Answer
a) See the detailed answer below.
b) See the figure below.
c) $T=144\;\rm N$
Work Step by Step
a) A 20-kg box is attached to a wire. The wire is attached to a pulley that pulls the wire up a 20$^\circ$ tilted surface. If you know that the coefficient of kinetic friction between the box and the surface is 0.20, find the tension exerted on the wire. Note that the box acceleration up the inclined is 2 m/s$^2$.
b) See the figures below.
c) From the first given formula,
$$T-0.2n-20g\sin20^\circ=20\cdot 2=40$$
$$T = 40+20g\sin20^\circ+0.2n\tag 1$$
From the second given formula,
$$n=20g\cos20^\circ$$
Plugging into (1);
$$T = 40+20g\sin20^\circ+0.2\cdot 20g\cos20^\circ $$
Plugging the known;
$$T = 40+9.8(20 \sin20^\circ+4 \cos20^\circ )$$
$$T=\color{red}{\bf 144}\;\rm N$$
