Question

A crate of mass 100.0 kg rests on a rough surface inclined at an angle of 37.0° with the horizontal. A massless rope to which a force can be applied parallel to the surface is attached to the crate and leads to the top of the incline. In its present state, the crate is just ready to slip and start to move down the plane. The coefficient of friction is 80% of that for the static case

a.    What is the coefficient of static friction?

b.    What is the maximum force that can be applied upward along the plane on the rope and not move the block?

c.     With a slightly greater applied force, the block will slide up the plane. Once it begins to move, what is its acceleration and what reduced force is necessary to keep it moving upward at constant speed?

d.    If the block is given a slight nudge to get it started down the plane, what will be its acceleration in that direction?

e.    Once the block begins to slide downward, what upward force on the rope is required to keep the block from accelerating downward?

Answer 1

the mass of the block M = 100 kg ,

the angle of the inclined plane is is 37 ^o

a) The coefficient of static friction is

putting the value we get

b) The maximum force that can be applied to move upward is

where g is the accleration due to gravity g = 9.8 m/s2

putting the value we get

c)The force required to move the block upward with constant speed is equal to friction force

the friction is

the coefficient of friction is gievn by

so ,

the friction force is

The accleration in the upward direction is a'

so the force eqn is

putting the value we get

a = 1.20 m/s2

d ) the accleration when it moves downawards is a

so , the force eqn is

so putting the values we get

a = 10.59 m/s2