Question

a body of mass m is kept on a rough horizontal surface of friction coefficient mue . a force is applied horizontally but the body is not moving. the net force F by the surface on the body will be?

Answer 1

A body of mass $m$ is kept on a rough horizontal surface of friction coefficient $\mu$ . A force is applied horizontally but the body is not moving. The net force $F$ by the surface on the body will be?

Solution: As you can see on the picture below, the body is affected to such forces as weight force $F_{w}$ , force of friction $F_{fr}$ , support reaction normal force $N$ and outer horizontal force $F$ . The body isn't moving, then all these forces are in equilibrium, according to the third Newton's law. They can be expressed through next equations: $F_{fr} = F$ , $N = F_{w} = m \cdot g$ , where $m$ is the mass of the body, $g = 9.81 \, \text{m/s}^2$ - standard gravity.

As you see, the surface exerts two forces on the body: force of friction $F_{fr}$ , and the support reaction normal force $N$ . The resultant force will be a vector sum of these two forces, and magnitude of the net force is: $F_{surf} = \sqrt{N^2 + F_{fr}^2} = \sqrt{m^2 \cdot g^2 + F^2}$

Answer: $\sqrt{m^2 \cdot g^2 + F^2}$ .