When a body is placed on a rough plane (coeff | vedclass

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(A) Consider a body of mass $m$ on an inclined plane with angle $	heta$. The forces acting on the body are:$1$. Gravitational force $mg$ acting verti

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$g(\sin 	heta - \mu \cos 	heta)$

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(A) Consider a body of mass $m$ on an inclined plane with angle $	heta$. The forces acting on the body are:$1$. Gravitational force $mg$ acting vertically downwards.$2$. Normal reaction $N$ perpendicular to the inclined plane.$3$. Frictional force $f$ acting up the plane,opposing the motion.The components of the gravitational force are $mg \sin 	heta$ (parallel to the plane) and $mg \cos 	heta$ (perpendicular to the plane).For equilibrium perpendicular to the plane,$N = mg \cos 	heta$.The frictional force is $f = \mu N = \mu mg \cos 	heta$.Applying Newton's second law along the plane:$mg \sin 	heta - f = ma$$mg \sin 	heta - \mu mg \cos 	heta = ma$Dividing by $m$,we get the acceleration:$a = g(\sin 	heta - \mu \cos 	heta)$

When a body is placed on a rough plane (coefficient of friction $= \mu$) inclined at an angle $\theta$ to the horizontal,its acceleration is (acceleration due to gravity $= g$)

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