Please help, I know that I should use Tarzan's weight but I don't know why.?

Question

Tarzan (m = 85 kg) tries to cross a river by swinging from a 10-m-long vine. His speed at the bottom of the swing (as he just clears the water) is 8.0 m/s. Tarzan does not know that the vine has a breaking strength of 1000 N. Does he make it safely across the river? Justify your answer.

Answer 1

There are two parts, the gravitational force, and the centripital force

gravitational force is proportional to mass...

F = M* g

F = 85 * 9.8 m/s^2

F = 833... more or less.

Tarzan's MASS produces a pull of just over 833 newtons as I said in the PREVIOUS answer.

Now, we need to know the centripital force on a 10 meter vine where 85 kg has a velocity of 8 m/s.

F = m (V^2 / R )

F = 85 ( 8 * 8 / 10)

F = 85 *64/10

F = 544 newtons.

add THAT 544 to his 833 newtons he WEIGHS (See previous answer) and you get almost 1400 newtons.

But the breaking strength of the vine is 1000 N, so, it's swimming time.

Answer 2

Imagine that the water on the river is perfectly horizontal.

A mass swinging at a ropes end will produce force outwards, from the point where the rope is tied to the mass, in this case, Tarzan, which is dependant on the speed at which the mass is moving. (Faster means more force.)

When Tarzan reaches the lowest point of his swing, that is when the rope is perfectly perpendicular to the water's surface, is also when the speed is the greatest, in the given scenario.

Given that the vine will snap if the amount of force is over a certain value, the question wants to you figure out the amount of force exerted by Tarzan on the vine at exactly this point in time.

Thoughts for out of question discussion:
Regardless of the width of the river, Tarzan would most likely hit the water if the vine snaps at this point in time. There is probably a small window of opportunity to use any lateral (vs his downward) momentum to cross the remaining width of the river. But I would also think that if Tarzan could do that, he'd probablu just long jump over the river anyway....

Answer 3

what distance does he need to cross the river?