Question

a particle of weight W rest on a rough horizontal plane. If the angle of friction be a, prove that the least force which will just make it move along the plane is P= Wsina

Answer 1

Answer:

Refer to the attachment for diagram !

We know that Friction acts opposite to the force given.

For the body to move the angle must be equal to Angle of repose.

So, Assuming the body to be at angle of repose, the force required according to the FBD is:

F = mg Sin∅

This is the required minimum force.

Hope it helped :)

We know that mg is the weight of the body.

Hence we can write it as :

F = W.sin∅

Answer 2

Solutions :-

Given :
Weight W rest on a rough horizontal plane.
Angle of friction = theta

We know that,
F = mg
mg = W

Angle of friction = Angle of repose

Since,
When a body is kept on an inclined plane inclined at an angle equal to angle of repose then it will be ready to move.

Therefore,

F = mg × sin theta
F = W sin theta

Hence,
W sin theta is the required answer.