Answer to Question #142131 in Physics for oe

Question

An object is moving to the right with an acceleration of 4m/s2. If the force of friction is 10N and the coefficient of friction is 0.2, what is the mass of the object? What is the net force and the applied force?

Answer 1

According to Newton's second law, the net force is mass times acceleration. The force of friction f opposes motion to the right, thus, it is directed to the left and we will include it with negative sign. The applied force supports motion to the right and it is positive:

$$F_\text{net}=ma,\\ F_\text{net}=F-f.\\ F-f=ma.$$

The force of friction on a horizontal surface is

$$f=\mu mg.\\\space\\ m=\frac{f}{\mu g}=\frac{10}{0.2\cdot9.8}=5.1\text{ kg}.$$

From newton's second law written above find the applied force:

$$F=f+ma=10+5.1\cdot4=30.4\text{ N}.$$