Uniform Circular Motion of Roller Coaster

In summary: There is also the force of inertia, which is the tendency of the book to keep moving in a straight line. So, the book has both a gravitational and inertial force acting on it at point A.
  • #1
Jdnotnice
2
0

Homework Statement


Assume the roller coaster cart rolls along the curved track from point A to point C under the influence of gravity. Assume the friction between the cart and track is negligible. What would be the direction of the carts acceleration at point A? (The question in the image does not match this question)
https://imgur.com/a/78YCo

Homework Equations


None[/B]

The Attempt at a Solution


I believe that the direction of acceleration is straight down, but people have been saying it goes down and to the right.[/B]
 
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  • #2
Hello. Welcome to PF!

The direction of the acceleration is determined by the direction of the net force acting on the cart.
upload_2017-11-8_13-20-47.png


So, decide what forces act on the cart at point A. Add the forces using vector addition in a sketch. Does the net force point straight down?

Note that the track at point A is essentially straight. So at point A, it's similar to a block sliding down an inclined plane. What is the direction of the acceleration of a block sliding down an inclined plane?
 

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  • #3
If you release the roller coaster from rest and the acceleration is straight down then the roller coaster will drop straight down just like a rock released from rest. Is that what happens, do you think?
 
  • #4
So, the acceleration is pointing up at point B because it is at equilibrium. I think at point a the cart has no momentum, so the only force acting on the cart would be gravity. Is this not correct?
 
  • #5
Jdnotnice said:
So, the acceleration is pointing up at point B because it is at equilibrium.
Equilibrium is when there is no acceleration. At point B the speed of the cart is not changing at that instant, but the cart can be thought of as moving along a circular arc at point B. When an object is moving in a circle at constant speed, does it have any acceleration? If so, what is the direction of the acceleration?

I think at point a the cart has no momentum, so the only force acting on the cart would be gravity. Is this not correct?
It is not correct. A book sitting on a table has no momentum. But gravity is not the only force acting on the book.
 

1. What is uniform circular motion?

Uniform circular motion is a type of motion in which an object moves in a circular path at a constant speed.

2. How is uniform circular motion related to roller coasters?

Roller coasters often use uniform circular motion to create thrilling and smooth rides. The circular motion allows the coaster to maintain a constant speed and direction, resulting in a continuous and exciting experience for riders.

3. What factors affect the uniform circular motion of a roller coaster?

The speed of the roller coaster, the radius of the circular path, and the mass of the roller coaster all affect the uniform circular motion. Additionally, external forces such as friction and air resistance can also impact the motion.

4. How is centripetal force involved in uniform circular motion of roller coasters?

Centripetal force is the force that keeps an object moving in a circular path. In the case of roller coasters, this force is provided by the track itself, which exerts a force towards the center of the circular path, allowing the coaster to maintain its motion.

5. Can the uniform circular motion of a roller coaster change?

Yes, the uniform circular motion of a roller coaster can change if there are changes in the factors that affect it, such as speed or radius. Additionally, external factors like wind or mechanical issues can also cause changes in the motion.

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