Figure shows, a `3.5 kg` block accelerated by a compressed spring whose spring constant is `740 N//m`. After, leaving the spring at the spring' s relaxed length, the block travels over a horizontal surfce, with a coefficient of kinetic friction of `0.25`, for a distance of `7.8 m` before stopping. `(g =9.8 m//s^(2))`.
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(a) What is the increase in the thermal energy of the block-floor system ?
(b) What is the maximum kinetic energy of the block ?
(c) Through that distance is the spring compressed before the block begins to move ?

Answer

A, B, C, D

Explanation

(a) Thermal energy =Work done against friction
`=mu_(k) mgd`
`=(0.25)(3.5)(9.8)(7.8) J`
`=66.88 J`
(b) Maximum kinetic energy
`=`work done against fricion
`=66.88 J`
(c) `1/2 kx_(m)^(2) =`maximum kinetic energy
`1/2 xx 640 xx x_(m)^(2) =66.88 cm`
`x_(m) = 0.457 m = 45.7 cm`