Question

A block of mass 2m is intially at rest on a rough inclined plane where ? < 30 and is connected to an object with mass m as shown. the rope may be considerd massless, and the pulley may be considerd frictionless . the cofficient of static friction between the block and the plabe is u_s and the cofficient of kinetic friction between the block and the plane is u_k.

1. What is the magnitude of the static frictional force acting on the block resting on the slope?

A) mgsin ? B) u_smgcos ? C) mg( 1 - u_s sin ? ) D) mg(1- u_s cos ? ) E) mg(1- 2sin ? )

2. What is the magnitude of the tension in the rope jpining the masses ?

A) mgsin ?   B) u_smgcos ?   C) mg( 1 - sin ? ) D) mg(1- u_s cos ? ) E) mg

3. If the rope were cut between theblock and the pulley , and the block on the inclined plane began to slide down, what would be the magnitude of the acceleration of this block down the plane?

A) g B) g( sin ? - u_ksin ? )   C) g - 2 u_kcos ? D) 2g (tan ? - u_k ) E) 2g (sin ? - u_kcos ?)

Answer 1

1)

equation of motion for mass "m" is,

tension T=m*g

equation of motion for mass "2m" is,

fs=T-2*mg*sin(theta)

fs=T-2*mg*sin(theta)

fs=T-2*mg*sin(theta)

fs=m*g*(1-2*sin(theta)) ------> option (E) is correct

2)

magnitude of the tension in the rope is, T=m*g ---->

option (E) is correct

3)

2m*a=2m*g*sin(theta)-uk*N

2m*a=2m*g*sin(theta)-uk*(2*mg*cos(theta))

a=g*(sin(theta)-uk*cos(theta))

acceleration is a=g*(sin(theta)-uk*cos(theta)) ---->