A block of mass m = 6.0 kg starts from rest at the top of a frictionless, icey c

Question

A block of mass m = 6.0 kg starts from rest at the top of a frictionless, icey circular half pipe of radius R = 2.0 m. When let go, it slides down to the bottom of the slope and continues horizontally, until it encounters a rough patch of ice & gravel of length 1.0 m, with a coefficient of kinetic friction between the block and the patch equal to 0.30. It then continues on frictionless ice until it reaches a spring attached to a wall, of spring constant k = 110 N/m. As the block compresses the spring, it slowly comes to a rest.

How much does the block compress the spring?

Explanation / Answer

Initial height, h = R = 2 m

Let x is the compresson of the spring.

Apply, Workdone by friction = change in mechaincal energy

Friction*d*cos(180) = 0.5*k*x^2 - m*g*h

mue_k*N*d*(-1) = 0.5*110*x^2 - 6*9.8*2

-0.3*6*9.8*1 = 0.5*110*x^2 - 117.6

0.5*100*x^2 = 117.6 - 0.3*6*9.8

x^2 = 2*99.96/100

x = sqrt(2*99.96/100)

= 1.414 m <<<<---------Answer

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