# A spring with a constant of #5 (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 #12 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

The mass is

The speed 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, you can use the conservation of mechanical energy. The initial kinetic energy of the object is equal to the potential energy stored in the compressed spring.

- Calculate the initial kinetic energy of the object.
- Use the spring constant and the formula for potential energy stored in a spring to find the compression.

Initial kinetic energy = 0.5 * mass * velocity^2 Potential energy stored in the spring = 0.5 * spring constant * compression^2

Set the initial kinetic energy equal to the potential energy stored in the spring and solve for compression.

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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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