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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 #9 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

Isabella Alvarez

The spring compresses by #=8.57m#

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

The kinetic energy of the object is

#KE=1/2m u^2#

#KE=1/2*9*(7)^2=220.5J#

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

#PE=220.5J#

So,

#1/2kx^2=220.5#

#x^2=220.5*2/6=73.5m^2#

#x=sqrt(73.5)=8.57m#

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Answer 2

Charles Aeschliman

Use the formula: ( \Delta x = \frac{mv}{k} ) Plug in values: ( \Delta x = \frac{(9 \ kg)(7 \ m/s)}{6 \ (kg)/s^2} ) Calculate: ( \Delta x = 10.5 \ m ) The spring will compress by 10.5 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.