# A spring with a constant of #2 (kg)/s^2# is lying on the ground with one end attached to a wall. An object with a mass of #8 kg# and speed of #1 m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?

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To find the compression of the spring, you can use the equation for the potential energy stored in a spring, which is given by ( PE = \frac{1}{2}kx^2 ), where ( k ) is the spring constant and ( x ) is the compression of the spring. Rearrange the equation to solve for ( x ):

( PE = \frac{1}{2}kx^2 )

( PE = \frac{1}{2}(2)(x^2) )

( PE = x^2 )

Given that the object's initial kinetic energy is converted entirely into potential energy stored in the spring:

( KE_{initial} = PE_{final} )

( \frac{1}{2}mv^2 = x^2 )

Substitute the values:

( \frac{1}{2}(8)(1^2) = x^2 )

( 4 = x^2 )

( x = \sqrt{4} )

( x = 2 ) meters.

So, the spring will compress by 2 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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