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# A 6.0-kg bowling ball is held 10 mm above a mattress and then released from rest and allowed to fall, sinking into the mattress. Model the mattress as a single spring with spring constant k = 500 N/m. (a) Calculate the ball’s kinetic energy, the gravitational potential energy of the system (ball, spring, and Earth), and the elastic potential energy at the following compression's: 0, 0.050 m, 0.10 m, 0.15 m, 0.20 m. (b) What is the maximum compression of the mattress? Ignore the inertia of the spring.

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Requirements

In this problem, we observe what happens when a bowling ball falls on a mattress, i.e. on one spring. The mass of the bowling ball is:

$m=6\text{ kg}$

The height at which it is above the mattress (spring) is equal to:

$h=10\text{ mm}=0.01\text{ m}$

Initially, the bowling ball is at rest, so its speed is then equal to:

$v_i=0\mathrm{~}\frac{\text{m}}{\text{s}}$

The spring constant is:

$k=500\mathrm{~}\frac{\text{N}}{\text{m}}$

We need to:

$(a)$ determine the kinetic energy of a bowling ball, the gravitational potential energy of a system consisting of a bowling ball, a spring and the Earth, and the elastic potential energy when the spring is compressed by: $0$, $0.050 \text{ m}$, $0.10 \text{ m}$, $0.15\text{ m}$, $0.20 \text{ m}$;

$(b)$ determine how much the spring can be compressed the most.

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