# How to find Vmax squared for circular motion?

In summary: So, when we fall for 1 second, our velocity increases by 9.81 m/s. After 2 seconds, our velocity will be 2 x 9.81 = 19.62 m/s. After 3 seconds, our velocity will be 3 x 9.81 = 29.43 m/s, and so on.The force of gravity pushing on an object is the mass of the object, multiplied by the acceleration of gravity (9.81 m/s²).In summary, the equation T= m*vmax^2/r represents the maximum tension Tarzan can tolerate while swinging on a vine, with a mass of 80 kg and a vine length of 4.5 m. Considering Tarzan
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

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.

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.

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?

The mass is his weight.

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.

## 1. How do you calculate Vmax squared for circular motion?

To calculate Vmax squared for circular motion, you can use the formula Vmax^2 = r * ω^2, where r is the radius of the circle and ω is the angular velocity. This formula is derived from the equation for centripetal acceleration, a = r * ω^2.

## 2. What is the significance of Vmax squared in circular motion?

Vmax squared represents the maximum velocity that an object can achieve in circular motion. It is important because it helps us understand the speed and acceleration of objects moving in circular paths.

## 3. Can Vmax squared be negative in circular motion?

No, Vmax squared cannot be negative in circular motion. This is because velocity and speed are always positive quantities, and squaring a negative number will result in a positive number.

## 4. How does Vmax squared change with radius in circular motion?

In circular motion, Vmax squared is directly proportional to the radius of the circle. This means that as the radius increases, so does Vmax squared. This relationship is described by the formula Vmax^2 = r * ω^2.

## 5. Is Vmax squared the same as tangential velocity?

No, Vmax squared and tangential velocity are not the same. Vmax squared represents the maximum velocity an object can achieve in circular motion, while tangential velocity is the instantaneous velocity of an object at a specific point on its circular path.

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