A 5kg box moving at 7m/s on a horizontal, frictionless surface runs into a light

Question

A 5kg box moving at 7m/s on a horizontal, frictionless surface runs into a light spring of force constant 80N/cm. use the work-energy thoerem to find the maximum compression of the spring. A 5kg box moving at 7m/s on a horizontal, frictionless surface runs into a light spring of force constant 80N/cm. use the work-energy thoerem to find the maximum compression of the spring. A 5kg box moving at 7m/s on a horizontal, frictionless surface runs into a light spring of force constant 80N/cm. use the work-energy thoerem to find the maximum compression of the spring.

Explanation / Answer

Initially the velocity of the box Vi = 7 m/s. Hence the initial kinetic energy of the box, KEi = (1/2)mVi2 = (0.5)x5x72 = 122.5 J.

The point where the compression of the spring is maximum the velocity of the box must be zero. Hence the final kinectic energy of the box, KEf = (1/2)mVf2 = 0.

Since there is only spring force that works upon the box during this motion. Hence work done by spring must be equal to change in kinetic energy of the box.

i.e. KEf - KEi = (1/2)k(xi2 -  xf2 )

or 122.5 = (0.5)(80*100)*x2

=> x = 17.5 cm

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