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.

Solution

Mass of the body, m = 5 kg
The given situation can be represented as follows:

The resultant of two forces is given by,
R = $square root of left parenthesis 8 right parenthesis squared plus left parenthesis negative 6 right parenthesis squared end root space equals space square root of 64 space plus space 36 end root space equals space 10 space straight N$
$straight theta$ is the angle made by R with the force of 8 N.
Therefore,
$straight theta space equals space tan to the power of negative 1 end exponent space open parentheses negative 6 over 8 close parentheses space equals space minus 36.87 to the power of straight o$
The negative sign indicates that θ is in the clockwise direction with respect to the force of magnitude 8 N.
According to Newton’s second law of motion
Acceleration (a) of the body is given as,
F = ma
Therefore,
a = $straight F over straight m space equals space 10 over 5 space equals space 2 space m divided by s squared$