A box is sliding up an incline that makes an angle of 21.8° with respect to the horizontal. The coefficient of kinetic friction between the box and the surface of the incline is 0.170. The initial speed of the box at the bottom of the incline is 3.48 m/s. How far does the box travel along the incline before coming to rest?

Answer 1

normal force = m g cos 21.8
max friction force down ramp
= .17 m g cos 21.8
gravity force down ramp = m g sin 21.8
so
total force down ramp =
m g (.17 cos 21.8 + sin 21.8)

work done by friction and against gravity sliding up a distance d
= d m g (.17 cos 21.8 + sin 21.8)
that energy comes from the initial kinetic energy (1/2) m v^2
so in the end
(1/2) m v^2 = d m g (.17 cos 21.8 + sin 21.8)
not m cancels and solve for d