Question

In the figure, a 4.3 kg block is accelerated from rest by a compressed spring of spring constant 620 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 μ_k = 0.284. 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?

Answer 1

given,

mass of block m = 4.3 kg

spring constnt, k = 620 N/m

coeffiecient of kinetic friction μ_k = 0.284

(a)

the thermal energy comes from the work done by the friction

       W_f = F_f .d = -F_f .d = -μ_k mg d = -( 0.284) (4.3 kg) ( 9.8 m/s²)(7.4 m) = - 88.65 J

b) this frictional force stopped the block

change in kinetic energy, ΔKE = KE_f - KE_i = 0 - KE_i

                                         W_f = - KE_i

- 88.65 J = - KE_i

maximum kinetic enegy of block KE = 88.65 J

c) this kinetic energy stored as potential enegy in the spring

       KE = ( 1/2) kx²

        x = √2KE/k = 0.535 m