Calculating Minimum Speed at Top of Vertical Loop

If so, you can use that to find the work done by friction, which is equal to the energy taken away from the car. Then, use that value to find the friction force, which can be used to find the coefficient of friction. Then, use that coefficient to find the maximum friction force that the car can experience before it slips. In summary, the problem involves finding the maximum amount of energy taken away from a roller coaster car by friction in order for it to successfully travel through a vertical loop with given parameters. This can be solved by using the work-energy theorem and considering the normal force and coefficient of friction.
  • #1
SamLing2000
6
0

Homework Statement


A 330 kg roller coaster car sits on a horizontal track. Ahead of it is a vertical loop with radius of 6.85 m. The car is given an initial speed of 23.4 m/s and the car successfully traverses the loop. What is the maximum amount of energy taken away from the car by friction so that the car successfully travels through the loop? (Hint: think about the normal force that the track exerts on the car at the top of the loop, this should give you a minimum speed at the top of the loop.)

m=330
vo = 23.4
r=6.85

Homework Equations


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The Attempt at a Solution


??
I am sorry but I have no clue as to how to approach this problem. Please point me in the right direction, hints and suggestions are extremely welcome.
I also find a Hint for the problem but i wasn't able to make as much use of this one as I thought.
(Hint: think about the normal force that the track exerts on the car at the top of the loop, this should give you a minimum speed at the top of the loop
 
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  • #2
Any help is appreicated.
 
  • #3
Have you learned about work-energy theorem?
 

1. How does a cart stay on a vertical loop track?

The cart stays on the vertical loop track due to the combination of centripetal force and gravity. The track is designed in a way that the cart maintains enough speed to produce the necessary centripetal force to keep it on the track while gravity pulls it downwards.

2. What is the minimum and maximum speed required for a cart to complete a vertical loop?

The minimum speed required for a cart to complete a vertical loop is when the centripetal force is equal to the force of gravity, which is at the top of the loop. The maximum speed is at the bottom of the loop, where the centripetal force is at its highest and gravity is at its lowest. The exact speeds vary depending on the dimensions of the loop.

3. How does the height of the loop affect the cart's speed and force?

The height of the vertical loop affects the speed and force of the cart by changing the amount of potential and kinetic energy it has. A higher loop will result in a higher potential energy at the top and a faster speed at the bottom. It also increases the centripetal force needed to keep the cart on the track.

4. Can a cart complete a vertical loop if it loses speed during the loop?

Yes, a cart can still complete a vertical loop even if it loses some speed during the loop. As long as it maintains enough speed to produce the necessary centripetal force to stay on the track, it will complete the loop. However, if it loses too much speed, it may not have enough force to complete the loop and will fall off the track.

5. What factors can affect the success of a cart completing a vertical loop?

The success of a cart completing a vertical loop can be affected by several factors, including the dimensions and shape of the loop, the initial speed of the cart, and the force of gravity. Friction and air resistance can also play a role in slowing down the cart and affecting its ability to complete the loop. Additionally, the weight and distribution of the weight of the cart can impact its speed and force during the loop.

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