Physics
posted by Drew .
A 2.5kg block is sliding along a rough horizontal surface and collides with a horizontal spring whose spring constant is 320 N/m. Unstretched, the spring is 20.0 cm long. The block causes the spring to compress to a length of 12.5 cm as the block temporarily comes to rest. The coefficient of kinetic friction between the block and the horizontal surface is 0.25. a) How much work is done by the spring as it brings the block to rest? b) How much work is done on the block by friction as the block is in contact with the spring? c) What was the speed of the block when it first came into contact with the spring?

mass, m = 2.5 kg
spring constant, k = 320 N/m
compression of spring, Δx = 0.075 m
Coefficient of kinetic friction, μ_{k} = 0.25
acceleration due to gravity, g = 9.8 m/s²
Let
initial velocity of block, u =u m/s
final velocity of block, v = 0 m/s
Work done by block, W
= loss of KE
= (1/2)mu²
Work done by friction, Wf
= μ_{k}mgΔx
Work done by spring, Ws
= (1/2)kΔx²
Equate total work:
W=Wf+Ws
(1/2)2.5u²=0.25*2.5*9.8*0.075+(1/2)*320*0.075²
Solve for u=3.157 m/s
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