A 3.00 kg box is attached to a spring which as a spring constant of 5.00 N/m. Th

Question

A 3.00 kg box is attached to a spring which as a spring constant of 5.00 N/m. The box is on a floor which is not frictionless (the coefficient of kinetic friction between the box and the floor is 0.75). The box is at rest when it is kicked so that it instantly reaches a speed of 4.00 ms; as it moves it stretches the spring. How much does the thermal energy of the box-floor-spring-Earth system change between the time the box begins to move and when it first returns to its original location momentarily comes to rest? A. 137 J B. 21.6 J C. 39.1 J D. 68.3 J E. 43.2 J

Explanation / Answer

Apply conservation of energy

1/ mv^2 - uk mg x = 1/2 k x^2

1/2 * 3 ( 4)^2 - 0.75 ( 3.0)(9.8 x) = 1/2 * 5 x^2

2.5 x^2 +22.05 x-24 = 0

solving quadratic eqution

x= 0.9796 m

formula for thermal energy

wf =f x

= uk mg x

=0.75 ( 3) (9.8) 0.9796)

=21.6 J

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