Answer to Question #150700 in Physics for Erica

Question

A 5 kg object is pushed along a horizontal plane by a force of 20 N. if the velocity is 20 m/sec at the foot of the plane and the coefficient of kinetic friction between the plane and the object is 0 25. how far the plane will the object go ?

Answer 1

Let's first find the acceleration of the object from the Newton's Second Law of Motion (we assume that when object reaches the velocity of 20 m/s at the foot of the plane, it releases and the only force of friction acts on it):

$$-F_{k.fr.}=ma,$$ $$-\mu_k mg=ma,$$ $$a=-\mu_kg=-0.25\cdot 9.8\ \dfrac{m}{s^2} = -2.45\ \dfrac{m}{s^2}.$$

The sign minus means that the object decelerates.

Then, we can find the distance traveled by the object until it finally stops:

$$v^2=v_0^2+2ad,$$ $$d=\dfrac{-v_0^2}{2a}=\dfrac{-(20\ \dfrac{m}{s})^2}{2\cdot (-2.45\ \dfrac{m}{s^2})}=81.6\ m.$$

Answer:

$d=81.6\ m.$