Question

An object of mass m is placed on an inclined plane with a rough surface. Derive an equation of the acceleration of the object sliding down the incline. [Be sure to include an appropriate diagram highlighting the relevant forces] 

Answer 1

Solution

let N is normal force.

f is frictional force.

a is acceleration

Diagram

Then net acceleration on mass m is given by

$F=mg+N+f$

Putting all values

$ma=mgsin\alpha-\mu mg con\alpha\\a=g(sin\alpha-\mu con\alpha)$