Question

A body of mass 400 g slides on a rough horizontal surface. If the frictional force is 3 N, find the magnitude of the contact force.

Answer 1

Step 1. Given data

Mass of the body, $m=400g$

Frictional force, $f=3newton$

Step 2. Assumptions

Frictional force $=f$

Contact force $=F$

Coefficient of friction $=\mu$

Normal reaction $=N$

Step 3. Calculation of contact force

The free-body diagram of the given system of forces is shown below.

$$\begin{gathered} N=mg=0.4\times 10 \\ N=4newton \end{gathered}$$

Contact force will be equal to the vector sum of frictional force and normal reaction.

$$\begin{gathered} F=\sqrt{N^2+f^2} \\ F=\sqrt{4^2+3^2} \\ F=\sqrt{16+9} \\ F=\sqrt{25} \\ F=5newton \end{gathered}$$

Hence, the magnitude of the contact force is equal to 5 newton.