Two blocks of masses $m_1$ and $m_2,$ respectively, are attached to a cable that is threaded over a massless,

frictionless pulley. The cable does not stretch.

Block $1$ rests on an incline of $=53\mathrm{.}1$ with respect to the horizontal. The mass of Block $1$ is $20\mathrm{.}0kg.$

The coefficient of kinetic friction between Block $1$ and the incline is ${}_k=0\mathrm{.}4.$ Block $2$ is found to descend

$4\mathrm{.}0m$ in the first $3\mathrm{.}0s$ after the system is released from rest with Block $1$ accelerating up the incline. Find

the mass of Block $2,m_2.$

$($a$)$ Briefly describe how the friction force between Block $1$ and the incline surface is calculated.

$($b$)$ Find the mass of Block $2,m_2.$

$($c$)$ Find how far Block $2$ has descended $($from its release$)$ after $5\mathrm{.}0s.$

$($d$)$ Find the tension in the cable.

Suppose with the calculated value of $m_2$ that the system is set at its initial position again and when it is

released there is no motion.

$($e$)$ Find the minimum coefficient of static friction between Block $1$ and the incline, ${}_s.$ Note:

Obviously, the coefficient of static friction will exceed ${}_k.$

$($f$)$ Find the tension in the cable.