Question

A car of mass m accelerates from speed v1 to speed v2 while going up a slope that makes an angle θ with the horizontal. The coefficient of static friction is μs, and the acceleration due to gravity is g. Find the total work W done on the car by the external forces. Express your answer in terms of the given quantities. You may or may not use all of them.

Answer 1

Answer:

The answer is $W=\frac{1}{2} m (v_2^{2} -v_1^{2} )$

Explanation:

Here you have to take into account the theorem of work and energy.  This theorem says that the total work done by external forces on a body is used to modify the kinetic energy. So the only thing you have to do is determine the kinetic energy in the initial $(K_1)$ and final moment $(K_2)$, then the diference between them is the amount of net work that act over the body.

$K_1=\frac{1}{2} m v_1^{2}$

$K_2=\frac{1}{2} m v_2^{2}$

$W=K_2-K_1=\frac{1}{2} m v_2^{2} - \frac{1}{2} m v_1^{2}=\frac{1}{2} m (v_2^{2} -v_1^{2} )$