Question

You are riding a roller-coaster going around a vertical loop, on the inside of the loop. If the loop has a radius of 56.0 m, how fast must the cart be moving in order for you to feel 3 times as heavy at the bottom of the loop? g

Answer 1

46.9 m/s

Step-by-step explanation:

When the cart is at the bottom of the loop, there are two forces acting on the person:

- The force of gravity, acting downward, of magnitude
`mg` (where m is the mass and g is the acceleration due to gravity)

- The normal reaction exerted on the person, acting upward, of magnitude N

Their resultant must be equal to the centripetal force, so the equation of the forces at the bottom of the loop is:

`N+mg=m(v^2)/(r)`

where v is the speed of the cart at the bottom of the loop and r the radius of the loop.

N represents the apparent weight of the person in the cart: here we are told that the person must feel 3 times as heavy, this means that

`N=3mg`

Substituting into the equation,

`3mg+mg=m(v^2)/(r)`

Which means

`v=√(4gr)`

Here the radius of the loop is

r = 56.0 m

So, the speed needed is:

`v=√(4(9.8)(56.0))=46.9 m/s`