths instructed.

7. Move the pendulum bob approximately 20 cm from the equilibrium (rest) position and let

swing. Be sure not to push the bob in any way. It must start it's trip from rest. Using the

stopwatch, determine the time for the pendulum to complete 20 full swing cycles. Record your

data into the data table. Repeat this step twice more.

8. Calculate the average of the three 20-swing measurement cycles and enter into the data

table. Remember to show all work.

9. Calculate the time of a single period of swing by dividing the answer obtained from Step 8 by

20. Enter this into the data table. Remember to show all work.

10. Repeat Steps 6 through 9 for the remaining pendulum lengths.

11. Substitute your data into Equation (2) and solve for g.

12. Perform a percent error analysis of your best results. Show all work

0.25

0.25

0.25

0.50

0.50

0.50

0.75

0.75

0.75

1.00

1.00

1.00

______

______

______

______

______

______

______

______

______

______

______

0.25

0.50

0.75

1.00

______

______

______

______

1. Discuss any possible sources and causes of error in your experiment. How might air resistance have affected your apparatus? Would air resistance have changed the period of swing? If so, how would it have affected your value of g?

2. Suppose our pendulum apparatus was dropped down an airless elevator shaft while it was in the middle of swinging. Do you think it would continue swinging while freely falling? Why or why not? (Think!)

3. Explain why the mass of the pendulum has no influence on period of swing. Would a pendulum of a given length on Earth have the same period as one on the Moon? (The Moon possesses 1/6 the mass of Earth.) Explain.

4. At which position(s) in its path is the pendulum moving at the fastest speed? Why does it keep moving when it reaches the bottom of its swing path? At which position(s) in its path is the pendulum moving at the slowest speed? Where in the pendulum does the greatest acceleration occur?

5. Describe a practical use of a pendulum.