i don't know how to solve this problem..
a box (m=30kg) is sliding along a path with initial speed of 5m/s. using the definition of energy and work determine how far the box will go before stopping. (uk=0.04)
Lets also assume that gravitational acceleration is g = 10 m/s/s.
So the initial kinetic energy of the box is
$\displaystyle E = \frac{1}{2}mv^2 = \frac{1}{2}\times 30 \times 5^2 = 375$ Nm
The frictional force opposing motion is
$\displaystyle F_f = \mu_k mg = 0.04 \times 30 \times 10 = 12$ N
So the work done by friction to overcome the initial kinetic energy is
$\displaystyle W = F_f d$
where d is the distance oevr which the force has acted. To stop the box the W = E, therefore
$\displaystyle d = \frac{E}{F_f} = \frac{375}{12} = 31.25$ m
Hope this helps.