Question

A mass of 5 kg is placed on a horizontal surface with a coefficient of kinetic friction of 0.4. A force is applied vertically downward to it and another force of 81 Newtons is applied at 14 degrees below the horizontal. As it moves 5 meters in the +x direction it loses 180 Joules of kinetic energy. What is the amount of the force which is applied downward in Newtons?

Answer 1

Where,

Force of friction

mass of the body = 5kg

g = 9.8 m/s² Acceleration adue to gravity

mg = 5 x 9.8 = 49 N Weight of the body

N is normal force

coefficient of friction

'a' is the net acceleration of the body (in positive x direction)

F₁ is the required force which is acting in downward direction

Now the force equations are (from the free body diagram),

   ....................................(1)

and ....................................(2)

We have,

or,

or,

or,   

or,   

Putting the value of 'f' in equation (2), we get

or,  

Here 'ma' is the total force acting on the body. So the workdone by total force, if the block moves 5m in +x direction, is

   (Here x = 5m in +x direction)

or, (As displacement and force both are in same direction)

or,   Joule

According to the question, the change in kinetic energy() of the block is 180 Joules.

Now applying work energy theorem,

  

or,

or,

or,

or,

or,

This is the required force, which is acting in downward direction.

For any doubt please comment.