Uniform Circular Motion of Roller Coaster

[Jdnotnice]

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]

 

[TSny]

Hello. Welcome to PF!

The direction of the acceleration is determined by the direction of the net force acting on the cart.

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?

 

[kuruman]

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?

 

[Jdnotnice]

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?

 

[TSny]

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.