How to find Vmax squared for circular motion?

[Jade_lowe]

Homework Statement

Tarzan plans to cross a gorge by swinging in an arc from a hanging vine. if his arms are capable of exerting a force of 1500 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 4.5 m long.

Relevant Equations

Fmax= mvmax^2/r

T= m*vmax^2/r 1500 = (80kg)vmax^2/4.5

 

[erobz]

Homework Statement:: Tarzan plans to cross a gorge by swinging in an arc from a hanging vine. if his arms are capable of exerting a force of 1500 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 4.5 m long.
Relevant Equations:: Fmax= mvmax^2/r

T= m*vmax^2/r 1500 = (80kg)vmax^2/4.5

You forgot to consider Tarzans weight.

 

[Jade_lowe]

The mass is his weight.

 

[erobz]

The mass is his weight.

No. It isn’t. Do a free body diagram of Tarzan at the base of the swing.

 

[Jade_lowe]

This is what the question gave me.

 

[erobz]

This is what the question gave me.

We’ll, they should have stated local $g$ too, but you can assume 9.81 m/s².

 

[erobz]

Think about Tarzan just hanging there with zero velocity. Does your equation make sense for $v=0$ in terms of the tension developed in his arms?

 

[Lnewqban]

The mass is his weight.

Welcome, @Jade_lowe !

Our weight is a force (measured in Newtons) with which gravity pulls the mass (measured in kilograms) of our bodies down.

In free fall, our bodies are accelerated (the falling velocity increases) at a rate of 9.81 meters per second, for each second that goes by.