# Toy car executing a vertical loop

• Jared C
In summary, the conversation discusses a problem involving a toy car sliding down an elaborate track and going around a vertical loop. The minimum speed the car needs to have at the bottom of the loop to make it all the way around without falling off is determined using the work-energy theorem and considering the forces and acceleration at the top of the loop. The solution involves calculating the speed at which the car just starts to lose contact at the top of the loop and using that to work backwards to determine the minimum speed at the bottom.
Jared C

## Homework Statement

A small toy car slides down an elaborate track. At one point during this trip, the car will go around a vertical loop with radius 15cm as shown. What is the minimum speed the car must have at the bottom of the loop in order to make it all the way around the loop without falling off?

## Homework Equations

Ki + Ui + WNC = Kf + Uf
K = (1/2)mv2
Ui = mgh
W = Fdcosx
F = ma
ac = v2/r

## The Attempt at a Solution

I tried using the work-energy theorem, using (1/2)mv2 = mgh to find the velocity needed for the car to have zero potential energy at the top of the loop, but I know this problem also involves centripetal acceleration and that the car would also need to have some velocity at the top of the loop to finish going around it (zero velocity would cause it to fall downward), but I have no clue how to use this to solve the problem

Last edited by a moderator:
The key to this problem is that when the car reaches the top of the loop, it is at the speed where it is just at the point where it starts to lose contact with the ramp. In other words, the normal force from the track is equal to 0. So at the bottom of the ramp, you could define that as the point where all of the car's energy is kinetic energy (0 potential energy). So you would have to calculate what speed it would be where the car just starts to lose contact at the top of the loop and work from there. I hope that helps.

Welcome to Physics Forums.

Jared C said:
zero velocity would cause it to fall downward
Quite so.
Draw a free body diagram for it when at the top of the loop. What forces act on it? What is the net force? What acceleration needs to result?

## 1. How does a toy car successfully execute a vertical loop?

A toy car can successfully execute a vertical loop by having enough speed and momentum to maintain its trajectory throughout the loop. It also needs a stable center of gravity and a smooth track with no obstructions.

## 2. What factors affect the toy car's ability to execute a vertical loop?

The main factors that affect the toy car's ability to execute a vertical loop are its speed, momentum, center of gravity, and the track's design and smoothness. Other factors such as the weight and size of the car may also play a role.

## 3. Can any toy car execute a vertical loop?

No, not all toy cars are designed to execute a vertical loop. Toy cars need to have specific features such as a low center of gravity, aerodynamic design, and a smooth underside to successfully complete a vertical loop.

## 4. How can I make a toy car execute a vertical loop?

If you want to make a toy car execute a vertical loop, you can try modifying its design by lowering its center of gravity, making it more aerodynamic, or adding weights to increase its momentum. You can also experiment with different track designs to find the best one for your toy car.

## 5. Is executing a vertical loop safe for the toy car?

It depends on the speed and design of the track and the toy car itself. If the car has enough speed and the track is smooth and obstacle-free, executing a vertical loop should not cause any harm to the toy car. However, if the car is not designed for vertical loops or the track is not suitable, it can result in damage to the car or even accidents.

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