Question

A body of mass 400 g slides on a rough horizontal surface. If the frictional force is 3 N, find the angle made by the contact force on the body with the vertical.

Answer 1

Step 1. Given data

Mass of the body, $m=400g$

Frictional force, $f=3newton$

Step 2. Assumptions

Frictional force $=f$

Coefficient of friction $=\mu$

Normal reaction $=N$

Step 3. Calculation of angle of contact (θ)

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

From the free-body diagram shown above, it is clear that, $\tan \theta =\mu N/mg$

But, $\mu N=f=3Newton$

$$\begin{gathered} \tan \theta =3/(0.4\times 10) \\ \tan \theta =3/4 \\ \theta ={\tan }^{-1}(3/4) \\ \theta ={37}^o \end{gathered}$$

Hence, the angle made by the contact force on the body with the vertical is equal to 37⁰.