Question

what is angle of friction? derive formula it​

Answer 1

Explanation:

The coefficient of friction between any two surfaces in contact is defined as the ratio of the force of limiting friction and normal reaction between them. u= F / R. Angle with the resultant of force of limiting friction F and normal reaction R makes with the direction of normal reaction R is angle of reaction.

Answer 2

Angle of Friction - definition

It is the angle ( α ), measured between the normal force (N) and resultant force (R). ... Frictional force is equal to limiting friction Flimiting, when this condition is satisfied the angle of applied force α will be greater than angle of friction α and block can move along the plane.

μ=tanθ

First remember that whenever you use the formula F=μFN, you are calculating the maximum friction force before the object begins to slip.

or

μ=FmaxFN

The coefficient of friction μ is the ratio of the maximum friction force and the normal force when we have impending slip.

The following two equations are derived below at the end of my answer. At impending slip:

Fmax=(mg)sinθ

FN=(mg)cosθ

μ=FmaxFN=(mg)sinθmg)cosθ=sinθcosθ

or

μ=tanθ

DERIVATION

Consider the free body diagram of a block on a 30∘ incline. A free body diagram shows all the forces acting on the object.

Notice that I have defined a rotated set of axes and I labelled them x’ and y’. The x’-axis is parallel to the plane and the y’-axis is perpendicular to the plane. I chose positive x’-axis down the plane.

The component of the weight (mg) acting down the plane is found by resolving the weight into components as shown below:

So the component of the weight acting down the plane is (mg)sinθ. The friction force acts opposite the direction of motion (up the plane) as shown on my free body diagram.

Now write Newton’s second law in the x’ direction:

ΣFx′=max′

(mg)sinθ−Ffric=ma

but the block is stationary, so a=0

(mg)sinθ−Ffric=0

or

Ffric=(mg)sinθ ——-equation 1

Once you know the friction force, you can determine the coefficient of friction using:

Ffric=μFN

To determine FN , write Newton’s second law in the y’ direction:

ΣFy′=may′

Since the block is not “lifting” off the ramp, there is no motion in the y’-direction, so ay′=0.

ΣFy′=0

FN−(mg)cosθ=0

FN=(mg)cosθ

Ffric=μFN

or

Ffric=μ(mg)cosθ

Substitute this into equation 1 (above)

μ(mg)cosθ=(mg)sinθ

or

μ(g)cosθ=(g)sinθ

or

μ=gsinθgcosθ

or

μ=tanθ

hope it helps you

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