Circular motion of a loop-the-loop machine

In summary, the minimum speed required for a cart to safely loop the loop on a loop-the-loop machine with a radius of 18m is dependent on energy conservation. The initial kinetic energy must equal the potential energy at the top of the loop. The cart must also have some excess velocity to maintain centripetal acceleration and the mass will not affect the calculation.
  • #1
busted
24
0
A loop-the-loop machine has radius R of 18m.
a)What is the minimum speed at which a cart must travel so that it will safely loop the loop?

I am unsure which formula to use as I know it has something to do with KE and GPE. I was thinking it might be :

v = square root ____(2GM)______
r

but it can't be as we don't the mass.

any ideas?
 
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  • #2
Hi there busted and welcome to PF,

Your an the right tracks with energy. Energy must be conserved, ignoring friction all the kinetic energy at the bottom of the loop will be converted into potential energy and the top of the loop. Therefore, at the minimum speed the initial kinetic energy must equal the potential energy at the top of the loop. Do you follow?
 
  • #3
The trick to this is to remember it needs to have some excess velocity (and therefore KE) to get round, it can't have v=0 at the top, else it would fall vertically. The constraint for the particle at the top of the turn is centripetal acc=g.

Also, the mass cancels.
 
Last edited:
  • #4
thanks guys i'll hav a go working it out
 

FAQ: Circular motion of a loop-the-loop machine

1. What is a loop-the-loop machine?

A loop-the-loop machine is a type of amusement park ride that consists of a track in the shape of a loop and a cart that travels along the track. The cart gains enough momentum to complete a full loop without falling off the track.

2. How does a loop-the-loop machine work?

A loop-the-loop machine works by using the principles of circular motion and centripetal force. The cart starts at the top of the loop with enough potential energy to overcome gravity and complete the loop. As the cart moves along the track, it experiences a constant change in direction, causing it to accelerate towards the center of the loop due to the centripetal force. This force keeps the cart on the track and prevents it from falling off.

3. What factors affect the speed of a loop-the-loop machine?

The speed of a loop-the-loop machine is affected by several factors, including the height of the loop, the mass of the cart, and the force of gravity. A higher loop will require more speed to complete the loop, while a heavier cart will need more energy to overcome gravity. The force of gravity also plays a significant role in determining the speed of the cart as it travels along the track.

4. Is it safe to ride a loop-the-loop machine?

Yes, it is generally safe to ride a loop-the-loop machine. These rides are designed with safety features such as restraints and emergency brakes to ensure the riders' safety. However, it is essential to follow all safety instructions and guidelines provided by the amusement park to prevent any accidents.

5. Can a loop-the-loop machine be used for educational purposes?

Yes, a loop-the-loop machine can be used for educational purposes. It demonstrates the principles of circular motion, centripetal force, and energy conservation. By studying the speed and height of the loop, students can also learn about the relationship between potential and kinetic energy. Many physics classes use loop-the-loop machines as a hands-on way to understand these concepts.

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