Question

You apply a horizontal force of 200N against a 50kg couch. The force of friction between the couch and the floor is 180N. If the couch is pushed 2 metres, the kinetic energy gained by the couch is: a) 0 b) 40 J c) 100 J d) 360 J e) 400 J

Answer 1

The kinetic energy gained is 40[J]

Step-by-step explanation:

This is a problem that applies the work and energy conservation. We must analyze the initial and final positions as well as the forces that act on the couch during displacement.

The working and energy conservation theorem says:

`E_(k1) + W_(1-2)= E_(k2)`

The above equation tells us that kinetic energy plus the work done to move an object from one position to another will be equal to kinetic energy in the last position.

The kinetic energy in the initial position is zero since the couch is at rest, Ek1=0

The work will be given by the force that drives the couch multiplied by the distance, and the friction force that acts in the opposite direction to the displacement.

`0+(200-180)*2= Ek2\\Ek2=20*2= 40 [J]`