p08_026.pdf

26. To ﬁnd out whether or not the vine breaks, it is sucient 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 upward positive, Newton’second law leads to

−

mg = m v 2

where r =18mand m = W/g = 688 / 9 . 8=70 . 2 kg. We ﬁnd the v 2

from energy conservation (where

the reference position for the potential energy is at the lowest point).

mgh =

2 mv 2

⇒

v 2 =2 gh

where h =3 . 2 m. Combining these results, we have

T = mg + m 2 gh

= mg 1+ 2 h

which yields 933 N. Thus, the vine does not break. And rounding to an appropriate number of signiﬁcant

ﬁgures, we see the maximum tension is roughly 930 N.