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"I is smooth wall, as shown in the diagram, making a variable angle \( \theta \) with the horizontal floor. There is no friction with the vertical wall. At which angle \( \theta \) will the normal force exerted by the floor upwards be at its maximum? Do not consider any motion by the plank (consider the forces exerted when the plank is perfectly still for a given angle \( \theta) \)

1. When \( \theta=0.00^{\circ} \) (the plank is horizontal)
2. When \( \theta=45.0^{\circ} \)
3. When \( \theta=90.0^{\circ} \) (the plank is vertical)
4. The angle \( \theta \) makes no difference E. More information is needed

Correct answer: When \( \theta=45.0^{\circ} \)

Solution

For a stationary plank, the forces must balance in both directions and in torque. The wall’s horizontal reaction and the floor’s vertical normal depend on the angle, and the floor normal is maximized when the geometry makes the torque arm balance most strongly at 45°.

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