Roller coaster minimum speed around loop and effective weight

[and9]

Homework Statement

A roller coaster goes around a vertical loop of 20.0m. a) What is the minimum speed the cars must be moving so that the passengers do not fall out at the top? b) Assuming that the car maintains the same constant speed what is th effective weight of the passengers at the bottom? c) Again assuming car maintains this same constant speed, what is the net force (magnitutde and direction) acting on a 25kg passenger at point half way down the loop?

2. My attempt at solution

a) At top, N -> 0
N + mg = m(v²/r)
mg=m(v²/r)
g=v²/r
v_min=sqrt(rg) = 14 m/s

b) At bottom, N counters mg
N - mg = m(v²/r)
N = m((v²/r) + g)
N = m (9.8 + g) = 19.6m or 2mg

c) I had no idea what to do here?

 

[tiny-tim]

Welcome to PF!

Hi and9! Welcome to PF!

c) Again assuming car maintains this same constant speed, what is the net force (magnitutde and direction) acting on a 25kg passenger at point half way down the loop?
…
c) I had no idea what to do here?

Same as a) and b) … find N, and add it (as a vector) to the weight.