Answer to Question #152740 in Classical Mechanics for GuardianVex

Question

A body of mass ‘m’ is placed on a rough inclined plane having coefficient of friction
µs. The inclination of plane is given as ‘θ’.
a) Which component of weight brings the body towards the bottom along the plane.
b) Find how much force is required to pull the body along the plane.

Answer 1

Solution,

Given

a) m = mass of body

$\mu$_s = coefficient of friction

Let F be the minimum force required to pull body along the plane. Diagram can be shown as below

Friction acts against the motion, Since body is moving up and friction acts down.

From the diagram,

$N = mg cos \theta$

And

$mg sin \theta$ component of weight brings the body towards the bottom along the plane.

b) F=mgsinθ+f

$F = mg sin\theta + \mu_s mg cos\theta$

Hence force required for pull body is

$F = mg(sin \theta+ \mu_s cos \theta)$