Question

A body of mass 3kg slides down a plane which is inclined at 30 degrees to the horizontal. Find the acceleration of the body, if there is a frictional resistance of 9N

Answer 1

First, draw the figure as per the question and mark all the forces.

Concept:

• Body will slide down in the effect of gravity and its motion will get opposed by the resistance of friction.

$\implies\bf F_{net} = F_{driving} - F_{opposing}$

$\implies\bf ma = F_{driving} - F_{opposing}$

$\implies\bf a = \dfrac{F_{driving} - F_{opposing}}{m}$

Solution:

• driving force = $\rm mgsin\theta$
• opposing force = resistive force =friction

$\to\rm a = \dfrac{F_{driving} - F_{opposing}}{m}$

$\to\rm a = \dfrac{mgsin30\degree - friction}{m}$

$\to\rm a = \dfrac{3\times 10\times 0.5 - 9}{3}$

$\to\rm a = \dfrac{15 - 9}{3} = \dfrac{6}{3}$

$\to\bf a = 2 \: ms^{-2}$

★ Acceleration of the body is 2m/s².