A block whose mass is 8.00 kg has an unknown initial velocity. It is moving to t

Question

A block whose mass is 8.00 kg has an unknown initial velocity. It is moving to the right and is initially on a frictionless surface. It then runs into a rough patch 2.50 m in length, with coefficients of friction 0.325 for both kinetic and static. At the end of the rough patch, the block is again on a frictionless surface and is stopped by a spring with a spring constant equal to k = 75.0 N/m. It is observed that the spring compresses a distance of 55.0 cm. Calculate the following:

a) Initial velocity of the block

b) Work done by friction in slowing down the block

C) The velocity of the block when it has left the rough patch and has yet to reach the spring.

Explanation / Answer

We need to do work from last to first

Work done by spring force = change in KE

0.5*k*x^2 = 0.5*m*v^2

0.5*75*0.55^2 = 0.5*8*v^2

v = 1.68 m/sec

Work done frictional force = change in KE

-mu_*m*g*S = o.5*m*(v^2-u^2)

-0.325*8*9.8*2.5 = 0.5*8*(1.68^2-u^2)

initial velocity is u = 4.32 m/sec

So the answers are

A) u = 4.32 m/sec

B) Work done by friction = -mu_*m*g*S = -0.325*8*9.8*2.5 = -63.7 J

C) v = 1.68 m/sec

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