2.Tarzan, who weighs 875 N, swings from a vine through the jungle. How much work is done by his weight as he drops through a vertical distance of 4m?Required to answer. Single choice.
Answers
ANSWER
(a) To find out whether or not the vine breaks, it is sufficient to examine it at the moment Tarzan swings through the lowest point, which is when the vine — if it didn't break — would have the greatest tension. Choosing an upward positive, Newton's second law leads to
T−mg=m
r
v
2
where r=18.0m and m=W/g=688/9.8=70.2kg. We find the v
2
from energy conservation (where the reference position for the potential energy is at the lowest point).
mgh=
2
1
mv
2
⇒v
2
=2gh
where h=3.20m. Combining these results, we have
T=mg+m
r
2gh
=mg(1+
r
2h
)
which yields 933N. Thus, the vine does not break.
(b) Rounding to an appropriate number of significant figures, we see the maximum tension is roughly 9.3×10
2
N.