Answer to Question #248909 in Classical Mechanics for Gabgan

Question

A 5.00-kg box slides 3.00 m across the floor before coming to rest. What is the coefficient of kinetic friction between the floor and the box if the box had an initial speed of 3.00 m/s?

Answer 1

Given:

$m=5.00\:\rm kg$

$d=3.00\:\rm m$

$v_0=3.00\:\rm m/s$

The enegry-work theorem says

$$\frac{mv_f^2}{2}-\frac{mv_0^2}{2}=W=-\mu m g d$$

So

$$\mu=\frac{v_0^2}{2gd}=\frac{3.00^2}{2*9.81*3.00}=0.153$$