Determining Speed of Toy at Top of Loop-the-Loop

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In summary, the conversation discusses the required speed for a 100g toy to successfully complete a loop-the-loop with a .5m diameter without falling. The solution involves considering the normal force and force of gravity at the top of the loop, and understanding that the normal force approaches 0 when the car is about to lose contact with the track.
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dranseth
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Homework Statement




A toy with a mass of 100g is going through a loop-the-loop with a diameter of .5m. How fast must the car be moving at the top of the loop in order to not fall.




The Attempt at a Solution



At the top of the loop, there is a normal force (Fn) and the force of gravity (Fg). I'm not sure how to do this. Do I neglect one of the forces? Set one to zero, or what?
 
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  • #2
What happens to the normal force when the car is just about to lose contact with the track?
 
  • #3
Fn approaches 0. Thanks.
 

1. What is the purpose of determining the speed of a toy at the top of a loop-the-loop?

The purpose is to understand the physics behind the toy's motion and to determine the minimum speed required for the toy to successfully complete the loop-the-loop without falling off.

2. How is the speed of the toy calculated at the top of the loop-the-loop?

The speed can be calculated using the formula v = √(gr), where v is the speed, g is the acceleration due to gravity (9.8 m/s²), and r is the radius of the loop-the-loop.

3. What factors can affect the speed of the toy at the top of the loop-the-loop?

The factors that can affect the speed include the initial velocity of the toy, the mass of the toy, the angle of the loop-the-loop, and the presence of any external forces such as friction or air resistance.

4. Can the speed of the toy at the top of the loop-the-loop be greater than the initial velocity?

Yes, it is possible for the speed at the top of the loop-the-loop to be greater than the initial velocity if the toy gains additional speed due to the force of gravity as it moves through the loop.

5. How can the speed of the toy at the top of the loop-the-loop be used to improve the design of the toy?

By determining the minimum speed required for the toy to complete the loop-the-loop successfully, designers can adjust the initial velocity and other factors to ensure that the toy is able to successfully complete the loop without falling off. This can lead to a more enjoyable and safe experience for users.

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