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

The answer is
`W=(1)/(2) m (v_2^(2) -v_1^(2) )`

Step-by-step 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=(1)/(2) m v_1^(2)`

`K_2=(1)/(2) m v_2^(2)`

`W=K_2-K_1=(1)/(2) m v_2^(2) - (1)/(2) m v_1^(2)=(1)/(2) m (v_2^(2) -v_1^(2) )`