Tarzan's River Crossing Dilemma: Can He Swing Across Safely?

[mikesown]

"Tarzan" problem

Homework Statement

"Tarzan (m=85kg) tries to cross a river by swinging from a 10.0m long vine. His speed at the bottom of the swing, just as he clears the water, is 8.0 m/s. Tarzan doesn't know that the vine has a breaking strength of 1.0 x 10^3 N Does he make it safely across the river? Justify your answer."

Homework Equations

$$F_{c}=\frac{mv_{t}^2}{r}$$

The Attempt at a Solution

I attempted to substitute in the variables as such:
$$F_{c}=\frac{85kg*\left(8.0\frac{m}{s}\right)^2}{10.0m}$$
I got 544N, which is not the answer(1.37x10^3N is his 'weight' at this point, greater than the rope). Am I missing something obvious?

 

[Gib Z]

You do not have the right formula. You are thinking of Centripetal Force, this is Pendulum Motion.

 

[PhanthomJay]

Homework Statement

"Tarzan (m=85kg) tries to cross a river by swinging from a 10.0m long vine. His speed at the bottom of the swing, just as he clears the water, is 8.0 m/s. Tarzan doesn't know that the vine has a breaking strength of 1.0 x 10^3 N Does he make it safely across the river? Justify your answer."

Homework Equations

$$F_{c}=\frac{mv_{t}^2}{r}$$

The Attempt at a Solution

I attempted to substitute in the variables as such:
$$F_{c}=\frac{85kg*\left(8.0\frac{m}{s}\right)^2}{10.0m}$$
I got 544N, which is not the answer(1.37x10^3N is his 'weight' at this point, greater than the rope). Am I missing something obvious?

You have correctly identified the centripetal force as 544N. The centripetal force is the net force acting up toward the center of the circle. The net force is a combination of the tension force up and his weight (not his 'weight' as you have described...his weight is m*g) down. Solve for T. Does the rope break?

 

[ShawnD]

The net force is a combination of the tension force up and his weight

This is correct. Add 544N to (85 x 9.8) and you get 1377N

 

[Gib Z]

Is it too late to pretend I haven't said anything? eep my bad, just ignore anything i say