Chapter 08, Problem 053 In the figure, a 3.3 kg block is accelerated from rest b

Question

Chapter 08, Problem 053

In the figure, a 3.3 kg block is accelerated from rest by a compressed spring of spring constant 650 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 = 0.281. The frictional force stops the block in distance D = 8.0 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?

Explanation / Answer

a) Frictional force on block f= uN = umg = 0.281*3.3*9.8 = 9.08754 N

Work done by friction = f*d = increase in thermal energy = 9.08754*8 = 72.7 J

b) Maximum KE = Energy lost by friction = 72.7J

c) Maximum KE = Potential energy of the spring = 0.5kx2 = 72.7

x = 0.47 m

Which is the original compression in the spring

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