Answer to Question #174247 in Physics for ghazal

Question

a box drops down from a lorry while moving with a speed of v zero on the road with inclination θ°, where the mass of the box and kinetic friction coefficient and me and u, respectively. for the moment that the box slides up and reaches a possible maximum height(L).

(a) what is work done done by friction?

(b)what is work done by gravity?

Answer 1

The initial kinetic energy of the box:

$$E_K=\frac12 mv^2.$$

This energy is wasted to move up the incline (acquire potential energy) and to overcome friction. Assume the maximum height is H above the horizontal:

$$E_P=mgH,\\ W=\mu mgx=\mu mg\frac{H}{\text{sin}\theta}.$$

According to conservation of energy:

$$E_K=E_P+W,\\\space\\ \frac12 mv^2=mgH\bigg(1+\frac{\mu}{\text{sin}\theta}\bigg),\\\space\\ H=\frac{v^2\text{ sin}\theta}{2g(\text{sin}\theta+\mu)}.\\\space\\ W=\frac{\mu mhv^2}{2(\sin\theta+\mu)}.$$