# Loop-the-loop Conservation of energy

• erice
In summary, the radius of the track has to be larger than the car's initial velocity in order to keep the car in contact with the track.
erice

## Homework Statement

A small car is given an initial velocity of 4 m/s (prior to reaching the loop), what is the largest value that the radius of a loop the loop can have so that the car remains in contact with the track at all times?

OK ... not sure if this is right... When the car is at the top of the loop the loop, the force of gravity has to equal the centrifugal force. If you draw a free body diagram at the moment it reaches the top of loop the loop, the car will have an arrow pointing downwards representing gravity and an arrow pointing upwards representing centrifugal force. Now, what is the equation for the centrifugal force? If you know that, equate the equation of gravity and the centrifugal force and solve for r.

Actually I think I'm wrong... Let me think about it a little more until I get the right answer and get back to you.

putongren said:
OK ... not sure if this is right... When the car is at the top of the loop the loop, the force of gravity has to equal the centrifugal force. If you draw a free body diagram at the moment it reaches the top of loop the loop, the car will have an arrow pointing downwards representing gravity and an arrow pointing upwards representing centrifugal force. Now, what is the equation for the centrifugal force? If you know that, equate the equation of gravity and the centrifugal force and solve for r.

Don't you have to take into account the loss of velocity as the car goes up the loop?

erice said:

## Homework Statement

A small car is given an initial velocity of 4 m/s (prior to reaching the loop), what is the largest value that the radius of a loop the loop can have so that the car remains in contact with the track at all times?

I'll give you a couple more hints. You need to use the fact that the centrifugal force and force of gravity must be equal and opposite and you need to note that the kinetic energy at the start goes into gravitational potential energy plus kinetic energy as the car goes up the loop. Thus you will have two equations for two unkonwns: the velocity at the top of the loop and the radius of the track.

## What is Loop-the-loop Conservation of energy?

Loop-the-loop Conservation of energy is a principle in physics that states that energy cannot be created or destroyed, but can only be transformed from one form to another. In the case of a loop-the-loop, the potential energy of the object at the top of the loop is transformed into kinetic energy as it moves down the loop, and then back into potential energy as it reaches the top again.

## How does Loop-the-loop Conservation of energy apply to roller coasters?

Roller coasters use the principle of Loop-the-loop Conservation of energy to provide a thrilling and safe ride. The initial potential energy of the coaster at the highest point is converted into kinetic energy as it moves down the first hill. The coaster then uses this kinetic energy to complete the loop-the-loop and continue along the track, while maintaining a constant overall energy throughout the ride.

## What factors affect the conservation of energy in a loop-the-loop?

The main factors that affect the conservation of energy in a loop-the-loop are the initial height of the object, the mass of the object, and the forces acting on the object, such as gravity and friction. Additionally, the shape and steepness of the loop can also impact the conservation of energy and determine whether the object successfully completes the loop or not.

## Can energy be lost in a loop-the-loop?

No, according to the principle of Loop-the-loop Conservation of energy, energy cannot be lost. However, some energy may be converted into other forms, such as heat or sound, due to external factors such as friction. This is why roller coasters have brakes to slow down and dissipate any excess energy.

## What are some real-life examples of Loop-the-loop Conservation of energy?

Aside from roller coasters, some other real-life examples of Loop-the-loop Conservation of energy include swinging pendulums, bouncing balls, and swinging on a playground swing. In all of these situations, the energy of the object is constantly being transformed from potential to kinetic and back again, while maintaining a constant overall energy.

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