Physics inclined plane question

Question

An inclined plane is slowly lifted and has a mass of 10-kg resting on it. At exactly 34 degrees, the mass breaks loose and starts to slide down the plane. What is the coefficient of friction? Is this the static or kinetic coefficient?

Answer 1

In all inclined plane problems, the Fg force due to gravity will be perpendicular to ground, while Fn Normal force will be perpendicular to the inclined plane.

In this case, since the tendency of the object to move down, the Ff Force due to Friction will be along the inclined plane upwards.

To solve for Normal, equate sum of all the forces in the direction perpendicular to plane to zero:

Fn - mg cos(x) = 0 where x = angle of the inclined plane.

max Frictional force = µ * Fn = µ * m * g * cos(x)

The component of the force of gravity along the plane = m * g * sin(x)

When this is equal to max Frictional Force, the object is ready to move.

m * g * sin(x) = µ * m * g * cos(x)

sin(x)/cos(x) = µ

therefore µ = tan(34)

This is static coefficient. The object has not started moving. When it starts moving the kinetic coefficient comes into play and the object will start moving down with increased acceleration.

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