Question

Cedar Point Physics Worksheet.

Show all work. Assume that the average rider is 60 kg and the average car is 300 kg. You may need to calculate how many passengers fit in a car or how many cars there are on a ride.

At the top of the first loop, how much greater than critical velocity is the Raptor moving? (velocity at the top of the loop = 15 m/s, radius of the loop = 15 m).

Answer 1

At topmost point, for critical velocity, no Normal force from the surface of loop is acting on the car and weight of the car accounts for centripetal force on the car

=> mg-N=mv²/r
since N=0

=> mg=mv²/r

( where r-> radius of loop
   m-> mass of car
   v-> critical velocity )

=> v_critical=(r*g)^0.5
=>v_critical=(15*9.81)^0.5
=> v_critical= 12.13 m/s

since car is going at 15m/s, hence it is moving at a speed of (15-12.13= 2.87m/s) higher than critical velocity.

Since mass term doesnt come in velocity calculation, hence passenger or car mass is irrelevant to the problem.