You ride a roller coaster with a loop-the-loop. Compare the normal force that the seat exerts on you to the force that Earth exe

Question

3 months ago

14

You ride a roller coaster with a loop-the-loop. Compare the normal force that the seat exerts on you to the force that Earth exe

rts on you when you are passing the bottom of the loop. Express your answer in terms of R (radius of the loop), vb (speed at the bottom of the loop), and constant g. Nbottom/mg

Physics

1 answer:

Softa [3K] · Answer 1 · 2026-02-28T20:11:37+03:00

Answer:

$N = mg + \frac{mv^2}{R}$

Explanation:

While at the loop's bottom, the normal force acts in opposition to my weight.

I am undergoing circular motion. Therefore,

$F_{net} = \frac{mv^2}{R}$

The connection between the normal force, my weight, my velocity, and the loop's radius is expressed as

$N - mg = \frac{mv^2}{R}\\mg = N - \frac{mv^2}{R}\\ N = mg + \frac{mv^2}{R}$

My weight (mg) remains unchanged. However, the normal force is inversely related to my velocity.

<pIf my velocity drops to zero, the normal force peaks and equals my weight. As my speed increases, the normal force rises as well.