Answer to Question #218130 in Classical Mechanics for Help

Question

Use 9.81m/s² for gravity if needed!

1) The magnitude of the restoring force that acts on a 1.0-kg pendulum when it is displaced 2.0° from equilibrium is ___ N. 

2) The magnitude of the restoring force that acts on a 1.0-kg pendulum when it is displaced 10.0° from equilibrium is ___ N. 

3)  On earth the period of a 1.50-m pendulum is ___s.

4) On the hypothetical planet Xeon, a pendulum with a length of 95.0 cm swings with a frequency of 1.50 Hz. The acceleration due to gravity on Xeon is ___ m/s².

5) A pendulum is swinging back and forth:

Which of the following factors affect the period of the pendulum:

I. length

II. mass

III. angle of release

IV. accleration due to gravity

A- I only

B- I and II

C- III and IV

D- I and IV

Answer 1

1)

$$F=(1)(9.8)\sin{2}=0.34\ N$$

2)

$$F=(1)(9.8)\sin{10}=1.7\ N$$

3)

$$T=2\pi\sqrt{\frac{1.5}{9.8}}=6.04\ s$$

4)

$$\frac{1}{1.5}=2\pi\sqrt{\frac{0.95}{g}}\\g=84.4\frac{m}{s^2}$$

5) D- I and IV