PURPOSE: To demonstrate how pulling angle affects the frictional force, and to show that the minimum force required to pull an object occurs when pulling at the angle of repose a, where the coefficient of friction u=tana.

DESCRIPTION: A wooden board of weight w, lying on a sandpaper surface, is pulled at an angle a by a string connected to a spring scale. The force F required to move the board is given by: F = w / [ (1/u)cosa + sina]. Differentiating F with respect to a, the minimum force is seen to occur at the angle of repose, u=tana. Pulling horizontally is definitely not the most efficient angle!

SUGGESTIONS: Pull horizontally to determine u, then check the angle of repose by tilting the sandpaper surface. Then pull at a variety of angles to demonstrate that pulling at the angle of repose requires the least force.


EQUIPMENT: Board with spring scale and string, sandpaper base wih clamp to attach to lecture table, demonstration protractor.

SETUP TIME: 5 minutes.

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