Question

An 30 kg object from rest was pulled horizontally by a pulling force 100 N applied along the direction of displacement line. The coefficient of kinetic friction between the surface and the object is 0.20 and the object was displaced at a distance of 40 meters. What is the final velocity of the object?

Answer 1

Let's first find the net force:

$$F_{net}=F_{pull}-F_{k.fr.},$$ $$F_{net}=F_{pull}-\mu_kmg,$$ $$F_{net}=100\ N-0.2\times30\ kg\times9.8\ N = 41.2\ N.$$

Then, we can find the net work:

$$W_{net}=F_{net}d=41.2\ N\times40\ m=1648\ J.$$

We can find the final velocity of the object from the work-kinetic energy theorem:

$$W_{net}=\dfrac{1}{2}mv^2,$$ $$v=\sqrt{\dfrac{2W_{net}}{m}}=\sqrt{\dfrac{2\times1648\ J}{30\ kg}}=10.5\ \dfrac{m}{s}.$$