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 \mu_s = mu_k = \mu 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 m) and the incline as a function of the angle of incline \theta (this is the angle that the incline makes with the horizontal)?

The magnitude of normal force equals mg and is independent of \theta
The magnitude of normal force decreases from mg to 0 as \theta increases from 0 to \pi/2
The magnitude of normal force increases from 0 to mg as \theta increases from 0 to \pi/2
The magnitude of normal force increases for \theta increasing from 0 to \tan^{-1}(\mu) and decreases for \theta increasing from \tan^{-1}(\mu) to \pi/2
The magnitude of normal force decreases for \theta increasing from 0 to \tan^{-1}(\mu) and increases for \theta increasing from \tan^{-1}(\mu) to \pi/2

2 Consider a situation where \mu_s = mu_k = \mu is the coefficient of static as well as kinetic friction between the block and the incline. Once the angle of the incline (denoted \theta) exceeds \tan^{-1}(\mu_s), the magnitude of downward acceleration a is an increasing function of \theta. What is its derivative with respect to \theta?

g(\sin \theta + \mu \cos \theta)
g(\sin \theta - \mu \cos \theta)
g(\cos \theta - \mu \sin \theta)
g(\cos \theta + \mu \sin \theta)