# Vertical circle in a pendulum ride -- tension force acting on the gondola

• Nikitta
In summary, the tension force at the bottom of the circle is greater than the weight force, as there must be a net force acting towards the center to provide the centripetal force for circular motion. When using the equation T = mv^2/r + mg to calculate the velocity of an object at the bottom of the circle, only the mass and radius are needed. To find the rotational kinetic energy for the top of the circle, the total energy of the system, gravitational potential, linear and rotational kinetic energy must be considered. However, if no data is given for rotational kinetic energy, it can be ignored. In terms of tension and reaction forces, the tension force on the gondola is equal to the reaction force that the g
Nikitta
Homework Statement
In a vertical circle more specifically in a pendulum ride, there is a tension force acting on the gondola and a reaction force by the gondola acting on the passengers. How do you know the tension force and reaction force are equal and how do you find the reaction/tension force at the bottom of the circle?
Relevant Equations
T = mv^2/r + mg
Ep=mgh
V (critical) = SQRT(gr) (velocity at top of circle)
Ek (lin) = 1/2mv^2
Ek (rot) = 1/2Iw^2
Ek (total) = 1/2mv^2 + 1/2Iw^2
At the bottom of the circle, the tension force is greater than the weight force as there must be a net force acting towards the centre to provide the centripetal force causing the centripetal acceleration and thus the circular motion. In the equation above (T = mv^2/r + mg) I only have the mass and radius. I tried to find the velocity of the object at the bottom of the circle by using conservation of energy (Ep lost = Ek gained). I tried to find the total energy of the system, gravitational potential, linear and rotational kinetic energy at the top, however, I could not find the rotational kinetic energy (don't have I). Does the rotational kinetic energy need to be taken into account (In other problems about vertical circle the rotational kinetic is usually not involved, is there any rotational kinetic energy?)

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Nikitta said:
there is a tension force acting on the gondola and a reaction force by the gondola acting on the passengers. How do you know the tension force and reaction force are equal
I wouid think the gondola has mass, and it is undergoing acceleration as well as being subject to gravity , so why would these two forces be equal? Is this the exact wording?
Nikitta said:
Does the rotational kinetic energy need to be taken into account
Technically, yes, but if you not given any data for that assume you are meant to ignore it.

haruspex said:
I wouid think the gondola has mass, and it is undergoing acceleration as well as being subject to gravity , so why would these two forces be equal? Is this the exact wording?

Technically, yes, but if you not given any data for that assume you are meant to ignore it.
in this video she says that the tension force on the cup (kind of like the gondola) is equal to the reaction force that the cup exerts on the water (kind of like the passengers)

Nikitta said:
in this video she says that the tension force on the cup (kind of like the gondola) is equal to the reaction force that the cup exerts on the water (kind of like the passengers)

Also how would you estimate the rotational inertia of an object, since for each object there is a different equation and for some there is no equation (could I just use 2 equations one for a rod and the other for a hoop and add them together?). I have the mass and length of the object.

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Nikitta said:
I have the mass and length of the object.
Nikitta said:
in this video she says that the tension force on the cup (kind of like the gondola) is equal to the reaction force that the cup exerts on the water
Only if the mass of the cup is ignored. It is rather more dubious to ignore the mass of a gondola, which may well exceed the mass of the occupants.

haruspex said:
Only if the mass of the cup is ignored. It is rather more dubious to ignore the mass of a gondola, which may well exceed the mass of the occupants.
I think I understand now. If I am calculating the tension force (T=mv^2/r + mg) at the bottom I would use the mass of the gondola and passengers combined, but if I am calculating the reaction force (Fn=mv^2/r + mg) I would only use the mass of the passenger. Is this correct? Thanks

haruspex said:
Sorry I can't edit the initial post. Mass (gondola + tube) = 12,000 kg, length (tube) = 15 m and the diameter of the gondola = 6 m. I don't think I have enough information to estimate the rotational inertia, I'm assuming that I would need to have the mass of the gondola and tube separate, but thanks for your help.

Nikitta said:
I think I understand now. If I am calculating the tension force (T=mv^2/r + mg) at the bottom I would use the mass of the gondola and passengers combined, but if I am calculating the reaction force (Fn=mv^2/r + mg) I would only use the mass of the passenger. Is this correct? Thanks
Yes.
Nikitta said:
Sorry I can't edit the initial post.
I meant, in future.

## 1. What is a vertical circle in a pendulum ride?

A vertical circle in a pendulum ride is a circular path that is perpendicular to the ground and has a constant radius. It is formed when a pendulum ride swings back and forth, creating a circular motion.

## 2. How does the tension force act on the gondola in a vertical circle?

The tension force acts on the gondola in a vertical circle by pulling it towards the center of the circle. This force is responsible for keeping the gondola moving in a circular path and preventing it from flying off the ride.

## 3. What factors affect the tension force in a vertical circle pendulum ride?

The tension force in a vertical circle pendulum ride is affected by the mass of the gondola, the speed at which it is moving, and the radius of the circle. The larger the mass or speed, the greater the tension force will be. Additionally, a smaller radius will also lead to a higher tension force.

## 4. Is the tension force constant throughout the vertical circle?

No, the tension force is not constant throughout the vertical circle. It is highest at the bottom of the circle when the gondola is accelerating downwards and decreases as it moves upwards. This is due to the change in direction of the velocity and acceleration vectors.

## 5. How does the tension force affect the riders on a vertical circle pendulum ride?

The tension force on a vertical circle pendulum ride can create a feeling of weightlessness or increased g-forces on the riders. This can add to the thrill and excitement of the ride. However, if the tension force is too high, it can also lead to discomfort or even injury for the riders.

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