Shortcut Methods
Shortcuts and Tricks for Solving Numerical Problems on Friction

Identify the forces acting on the object. The forces acting on an object on a horizontal surface are the force of gravity ((mg)), the normal force ((N)), and the force of friction ((f_k)). On an inclined plane, the force of gravity is resolved into components parallel and perpendicular to the plane.

Use Newton’s second law ((\sum F = ma)) to write equations of motion. For an object in equilibrium, the sum of forces in each direction is zero. For an object in motion, the sum of forces is equal to the mass of the object times its acceleration.
$$f_k =\mu_k N$$ $$f_s \le \mu_s N$$

Use the coefficient of friction to calculate the force of friction. The coefficient of friction is a measure of the resistance of two surfaces to sliding against each other. The force of friction is equal to the coefficient of friction multiplied by the normal force between the surfaces.

Use kinematic equations to calculate displacement, velocity, and acceleration. Kinematic equations relate the displacement, velocity, and acceleration of an object in motion. These equations can be used to solve for any one of these quantities if the other two are known.

Remember that the force of friction always opposes the motion of the object. The force of friction acts in the opposite direction to the direction of motion. This means that the force of friction will always tend to slow down the object.