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/s^{2})(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)
kx^{2}

x = √2KE/k = 0.535 m

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