$0($Average$)$ An exhausted Vanier student is dragging her backpack down the ramp near the library. The bag contains physics, chemistry and math textbooks whose total mass is $10kg.$ The ramp slopes at $20$ to the horizontal; coefficients of friction between the bag and the ramp are ${}_k=0\mathrm{.}4,{}_n=0\mathrm{.}75.$ The rope is at an angle of $60$ above the slope as shown.

$($a$)$ If the bag is initially at rest, what is the smallest tension needed to cause the bag to start moving?

Ais: $30$:$1$N$.$

$($b$)$ If the bag is moving already, what is the smallest tension needed to keep it moving with a constant speed?

Ans: $3\mathrm{.}9N.$

$($c$)$ If the rope has tension $20N$ and the bag is already sliding down the ramp, find its acceleration.

Aris: $1\mathrm{.}36\frac{m}{s^2}$ downhill.