Question

# In the figure, a 4.3 kg block is accelerated from rest by a compressed spring of...

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 μk = 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?

#### Homework Answers

Answer #1

given,

mass of block m = 4.3 kg

spring constnt, k = 620 N/m

coeffiecient of kinetic friction μk = 0.284

(a)

the thermal energy comes from the work done by the friction

Wf = Ff .d = -Ff .d = -μk 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 = KEf - KEi = 0 - KEi

Wf = - KEi

- 88.65 J = - KEi

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

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