# Friction

5. A rectangular block twice as high as it is wide is resting on a board. The coefficient of static friction between board and incline is .63. If the board is tilted will the block first tip over or begin sliding?

6. A uniform pole of mass M is at rest on an incline of angle secured by a horizontal rope. For what angle does the situation require the greatest coefficient of friction.

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#### Solution Preview

5. Let the width of the block be a and its height 2a. Let the angle of sliding (angle of the board at which the block just starts sliding) be Î±. Then, coefficient of friction Î¼ = tanÎ± or 0.63 = tanÎ± or Î± = 32.21O.

Let the board be tilted at an angle Î¸. Then, for the block to tip over, net torque about the forward edge of the block must be counter clockwise. Hence,

mgsinÎ¸ x a > mgcosÎ¸ x a/2

Or tanÎ¸ > Â½ or Î¸ > 26.56O

The block will tip over as soon as Î¸ exceeds 26.56O whereas it will slide when the angle ...

#### Solution Summary

A step by step solutions provided to determine the friction on an incline plane. A uniform pole of a mass is also determined.