1.A spring 1.50 m long with force constant 427 N/m is hung from the ceiling of a

Question

1.A spring 1.50 m long with force constant 427 N/m is hung from the ceiling of an elevator, and a block of mass 11.7 kg is attached to the bottom of the spring.

a)By how much is the spring stretched when the block is slowly lowered to its equilibrium point?

b)If the elevator subsequently accelerates upward at 1.97 m/s2, what is the position of the block, taking the equilibrium position found in part (a) as y = 0 and upwards as the positive y-direction.

c) If the elevator cable snaps during the acceleration, describe the subsequent motion of the block relative to the freely falling elevator. What is the amplitude of its motion?

2.A 2.16-kg object on a frictionless horizontal track is attached to the end of a horizontal spring whose force constant is 5.00 N/m. The object is displaced 3.58 m to the right from its equilibrium position and then released, initiating simple harmonic motion.

  (a) What is the force (magnitude and direction) acting on the object 3.50 s after it is released?

(b) How many times does the object oscillate in 3.50 s? (Do not round your answer to an integer.)

3.A pendulum clock that works perfectly on Earth is taken to the Moon. Assume that the free-fall acceleration on the Moon is 1.63 m/s2.

(a) Does it run fast or slow there?

fast, slow or Neither, it runs the same as on Earth.

(b) If the clock is started at 12:00 midnight, what will it read after 18.9 h? (Enter the time to the nearest minute.)

_____ AM

4.A "seconds" pendulum is one that goes through its equilibrium position once each second. (The period of the pendulum is 2.000 s.) The length of a seconds pendulum is 0.9927 m at Tokyo and 0.9942 m at Cambridge, England. What is the ratio of the free-fall accelerations at these two locations?

(Cambridge/Tokyo) = 1 +

Explanation / Answer

a)

for slowly lowerimng the mass

F = mg = k*x

x = 11.7 * 9.8/427

x = 0.269 m

the change in length is 0.269 m

b)

for elevator accelerating upwards

y = - 11.7 * 1.97/427

y = -0.054 m

c)

if the cable snaps , the mass will move upwards relative to elecvator ,

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