Step-by-step explanation:
Let
T
be the tension of the cable and m
g
be the force of gravity. If the upward direction is positive, then Newton’s second law is T−mg=ma, where a is the acceleration. Thus, the tension is T=m(g+a). We use constant acceleration kinematics (Table 2-1) to find the acceleration (where v=0 is the final velocity, v
0
=−12m/s is the initial velocity, and y=−42m is the coordinate at the stopping point). Consequently, v
2
=v
0
2
+2ay leads to
a=−
2y
v
0
2
=−
2(−42m)
−12m/s
=1.71m/s
2
We now return to calculate the tension:
T=m(g+a)
=(1600kg)(9.8m/s
2
+171m/s
2
)
=1.8×10
4
N