Question

If an object with initial speed given encounters a constant frictional force and comes to a stop in a certain distance, relate the work done by the kinetic force of friction to various initial quantities for the object.

Please explain in simplest terms and give an example using units given.

Answer 1

Kinetic energy is given by: 1/2 mv2, where m is mass and v is velocity.

Also, work done is given by: Fscos, where F is force, s is displacement and is the angle between force and displacement vectors.

Now, initial kinetic energy=1/2mv2, where v is initial velocity and m is mass of the given object.

Final kinetic energy = 0, as finally, the object is at rest and hence ,velocity =0 m/s.

So,change in kinetic energy=final kinetic energy-initial kinetic energy = 0-1/2mv2 = - 1/2mv2

Accoring to work energy theorem, work done=change in kinetic energy

=> work done = - 1/2mv2