You want to design a pendulum for a grandfather clock so that it has a period of

Question

You want to design a pendulum for a grandfather clock so that it has a period of 2.00 seconds (one "tick" plus one "tock" occur during one complete period). The pendulum has a heavy 4.50-kg bob. (Throughout this problem, assume that the pendulum's arm has negligible mass, that the bob can be approximated as a "point mass," and that the initial angle of displacement is small.)

a. If you use the clock on surface of the Earth near sea level (g=9.80 m/s^2), what length should you use for pendulum arm?

b. If the finished pendulum clock in part (a) is moved to the top of a (ficitiously) high mountain where g=9.70 m/s^2, the pendulum's period will...

1. lengthen (causing the clock to "run slow")

2. shorten (causing the clock to "run fast")

3. remain unchanged (so that clock continues to keep continue to keep good time)

c. The clock is returned to sea level. Suppose that a mischievous child attaches a wad Play-Doh (clay) to the bob, thereby increasing bob's mass by 2.00%. The pendulum's period will...

1. increase by < 2.00%

2. increase by 2.00%

3. increase by > 2.00%

4. shorten by < 2.00%

5. shorten by 2.00%

6. shorten by >2.00%

7 remain unchanged

d. The clock is at sea level, and the bob is returned to its original mass. Suppose that the clock's temperature gets much warmer, and the length of the pendulum's arm grows by 2.00%. The pendulum's period will...

1. increase by < 2.00%

2. increase by 2.00%

3. increase by > 2.00%

4. shorten by < 2.00%

5. shorten by 2.00%

6. shorten by >2.00%

7 remain unchanged

e. Suppose that the swinging pendulum in part (a) experiences some small air resistance that causes the angular size of the pendulum's swings to slowly dimish over time. The pendulum's period will...

1. lengthen (causing the cloak to "run slow")

2. shorten (causing the clock to "run fast")

c. remained unchanged (so that the clock continues to keep good time)

Explanation / Answer

a) Pendulum period in seconds
T ? 2??(L/G)
L is length of pendulum in meters
G is gravitational acceleration = 9.8 m/s

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