Question

A small block of mass m is pushed up on a rough hillof coefficient of friction meu,using a tangential force .the work done by the frictional force on the block till it reach top of hill from the base wil be

Answer 1

Given :

Mass of body = m

Coefficient of friction :

$\mu$

To find :

Work done by frictional force to reach at top.

Solution :

Frictional force : It is the force which opposes the relative motion object against any kind of surface.

It is created by two surfaces which tries to move in same or opposite direction to each other.

The formula of frictional force :

$\bf \: F = \mu \: N \:$

where

N = Normal force applied on the object.

Here

let the height of hill = h

and length of base = l

length of altitude = a

The Normal force applied in this case is equal to gravitational force applied on the object.

So,

N = mg

Work done by a force :

$\bf \:W = F\cdot ds \:$

where ds is the total path covered.

Work done is path indipendent, so it will be same when we move object throgh any path.

So

The object travels through altitude to reach at top of hill.

So

$\bf \:W = F\cdot ds \: = F\cdot a = Fa \cos \: \theta$

In this case

acosθ = l (base of hill)

so putting the values of force F and acosθ in the formula of work, we get

Work done by frictional force :

$\bf \:W = Fa \cos \theta = \mu \: mg \: l$

So Work done :

W =(μN)l = μmgl