Answer to Question #124672 in Physics for Dr. Horus

Question

The top of a 4.5m long inclined plane is 2.6m above the horizontal. An 8.0kg load slides down the inclined, its motion impeded by a 21.1N frictional force.
Calculate (i) the acceleration of the load down the plane
(ii) the coefficient of kinetic friction between the load and the plane.

Answer 1

Calculate the angle that the incline makes above the horizontal:

$$\theta=\text{arcsin}(h/l)=35°.$$

According to Newton's second law, if we point the x-axis down the incline, the acceleration can be expressed as

$$ma=mg\text{ sin}\theta-f,\\ a=g\text{ sin}\theta-f/m=3\text{ m/s}^2.$$

The frictional force is the normal force times coefficient of friction:

$$f=\mu N,\\ N=mg\text{ sin}\theta,\\ \mu=f/(mg\text{ sin}\theta)=0.47$$