Question

does kinetic friction speed up or slow down an object? Therefore, which type of work iis done by kinetic friction?

Answer 1

Speed up, friction is the force applied when slowing down.

It would be positive work because an applied force would cause an object to displace and go into a certain direction sending it into a state of motion, hence generating kinetic energy.

What is kinetic energy?

In the ordinary sense, the kinetic energy of a body is the energy that it possesses by virtue of its motion. In fact it is equal to the work that a moving body can do before coming to rest. In other words, it is equal to the amount of work required to stop a moving body.

Using the elementary third equation of motion and Newton's second law, the kinetic energy of a body of mass m and velocity v is given by the simple mathematical relation:

`K=(mv^2)/(2)`

But this identity holds good provided that the body moves with a velocity much smaller than the velocity of light in vacuum.

Now what happens if the velocity of the body is sufficiently large?

From the expression from the relativistic linear momentum of a body of rest mass
`m_0` moving with velocity
`v` is given by

p=m0v1−v2c2−−−−−−√=m0γv

∴K=∫vd(m0γv)

=v.m0γv−∫m0γvdv

=m0γv2−m0∫vdv1−v2/c2−−−−−−−−√

Let u=1−v2/c2⟹du=−2vc2dv

∴K=m0γv2+m0c22∫du√u

=(m0v2+m0c2(1−v2c2))γ−E0

K=m0γc2−E0

Now if the magnitude of velocity is zero, then the above equation takes the form

0=m0c2−E0⟹E0=m0c2

So finally the kinetic energy of a body is given by the general relation:

K=m0γc2−m0c2=m0c2(γ−1)

Now if the velocity is small enough, then this equation closely approximates the classical relation for kinetic energy which can be ensured by expanding γ

by the binomial theorem.