Question

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

Answer 1

Explanation:

The angle of repose, or critical angle of repose,[1] of a granular material is the steepest angle of descent or dip relative to the horizontal plane to which a material can be piled without slumping. At this angle, the material on the slope face is on the verge of sliding. The angle of repose can range from 0° to 90°. The morphology of the material affects the angle of repose; smooth, rounded sand grains cannot be piled as steeply as can rough, interlocking sands. The angle of repose can also be affected by additions of solvents. If a small amount of water is able to bridge the gaps between particles, electrostatic attraction of the water to mineral surfaces will increase the angle of repose, and related quantities such as the soil strength.

Answer 2

Answer:

Hey mate! Here is your answer. Please mark the answer as the brainliest.

Explanation:

Angle of Friction: The angle of Friction is represented by the Greek letter φ.

We can define the angle of friction as follows:

The angle made by the resultant of normal reaction and limiting frictional force with the normal reaction is called angle of friction. The angle of friction is shown in figure one.

Angle of Repose: The angle of repose is represented by the Greek letter θ.

We can define the angle of repose as follows:

The minimum angle of the plane at which the body kept on it starts to slide due to its own weight and this is called the angle of repose. The angle of repose is shown in figure two.

Now lets prove that the Angle of friction is equal to the Angle of Repose.

To prove: φ = θ

Proof:

∑$Fy = 0$

N - W cosθ = 0

N = W cosθ

∑Fx = 0

- W sinθ + F = 0

F =  W sinθ

μW cosθ =  W sinθ

μ = tanθ

But we know that μ = tanφ

tanφ = tanθ

So tan and tan gets cancelled and we are left with,

φ = θ

Hence Proved..

Hope helps..