1. The maximum speed of a 3.7 kg mass attached to a spring is 0.66 m/s. The ampl

Question

1. The maximum speed of a 3.7 kg mass attached to a spring is 0.66 m/s. The
amplitude of motion of the spring is 0.15m. Find the spring constant (k) for this
spring.

2. A simple pendulum of length 2.5 m makes 20 complete swings in 64 s. This
pendulum oscillates near the surface of a planet with radius equal to Earth’s radius.
Is the mass of this planet equal to, greater than, or less than the mass of earth?
Explain your answer.

3. A satellite orbits Earth in a geosynchronous orbit (always stays above the same point on the equator), above the equator. What is the tangential speed of the satellite?

4. A long thin rod of length L = 0.500m and mass M = 500g is used to make a
physical pendulum. How far from the Center of Mass should the pivot be to produce
a period of 1.50s?

5. The distance from the center of the Mars to the center of the Sun is 2.279x10
8km. Given that the mass of the Mars is 6.45x10^23 kg and the mass of the Sun is
2.00x10^30 kg. Assuming that Mars follows a circular orbit and using your answer from
part (a), find the orbital period of the Mars in years.

Explanation / Answer

Mass (m) of the object = 3.7 kg Amplitude (A) of motion of the spring = 0.15 m Speed (v) of the object = 0.66 m/s Then according to the law of conservation of energy,             (1/2)kA2 = (1/2)mv2                       k = (m)(v2 / A2)                          = (3.7 kg)(0.66 m/s)2 / (0.15 m)2                          = 71.6 N/m Hence, spring constant (k) of the spring = 71.6 N/m According to CRAMSTER rules, one question should be done per each post. So please post the remained questions as separate.

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