# Physics

posted by .

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 -

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 -

thank you sooo much!

## Similar Questions

1. ### physics

Tarzan tries to cross a river by swinging from one bank to the other on a vine that is 9.0 m long. His speed at the bottom of the swing is 8.8 m/s. Tarzan does not know that the vine has a breaking strength of 1.0 103 N. What is the …
2. ### physics

Tarzan tries to cross a river by swinging from one bank to the other on a vine that is 9.0 m long. His speed at the bottom of the swing is 8.8 m/s. Tarzan does not know that the vine has a breaking strength of 1.0 103 N. What is the …
3. ### Physics

Tarzan tries to cross a river by swinging from one bank to the other on a vine that is 8.8 m long. His speed at the bottom of the swing is 7.2 m/s. Tarzan does not know that the vine has a breaking strength of 1.0 multiplied by 103 …
4. ### Physics

Tarzan tries to cross a river by swinging from one bank to the other on a vine that is 11.6 m long. His speed at the bottom of the swing is 7.4 m/s. Tarzan does not know that the vine has a breaking strength of 1.0 ✕ 103 N. …
5. ### Physics

Tarzan tries to cross a river by swinging from one bank to the other on a vine that is 8.2 m long. His speed at the bottom of the swing is 7.2 m/s. Tarzan does not know that the vine has a breaking strength of 1.0 ✕ 103 N. What …
6. ### Physics

Tarzan tries to cross a river by swinging from one bank to the other on a vine that is 8.2 m long. His speed at the bottom of the swing is 7.2 m/s. Tarzan does not know that the vine has a breaking strength of 1.0 ✕ 103 N. What …
7. ### physics

Tarzan tries to cross a river by swinging from one bank to the other on a vine that is 12.2 m long. His speed at the bottom of the swing is 8.6 m/s. Tarzan does not know that the vine has a breaking strength of 1.0 ✕ 103 N. …
8. ### NEED HELP PHYSICS!!!

Tarzan (m = 78.4 kg) tries to cross a river by swinging from a vine. The vine is 10 m long. Tarzan doesn't know that the vine has a breaking strength of 1045 N. What maximum speed (in m/s) can Tarzan have at the bottom of the swing …
9. ### Physics

Tarzan tries to cross a river by swinging from one bank to the other on a vine that is 11.2 m long. His speed at the bottom of the swing is 7.0 m/s. Tarzan does not know that the vine has a breaking strength of 1.0 ✕ 103 N. …
10. ### physics

Tarzan tries to cross a river by swinging from one bank to the other on a vine that is 11.2 m long. His speed at the bottom of the swing is 7.4 m/s. Tarzan does not know that the vine has a breaking strength of 1.0 ✕ 103 N. What …

More Similar Questions