Some astronauts are performing an experiment in deep outer space, far away from

Question

Some astronauts are performing an experiment in deep outer space, far away from the gravitational pull of the sun or any planets. There is a   3.22 kg   ball attached to an approximately massless spring. Initially, the spaceship is accelerating, with a constant acceleration of   4.65 m/s2   . During this time, the spring is stretched, but the ball is not oscillating. The spring has a sping constant   223 N/m   .

Suddenly, when the vehicle's speed has reached 45.0 m/s, its engines turn off, thus eliminating its acceleration but not its velocity.

Part A

During the time that the spaceship is accelerating, how much is the spring stretched by? (I want the magnitude of the distance stretched by- the sign depends on how you set up your coordinate system.)

Part B

Immediately after the ship stops accelerating, what the speed of the ball with respect to the spaceship?

Part C

After the spaceship stops accelerating, the ball starts oscillating (with respect to the spaceship). Find the amplitude.

Part D

Find the frequency of the resulting oscillations of the ball.

Part E

What will be the ball's maximum speed relative to the vehicle?

This is my last part of my assignment and I have been staring at it trying to figure it out. Help!

Explanation / Answer

To find the amplitude b

ma = k*x; where a - acceleration, k - force constant of the spring, x - shift from the initial length of the spring.

b = x = ma/k = 3.22 * 4.65 / 223 = 0.06714 m..............Ans. of Part A & C.

Frequency of the oscillations f = sqrt(k/m)/ (2 pi) = sqrt(223/3.22) / 6.28 = 1.325 Hz..................Ans. of Part D

One data is missing to solve the velocity

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