Quiz:Sliding motion along an inclined plane

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 $\theta$?

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