extra force

[Gareth56]

At the top of a rollercoaster loop gravity is sufficient to provide the necessary centripetal force, however at the bottom of the loop gravity is pointing away from the centre so other than the normal force (which I presume balances mg) where does the extra inward force come from which supplements the normal force thus contributing to the feeling of heaviness and keeps you moving in a circle?

 

Thanks

[Sisyphus]

It is only the normal force. It doesn't have to balance mg, it just does when you're standing there because that's how much you're exerting on the ground.

[Gareth56]

Thanks but I don't suppose you could expand your reply for layman

What the difference (physics wise) from the normal force when your standing still and when siting in a rollercoaster car.

[swansont]

the normal force (which I presume balances mg)

 

You presume too much.

 

If an object is moving in a circle, there must be a net force toward the center, equal to mv^2/r, thus the normal force can't cancel/balance mg

[Gareth56]

So if the normal force balances the gravitational force when I'm standing still why does the magnitude of the normal force increase and where does the "extra" normal force come from when I'm travelling through the bottom of roller coaster loop.

[D H]

One way to look at the normal force is as a constraint force. In the case of the roller coaster, you know the net force (the force needed to make the roller coaster behave as it does). You also know that the only forces acting on the roller coaster are gravity and the normal force:

 

[math]{\mathbf F}_{net} = {\mathbf F}_{grav} + {\mathbf F}_{normal}[/math]

 

and thus you know what the normal force must be in order to yield the constrained behavior.

 

Asking where the "extra" normal force comes from begs the question, where does the normal force come from, period. The normal force is a macroscopic-world manifestation of the electrostatic force.

 

Suppose an empty roller coaster car is standing still on a rail. The car is not sitting directly on the rail. It is instead hovering above the rail by a tiny, tiny amount. The electrons in the car's wheels and the electrons in the rail repulse one another. The separation distance between the wheels and tracks is just that needed to make the electrostatic force balance the weight of the car. If the separation distance is greater than this balance point (i.e., the car is floating a bit too high above the tracks), the repulsive force will be less than needed, making for a downward net force that decreases the separation distance. The opposite happens when the separation distance is too small. The net force will be upward, increasing the separation distance.

 

Now imagine some people get in the car. The separation distance needs to decrease to balance the increased weight of the car. The exact same thing happens when the car is moving around the loop. So, to answer the question "where does the 'extra' normal force come from", it comes from a decreased separation distance between the wheels and the rails.

[Gareth56]

Thanks D H, I think I followed that however I did think that the car was in intimate contact with the rails.

 

Would the same happen i.e. a feeling on heaviness at the bottom of a loop if the car was in magnetic contact with the rails like a maglev train?

[swansont]

Thanks D H, I think I followed that however I did think that the car was in intimate contact with the rails.

 

Depends on how closely you look, and how you define "contact."

 

Would the same happen i.e. a feeling on heaviness at the bottom of a loop if the car was in magnetic contact with the rails like a maglev train?

 

Sure. If you are moving in a circle, the centripetal acceleration equation must be satisfied.

[D H]

Thanks D H, I think I followed that however I did think that the car was in intimate contact with the rails.

On an atomic scale there is no such thing as "intimate contact". For example, the atoms in the steel roller coaster rails are separated by about 300 picometers. The atoms can get quite a bit closer under extreme compression because there's a lot of empty space even inside the rails.

 

Would the same happen i.e. a feeling on heaviness at the bottom of a loop if the car was in magnetic contact with the rails like a maglev train?

You will feel the same thing. There's just a different mechanism supplying the constraint force.