Question

If an object is moving at `6 m/s` over a surface with a kinetic friction coefficient of `u_k=20 /g`, how far will the object continue to move?

Answer 1

I found `0.9m`

Explanation:

Your object will move under the acton of Friction that wll produe a negative acceleration and eentually stop it.

To find this acceleration we can use Newton's Second law:

`SigmavecF=m veca`

where the only force will be friction (in the opposite direction to the movement so it will need to enter Newton's Law with a minus sign) given as:

`f_k=u_kN`

where:

`N=`normal reaction`=`Weight`=mg` in this case of horizontal movement.

So you have:

`-f_k=ma`
`-u_kN=ma`
`-u_kmg=ma`
`-20/cancel(g)cancel(m)cancel(g)=cancel(m)a`
so that `a=-20m/s^2`
we now use the relationship:
`v_f^2=v_i^2+2ad`
where `v_f=0` (stops)
`0=6^2-2*d*20`
`d=36/40=0.9m`