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Laws Of Motion

Question
CBSEENPH11016785

A body of mass m is placed on a rough inclined plane of inclination θ and coefficient of friction μ, such that tan θ > μ. Find the acceleration of body down the inclined plane.

Solution

Let a body of mass 'm' be placed on the inclined plane of inclination θ as shown in the figure. Since tan θ > μ.

Therefore,
Body will accelerate in downward direction and is in equilibrium perpendicular to inclined plane.
Now,
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#6 {main}</pre>
Net force acting on the body in downward direction along the plane is, 
straight F equals mg space sinθ minus straight mu space mg space cosθ
Acceleration of body along inclined plane is,
straight a equals straight F over straight M equals straight g left parenthesis sinθ minus μcosθ right parenthesis