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

46.9 m/s

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 (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:

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

Substituting into the equation,

Which means

Here the radius of the loop is

r = 56.0 m

So, the speed needed is:

yea sure

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