Rollercoasters and Loops and Normal Forces

In summary, the task is to find the normal force at the top of a loop, given the variables m, g, and r. The solution involves using the equation ∑F = Fc = FN+Fg, and after some calculations, the general equation for the normal force at the top of the loop is found to be N = mV2/r - mg. The previous attempt at solving for the normal force only yielded the minimum height, so the general equation is needed. An image of the work is also provided.
  • #1
komarxian
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Homework Statement


<I will attach a diagram below> In terms of m, g and r. FInd the normal force at the top of the loop.

Homework Equations


∑F = Fc = FN+Fg ∴ Fc=FN+Fg ∴FN = Fc - Fg ∴ N=mV2/r - mg

The Attempt at a Solution


Fc=mV2/r - mg and V2=ra and a=g ∴C=mrg/r ∴C = mg ∴mg-mg=N ∴ N=0 N. BUT after discussing with a guy in AP Physics C at my school, he said that this is solving for the minimum height. SO I think I need to solve for the general equation to solve for the normal force at the top of the loop at any height using the variables m, g, and r only (I'm pretty sure that's what my instructions meant). Could anyone help please? I will send an image of my work as well.
 
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Related to Rollercoasters and Loops and Normal Forces

1. How do roller coasters stay on their tracks?

Roller coasters have wheels attached to the bottom of the cars that run along the track, keeping the cars securely on the track. In addition, the track is specifically designed with dips, curves, and loops to maintain the momentum and prevent the cars from flying off.

2. What is the purpose of loops in roller coasters?

Loops are designed to provide thrill and excitement for riders. They also increase the vertical and lateral g-forces experienced by riders, adding to the feeling of weightlessness and intensity of the ride.

3. How do roller coasters create normal forces?

Normal forces are created by the track pushing back on the car and the riders. As the car travels through loops and curves, the track exerts a force on the car in the opposite direction to keep it on the track. This force is what riders feel as they are pressed into their seats or pushed against the restraints.

4. Are normal forces dangerous on roller coasters?

No, normal forces are not dangerous as long as they are within a safe range. The human body can typically handle up to 5 g-forces before experiencing discomfort or potential injury. Roller coasters are designed with this in mind and are tested rigorously to ensure the normal forces are within a safe range for riders.

5. How do engineers design roller coasters to minimize the effects of normal forces on riders?

Engineers use various design techniques, such as banked turns and gradual changes in velocity, to minimize the effects of normal forces on riders. By carefully calculating and adjusting the track's shape and speed, engineers can create a smooth and enjoyable ride while still maintaining the thrill and excitement of a roller coaster.

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