A block with mass $m_1=1kg$ sits at rest on a ramp with an incline of $=20.$ A second block of mass $m_2$ is attached to the first block via a pulley, as shown below. The coefficients of friction between the block and the ramp are ${}_s=0\mathrm{.}5$ and ${}_k=0\mathrm{.}3.$

a$)$ Draw a free$-$body diagram for each of the blocks, labeling all forces and drawing arrows with the correct relative sizes.

b$)$ What is the maximum mass $m_2$ that can be hung from the pulley so that the block on the ramp remains at rest?

c$)$ Assume the mass $m_2$ has the value calculated in part b$.$ If the mass $m_1$ is lightly tapped so that it begins to move up the ramp, will it continue to move at a constant speed, accelerate, or decelerate until it comes to a stop?

d$)$ Calculate the magnitudes of $($i$)$ the tension in the rope and $($ii$)$ the acceleration of the blocks for the situation described in part c$.$