# A spring with a constant of #6 (kg)/s^2# is lying on the ground with one end attached to a wall. An object with a mass of #3 kg# and speed of #7 m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?

The compression is

The spring constant is

The kinetic energy of the object is

This kinetic energy will be stored in the spring as potential energy.

So,

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To find the compression of the spring, use the equation for the conservation of mechanical energy:

1/2 * k * x^2 = 1/2 * m * v^2

where: k = spring constant (6 kg/s^2) x = compression of the spring (unknown) m = mass of the object (3 kg) v = velocity of the object (7 m/s)

Rearrange the equation to solve for x:

x = sqrt((m * v^2) / k)

Plug in the given values:

x = sqrt((3 kg * (7 m/s)^2) / 6 kg/s^2) x = sqrt((3 * 49) / 6) x = sqrt(147 / 6) x ≈ sqrt(24.5) x ≈ 4.95 meters

Therefore, the spring will compress by approximately 4.95 meters.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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