Question

A 0.2kg is drag 0.5m upward with a uniform velocity along a plane inclined 30° with the horizontal by a force parallel to the incline. The coefficient of kinetic friction between the object and the plane is 0.25. How much work is done by the applied force? Show complete solution.

Answer 1

Let's first find the applied force :

$$F_{appl}-F_{fr}-mgsin\theta=0,$$ $$F_{appl}=mgsin\theta+\mu_k mgcos\theta=mg(sin\theta+\mu_k cos\theta).$$

Finally, we can find the work done by the applied force:

$$W_{appl}=F_{appl}d=mgd(sin\theta+\mu_k cos\theta),$$ $$W_{appl}=0.2\ kg\times9.8\ \dfrac{m}{s^2}\times0.5\ m\times(sin30^{\circ}+0.25\times cos30^{\circ}),$$ $$W_{appl}=0.7\ J.$$