Question

If an object is moving at `4 m/s` over a surface with a kinetic friction coefficient of `u_k=80 /g`, how far will the object continue to move?

Answer 1

The object will travel only `0.10m` (because a kinetic coefficient of `80/g` is very large!)

Explanation:

This problem is most easily done by conservation of energy.
Two energy forms are involved:
A change in kinetic energy: `1/2mv_f^2-1/2mv_i^2`

Frictional heating: `muF_NDelta d`

The equation for conservation of energy is, in this case

`1/2mv_f^2-1/2mv_i^2+mumgDelta d=0`

Notice that we can divide every term by the mass m, (including the right side of the equation)

Also, `v_f=0` , and inserting the values for `mu`, `v_i` and g, we get:

`-1/2(4)^2+(80/g)(g)Delta d=0`

Cancel the two `g`'s

`-1/2(4)^2+(80)Delta d=0`

`-8+80Delatd=0`

`80Deltad=8`

`Deltad=0.1m`