Question

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 exerts 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

Answer 1

Answer:

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

Explanation:

At the bottom of the loop, the normal force is opposite to my weight.

I am making a circular motion. So,

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

The relationship between the normal force, my weight, my speed and the radius of the loop is

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

Here, my weight (mg) is constant. But the normal force is inversely proportional to my speed.

If my speed is zero, the normal force would be maximum and equal to my weight. If my speed is to much, then the normal force would be equally high too.