Posted by Becky on .
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?

Physics 
Count Iblis,
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. 
Physics 
Becky,
thank you sooo much!