# Finding Centripetal acceleration in a vertical system

• Anonymous117
In summary, Tarzan, who has a mass of 78 kg, plans to cross a gorge by swinging from a hanging vine with a length of 5.2 m. At the point where the vine makes a 45 degree angle from the vertical, assuming maximum speed, his arms can exert 1350 N of force. Using this information, his acceleration at this point is 12.5 m/s/s inward.
Anonymous117

## Homework Statement

Tarzan plans to cross a gorge by swinging in an arc from a hanging vine. If his arms are capable of exerting 1350 N on the vine, what is his acceleration at the point where the vine makes an angle of 45 degrees from the vertical assuming maximum speed at this point. His mass is 78 kg and the vine is 5.2 m long.

## Homework Equations

Maybe I plugged in some of the numbers wrong and if I did, did I at least tackle the problem correctly?

## The Attempt at a Solution

I feel like I am missing something when I go through this but what I did was:
Tension would have to be 1350 right so
x direction: Fcx=Tsin(45) => 954.6N=Fcx
y direction: Fcy=Tcos(45)+Fg => 954.6 N - 764.4 N = 190.2 N = Fcy

(Fcx^2+Fcy^2)^0.5 = Fc = 973.4 N

973.4 N / 78 kg = 12.5 m/s/s inward

Anonymous117 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 1350 N on the vine, what is his acceleration at the point where the vine makes an angle of 45 degrees from the vertical assuming maximum speed at this point. His mass is 78 kg and the vine is 5.2 m long.

## Homework Equations

Maybe I plugged in some of the numbers wrong and if I did, did I at least tackle the problem correctly?

## The Attempt at a Solution

I feel like I am missing something when I go through this but what I did was:
Tension would have to be 1350 right so
x direction: Fcx=Tsin(45) => 954.6N=Fcx
y direction: Fcy=Tcos(45)+Fg => 954.6 N - 764.4 N = 190.2 N = Fcy

(Fcx^2+Fcy^2)^0.5 = Fc = 973.4 N

973.4 N / 78 kg = 12.5 m/s/s inward
It looks correct.

## 1. What is centripetal acceleration?

Centripetal acceleration is the acceleration that an object experiences when moving in a circular path. It is always directed towards the center of the circle and its magnitude is given by the equation: a = v^2/r, where v is the velocity and r is the radius of the circle.

## 2. How is centripetal acceleration different in a vertical system?

In a vertical system, gravity also plays a role in the acceleration of an object. This means that the total centripetal acceleration is a combination of the acceleration due to circular motion and the acceleration due to gravity. The direction of the centripetal acceleration in a vertical system may also change as the object moves through different points in the circle.

## 3. How do you calculate centripetal acceleration in a vertical system?

To calculate the centripetal acceleration in a vertical system, you need to take into account both the acceleration due to circular motion and the acceleration due to gravity. You can find the total centripetal acceleration by using the equation: atotal = sqrt((acircular)^2 + (ag)^2), where acircular is the acceleration due to circular motion and ag is the acceleration due to gravity.

## 4. What factors affect the centripetal acceleration in a vertical system?

The centripetal acceleration in a vertical system is affected by the speed of the object, the radius of the circle, and the acceleration due to gravity. Increasing the speed or decreasing the radius will result in a larger centripetal acceleration, while increasing the acceleration due to gravity will decrease the centripetal acceleration.

## 5. How is centripetal acceleration used in real-world applications?

Centripetal acceleration is used in various real-world applications, such as amusement park rides, roller coasters, and satellite orbits. It is also essential in understanding the behavior of objects moving in circular paths, such as cars turning a corner or planets orbiting around the sun.

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