Question

Tarzan, who weighs 688 N, swings from a cliff at the end of a vine 18 m long (Fig. 8-40). From the top of the cliff to the bottom of the swing, he descends by 3.2 m.The vine will break
if the force on it exceeds 950 N. (a) Does the vine break? (b) If no, what is the greatest force on it during the swing? If yes, at what angle with the vertical does it break?

Redo the problem with the vine breaking if the force on it exceeds 700 N. Find the angle with the vertical at which the vine breaks.

I gog the answer of the original problem, but need to answer the second part in bold, thanks.

Answer 1

Part a)

Conserve energy between highest and lowest points
mgh=mv^2/2
v=sqrt(2gh)

Put values
v=sqrt(2*9.81*3.2)
=7.9236 m/s
Then at the lowest point
T-mg=mv^2/r

Put values
T=688+(688/9.81)*7.9236^2/18
=932.62 N< 950 N
So it doesn't break.

Part b)

T=700 N, Then it will break, because Tmax exceeds 700 N

=> 700N =244.6 +688 cos theta

(Then (932.62-688=244.6) )

=> cos theta=0.6619

=> 48.55°

So for all cos theta greater than 0.6619, i.e for all

(Theta<48.55°) The vine will break.

I hope help you.