Question

DERIVE AN EXPRESSION FOR ACCELERATION OF A BODY ON A ROUGH INCLINED PLANE SLIDING DOWN THE PLANE IN BRIEFLY

Answer 1

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Fn = normal force on the body by the surface of incline

m = mass of the body

θ = angle of incline

μ = coefficient of kinetic friction

a = acceleration of the body

$f$ k = kinetic frictional force

perpendicular to incline surface , force equation can be given as

Fn = mg Cosθ                                  eq-1

kinetic frictional force is given as

$f$ k= μ Fn

using eq-1

Fk = μ mg Cosθ                              eq-2

parallel to incline , force equation is given as

mg Sinθ - Fk = ma

using eq-2

mg Sinθ - μ mg Cosθ = ma

a = g (Sinθ -  μ Cosθ )

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