Question

A) You are on an rollercoaster at an amusement park. When you are upside-down at the top of a circular loop with a radius of 30 m, you feel 5.5 times heavier than usual.
What is your actual weight as you go through the top of the loop? (apparent weight at the top)
6.5mg, upward
5.5mg, upward
5.5mg, downward
4.5mg, downward
mg, downward

B) What is the normal force acting on you as you are upside-down going through the top of the loop?
mg, upward
mg, downward
6.5mg, upward
5.5mg, upward
5.5mg, downward

C) What is the total force acting on you as you are upside-down going through the top of the loop?
6.5mg, upward
0
4.5mg, upward
mg, upward
6.5mg, downward

D) What is your acceleration as you are upside-down going through the top of the circular loop?
mg, downward
v²/r, upward
mg, upward
0
v²/r, downward

E) Using Newton's 2nd Law and your answers to the previous questions, find how fast are you moving while are you upside-down at the top of the loop.

43.7 m/s	17.1 m/s	0 m/s	40.2 m/s	36.4 m/s

Answer 1

A)

for the actual weight as you go through the top of the loop

as the actual weight is same at all points near the surface of earth

mg , downwards

B)

for the normal force

Normal force = 5.5mg , downward

the normal force is 5.5mg , downwards

C)

for the total force

total force = 5.5g + mg = 6.5 mg

the total force 6.5 mg downwards

D)

for the acceleration

the acceleration is centripetal

the correct option is v^2/r , downwards

E)

let the speed is v

v^2/R = 6.5 * g

v^2/30 = 6.5 * 9.8

solving for v

v = 43.7 m/s

the speed is 43.7 m/s