Swing problem?

Question

Tarzan, who weighs 608N, swings from a cliff at the end of a convenient vine that is 22.0m long. From the top of the cliff to the bottom of the swing, he descends by 3.2m.
If the vine doesn't break, what is the maximum of the tension in the vine?

Answer 1

The tension on the vine (Ft) is the sum of his weight (w) and centripetal force (Fc) due to centripetal acceleration (ac)

w=mg=608N
Fc=m (ac)
ac= v^2/R
v- velocity at the lowest point
R - radius of the swing (22.0m)

To find the velocity we equate potential energy he had on the cliff to kinetic energy as he swings trough the lowest point.

Pe=Ke
mgh=.5mv^2
v^2=2mgh/m=2gh

so since ac= v^2/R now
ac=2gh/R
Fc=2mgh/R
m=w/g
Fc=2wgh/gR
Fc=2wh/R

Ft=w+2wh/R=w(1+2h/R)
Ft=608(1+2 3.2/22.0)
Ft=785 N

I hope it helps