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?

Answer 1

The compression is #=4.95m#

The spring constant is #k=6kgs^-2#

The kinetic energy of the object is

#KE=1/2m u^2#

#KE=1/2*3*(7)^2=73.5J#

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

#PE=73.5J#

So,

#1/2kx^2=73.5#

#x^2=73.5*2/(6)=24.5m^2#

#x=sqrt(24.5)=4.95m#

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Answer 2

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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Answer from HIX Tutor

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.

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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