A block is at rest on a rough inclined plane and is connected to an object with

Question

A block is at rest on a rough inclined plane and is connected to an object with the same mass as shown. The rope may be considered massless; and the pulley may be considered frictionless.

1. What is the magnitude of the static friction force acting on the block?

A: mg (1-sin theta)

2. IF the rope were cut between the block and pulley, what would be the magnitude of the acceleration of the block down the plane?

A: g (sin theta- coefficient of kinetic friction x cos theta)

3. If the mass of the suspended object is doubled, what will be the acceleration of the block up on the plane?

A: g ((2- sin theta)- (coefficient of kinetic friction x cos theta))

Could you walk me through how these answers are derived? Thank you so much!

Explanation / Answer

T=mg T=mg sin theta+f so f=T-mg sin theta 1.static friction=mg-mg sin theta=mg(1-sin theta) 2.if rope is cut F=mg sin theta-f f=u*mg cos theta [N=mg costheta] so F=mg sin theta-u*mg cos theta so F/m=a=g (sin theta- coefficient of kinetic friction x cos theta) 3.2mg-T=2ma T-mg sin theta-umgcos theta=-ma so adding 2mg-mg sin theta-umgcos theta=ma so a= g ((2- sin theta)- u x cos theta))

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