Question

A car of mass m accelerates from speed v_1 to speed v_2 while going up a slope that makes an angle theta with the horizontal. The coefficient of static friction is mu_s, and the acceleration due to gravity is g. Find the total work W done on the car by the external forces.

Answer 1

Work done by external force is given as

`Work_(external) = mgLsin\theta + \mu mgLcos(\theta) + (1)/(2)mv_2^2 - (1)/(2)mv_1^2`

Step-by-step explanation:

As per work energy Theorem we can say that work done by all force on the car is equal to change in kinetic energy of the car

so we will have

`Work_(external) + Work_(gravity) + Work_(friction) = (1)/(2)mv_2^2 - (1)/(2)mv_1^2`

now we have

`W_(gravity) = -mg(Lsin\theta)`

`W_(friction) = -\mu mgcos(\theta) L`

so from above equation

`Work_(external) - mgLsin\theta - \mu mgLcos(\theta) = (1)/(2)mv_2^2 - (1)/(2)mv_1^2`

so from above equation work done by external force is given as

`Work_(external) = mgLsin\theta + \mu mgLcos(\theta) + (1)/(2)mv_2^2 - (1)/(2)mv_1^2`