Limiting angle of friction | Formula

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Definition of limiting angle of friction: 


The angle between resultant reaction R and normal reaction RN is known as limiting angle of friction. Let us check out the formula of the limiting angle of friction to know more about it. 

Limiting angle of friction
Limiting Angle of friction


Let us consider an object of weight W resisting on a horizontal plane B. A horizontal force P is applied to the body, no relative motion takes place until the force P applied is equal to the force of friction F, acting opposite to the normal direction. The magnitude of the force of friction is given by the formula below. 

F = µ W = µ RN 
Where RN = Normal reaction 

When the body just begins to move, it is in equilibrium under the action of a force which is following below, in the limiting case. 
  • Weight of the body W
  • A horizontal force applied P
  • Reaction R between the body and the plane 
The resultant reaction R which makes and angle ϕ with the normal reaction RN and it must be equal and opposite to the resultant of W and P The angle ϕ is called the limiting angle of friction. We can check out the formula of limiting angle ϕ following below. 

tan ϕ = F / RN = µ ×RN / RN = µ

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