In the figure, a 3.9 kg block is accelerated from rest by a compressed spring of

Question

In the figure, a 3.9 kg block is accelerated from rest by a compressed spring of spring constant 630 N/m. The block leaves the spring at the spring's relaxed length and then travels over a horizontal floor with a coefficient of kinetic friction k = 0.231. The frictional force stops the block in distance D = 7.4 m. What are (a) the increase in the thermal energy of the block-floor system, (b) the maximum kinetic energy of the block, and (c) the original compression distance of the spring? 0000400600 No friction (HR (a) Number (b) Number (c) Number Units Units Units

Explanation / Answer

given,

mass of block, m = 3.9 kg

spring constnt, k = 630 N/m

coefficient of kinetic friction, k = 0.231

(a) thermal energy comes from the work done by the friction, Wf = - Ff d = -k mg d

= -0.231 x 3.9 x 9.8 x 7.4 = - 65.33 J

b) frictional force stopped the block

change in kinetic energy, KE = KEf - KEi = 0 -KEi

                                         Wf = - KEi

                                      - 65.33 J = - KEi

maximum kinetic enegy of block KE = 65.33 J

c) this kinetic energy stored as potential enegy in the spring, KE = (1/2) kx2

        x = 2KE/k = 0.455 m

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