Question

A body of mass 5 kg is acted upon by two perpendicular forces 8 N and 6 N. Give the magnitude and direction of the acceleration of the body.

Answer 1

2 m/s2, at an angle of 37° with a force of 8 N
Mass of the body, m = 5 kg
The given situation can be represented as follows:
The resultant of two forces is given as:
R = $\sqrt{(8)^2+(6)^2}$ = $\sqrt{64+36}$ = 10 N
θ is the angle made by R with the force of 8 N
∴ θ = tan-1($-\frac{6}{8}$) = -36.87°
The negative sign indicates that θ is in the clockwise direction with respect to the force of magnitude 8 N.
As per Newton’s second law of motion, the acceleration (a) of the body is given as:
F = ma
∴ a = $\frac{F}{m}$ = $\frac{10}{5}$= 2 m/s2