why are the angle of repose and the angle of friction equal? can it be proven numerically??

dear ash,

Consider a block placed on a rough floor. Now, the reaction force is because it is equal and opposite to the weight . Now apply a horizontal force so that the block just begins to slide, i.e., the frictional force is equal to the limiting friction. When this condition is satisfied, the angle which the resultant (between the normal and external force) makes with the vertical is called the angle of friction.

The tangent of the angle of friction is equal to the coefficient of static friction

The weight W can be resolved into two rectangular components. W cos f and W sin f. The component W cos f balances the normal reaction R while the component W sin f is equal to the limiting friction f_limiting.

We notice that the angle of repose or sliding and the angle of friction are both equal.

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