How to find Vmax squared for circular motion?

AI Thread Summary
To find Vmax squared for Tarzan's swing, the equation T = m*vmax^2/r is used, where T is the maximum force exerted (1500 N), m is Tarzan's mass (80 kg), and r is the vine length (4.5 m). The discussion highlights the importance of considering gravitational force, as Tarzan's weight affects the tension in the vine. A free body diagram is suggested to clarify the forces at play when Tarzan is at the lowest point of his swing. The gravitational acceleration is assumed to be 9.81 m/s², which is essential for accurate calculations. Understanding these dynamics is crucial for determining the maximum speed Tarzan can tolerate during his swing.
Jade_lowe
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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
 
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Jade_lowe said:
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.
 
The mass is his weight.
 
Jade_lowe said:
The mass is his weight.
No. It isn’t. Do a free body diagram of Tarzan at the base of the swing.
 
This is what the question gave me.
 
Jade_lowe said:
This is what the question gave me.
We’ll, they should have stated local ##g## too, but you can assume 9.81 m/s².
 
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?
 
Jade_lowe said:
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.
 
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