Question

How much work is it to push a box (mass 150 kg) up an incline (angle 15 degrees with the horizontal) that is 8.1 meters long, if the coefficient of kinetic friction between the box and the incline is 0.4

Answer 1

Given that,

Mass of a box, m = 150 kg

It is pushed at an angle of 15 degrees with the horizontal.

It is 8.1 m long.

The coefficient of kinetic friction between the box and the incline is 0.4

To find,

The work done in pushing the box.

Solution,

First let's see the net force acting on the box.

`F_(net)=mg\sin\theta+f_k\\=mg\sin\theta+\mu_k mg\cos\theta`

Work done is given by :

W = force × displacement

`W=(mg\sin\theta+\mu_k mg\cos\theta)* s\\\\=150* 10(\sin15+8.1* \cos15)* 8.1\\\\=98206.24\\\\or\\\\=98.2\ kJ`

So, the required work done is 98.2 kJ.