A roller-coaster vehicle has a mass of 507 kg when fully loaded with passengers

Question

A roller-coaster vehicle has a mass of 507 kg when fully loaded with passengers (see figure).

(a) If the vehicle has a speed of 22.0 m/s at point A, what is the force of the track on the vehicle at this point?
N

(b) What is the maximum speed the vehicle can have at point B in order for gravity to hold it on the track?
m/s

A roller-coaster vehicle has a mass of 507 kg when fully loaded with passengers (see figure). (a) If the vehicle has a speed of 22.0 m/s at point A, what is the force of the track on the vehicle at this point? N (b) What is the maximum speed the vehicle can have at point B in order for gravity to hold it on the track? m/s

Explanation / Answer

a) N = m*g + m*v^2/r

= 507*9.8 + 507*22^2/10

= 29507 N

b)

N = 0

m*v^2/r - m*g = 0

m*v^2/r = m*g

v^2/r = g

v = sqrt(g*r)

= sqrt(9.8*15)

= 12.12 m/s

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