Question

define angle of friction and angle of repose and hence show that they are numerical equal​

Answer 1

Answer:

❇ ️Angle of friction (φ): Angle made by the resultant of normal reaction and limiting frictional force with the normal reaction is called angle of friction.

❇️ Angle of repose (θ): The minimum angle of the plane at which the body kept on it starts to slide due to its own weight is called angle of repose.

Explanation:

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Answer 2

The minimum angle made by inclined plan is the angle of repose, while angle made between two forces is angle of friction.

• Angle made by normal reaction resulting and limiting frictional force with normal reaction is called friction angle.
• The minimum angle of the plane at which the body stays on it begins to move because of its own weight is called the angle of rest
• It can be described numerically as -

1. Let normal reaction of the body be = r and frictional force = f
2. mgsinθ  = -F and mgcosθ  = -R
3. mgsinθ/mgcosθ = -F/-R or Tan = F/R Or, Tanθ = µ, where ‘µ’ is the coefficient of friction
4. This can be written as Tan = Tana ( where a is the angle of friction)
5. Thus, θ = a