# A spring with a constant of #3 (kg)/s^2# is lying on the ground with one end attached to a wall. An object with a mass of #2 kg# and speed of #9 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, we can use the principle of conservation of mechanical energy. The initial kinetic energy of the object is equal to the potential energy stored in the compressed spring.

The initial kinetic energy of the object is given by: (KE_{initial} = \frac{1}{2}mv^2) (KE_{initial} = \frac{1}{2}(2 , kg)(9 , m/s)^2) (KE_{initial} = 81 , J)

The potential energy stored in the spring is given by: (PE_{spring} = \frac{1}{2}kx^2) Where (k) is the spring constant and (x) is the compression distance.

Setting the initial kinetic energy equal to the potential energy stored in the spring: (KE_{initial} = PE_{spring}) (81 , J = \frac{1}{2}(3 , kg/s^2)x^2)

Solving for (x): (x^2 = \frac{2 \times 81}{3}) (x^2 = 54) (x \approx 7.35 , m)

Therefore, the spring will compress approximately (7.35 , m).

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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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