Question

A 4.0 kg bundle starts up a 30° incline with 200 J of kinetic energy. How far will it

slide up the incline if the coefficient of kinetic friction between the bundle and the incline is

0.42?

Answer 1

Apply conservation of energy. The initial energy will be spent to lift the block up the slope (increase its potential energy) and overcome friction along the incline:

$$E=mgL\sin\theta+\mu mgL\cos\theta,\\\space\\ L=\frac E{mg(\sin\theta+\mu \cos\theta)}=5.9\text{ m}.$$