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The Effect of Height on a Normal Force

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Sarah Jane Smith rides a friction less roller coaster with an initial hill height H (on top of which the car is barely moving. At the bottom, where the track has a radius of curvature R, the car has a speed V and she feels 25% heavier than her actual weight (that is, Fn = 1.25 Fg, where Fn is the normal force the seat exerts on her).
If the hill were four times as tall, the magnitude of the normal force acting on her at the bottom would be?

The answer is 2Fg.
I need help understanding why that is the answer.
On my own I have worked out that with 4x the height the velocity of the cart will double and that Fnet= Fnormal -Fgravity so Fnormal= Fnet + Fgravity.

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This solution provides steps to determine the effect of height on a normal force.

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Hello and thank you for posting your question to Brainmass.

At the bottom of the hill indeed we have:

N = W + Fc

Where N is the normal force and Fc is the centripetal force due to the curvature of the road.

Both the weight W and the centripetal force Fc point down at the ...

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