Question

Tarzan tries to cross a river by swinging from one bank to the other on a vine that is 10.2 m long. His speed at the bottom of the swing is 7.6 m/s. Tarzan does not know that the vine has a breaking strength of 1.0 103 N. What is the largest mass that Tarzan can have and still make it safely across the river?

Answer 1

At the bottom, Tarzan has a speed of

v = 7.6 m/s

This means that at that point he is actually accelerating upoward at the centripetal acceleration of:

a = v^2/r

where

r = 10.2 m

The centripetal acceleration arises because if you change direction the velocity vector changes, even if the speed itself doesn't change.

You then apply Newton's second law:

F = m a

The total force acting on Tarzan must be equal to his mass times his acceleration. If you take the upward direction as positive, then you can write this as:


F_vine - m g = m a

Where F_vine is the force exerted on Tarzan by the vine and m g is, of course the force exerted by the Earth's gravity field on Tarzan, which enters the equation with a minus sign because we've chosen the convention to take the upward direction as positive.

So, you see that:

F_vine = m (a + g)

Then, by Newton's third law, the force exerted by the Vine on Tarzan is minus the force exerted by Tarzan on the vine. Now the magnitude of this force can be 1.0 10^3 N at most. So, you can use this to solve for the maximum value for m.

Answer 2

thank you sooo much!