Quiz:Sliding motion along an inclined plane

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See sliding motion along an inclined plane for background information.

Force diagram and acceleration analysis

1 Consider a situation where is the coefficient of static as well as kinetic friction between the block and the incline. What can we say about the normal force between the block (of mass ) and the incline as a function of the angle of incline (this is the angle that the incline makes with the horizontal)?

The magnitude of normal force equals and is independent of
The magnitude of normal force decreases from to 0 as increases from 0 to
The magnitude of normal force increases from 0 to as increases from 0 to
The magnitude of normal force increases for increasing from 0 to and decreases for increasing from to
The magnitude of normal force decreases for increasing from 0 to and increases for increasing from to

2 Consider a situation where is the coefficient of static as well as kinetic friction between the block and the incline. Once the angle of the incline (denoted ) exceeds , the magnitude of downward acceleration is an increasing function of . What is its derivative with respect to ?