Hey, /sci/, looking for physics help. I'm not understanding this problem, not looking for homework help per se, just comprehension.
So on a rollercoaster, at the top of a loop (pic related), what is the direction of the centripetal force?
My understanding was that it was always toward the center of rotation. A friend explained that in this case, gravity and normal force (from the tracks pushing back on the car) keep the car in rotation and the centripetal force is negative keeping the riders in the car.
Is this accurate?
Your friend is wrong and probably gay. Centripetal force is always radial and directed to the center. What is keeping the cart moving is the inertia of the tangential velocity at every point.
The plot thickens.
This is my exact problem with the correct answer and in the solution centripetal force is explained to be upward.
How does that make sense?
Centripital force is NOT outward.
Imagine spinning a ball in a string. If the force were radially outward, then upon cutting the string the ball would fly radially away, rather than tangentially.
That answer is wrong and stupid. Centripetal force is towards the center by definition. If the NET force were upward, it would be ACCELERATING upward, because f=ma. But it's not, it's accelerating downwards, i.e. moving in a circle.
So, moving on:
>What I'm not understanding is the direction and role of centripetal force in this case.
Centripetal force is towards the center, by definition. It's "role" is moving something in a circle. At that moment, gravity and normal force are both centripetal. Anything moving in a circle must have a net force directed towards the center.
>And what force is pushing upward (keeping the riders from falling out).
There are no forces pushing upward. That's why it's accelerating downwards.
centripidal force is always toward the center
I learned this in an algebra based physics class and it's one of the basic things needed to solve these kinds of problems, your friend is either retarded or doesn't study enough
Newton wanted to get rid of force in favor of acceleration. You can describe the dynamics in terms of a circular orbit, a balance of radial accelerations. Acceleration means force per mass, newton per kilogram. To stay on the track at the top, the balance requires that w^2*r (or v^2/r because v=w*r) is equal or greater than g, independent of mass.
In a similar manner you can use potential rather than energy. Potential is potential energy divided by the 'actor', in this case the mass. If you want to find the minimum initial velocity of the object at the bottom required to complete the loop, you look for the necessary kinetic potential (v^2/2) that meets the contact condition at the top after part of it has been converted to gravitational potential (g*h). This works whenever the process is lossless and does not depend on mass.
required radial acceleration at the top:
v1^2/r - g = 0 -> v1 = sqrt(g*r)
required kinetic potential at the top:
Uk1 = v1^2/2 = g*r/2
required kinetic potential at the bottom:
Uk0 - Ug = Uk1 -> Uk0 = Uk1 + Ug
v0^2/2 = g*r/2 + g*h, where h = 2r
v0^2/2 = g*r/2 + 2*g*r
v0^2 = 5*g*r
minimum velocity at the bottom:
v0 = sqrt(5*g*r)
He says "not looking for homework help per se, just comprehension" - increasing scientific understanding is one of the purposes of this board. Would you prefer another memedrive thread?
At the top of the loop, gravity IS the centripetal force.
Let me explain.
Consider the loop with the spinning car and no gravity. Where is the centripetal force in this scenario. Well, we know that in Newtonian physics, objects travel in straight lines at constant speed unless acted upon by a force. So the force is pointed inward toward the center, keeping the cart always moving around the loop.
So where does the force come? Easy, the loop itself. The material of the loop has a contact force that pushes the cart toward the center (the cart also exerts and equal-opposite force onto the loop).
Now add the gravity. At the bottom of the loop, gravity is added to the force of the loop, making you feel heavier. At the top of the loop, gravity is subtracted from the floop-pushing force, making you feel lighter (i.e. the cart pushes less against the loop).
In other words, gravity, in a matter of speaking, takes over some of the centripetal force burden away from the loop. The centripetal force equals the loop force plus gravity.
From this, we can see that is the loop force is zero (i.e., you are about to fall), gravity is the only force acting as the centripetal force.
The cart falls when the centripetal force acting on the cart is less than gravity.