At point "b" the roller coaster has reached a speed of 15 m/s. How large must the radius of the valley be so that a 50 kg rider will experience a normal force of five times their weight (5 G's)?

Question

a. 5.6 m

b. 1.2 m

c. 11.5 m

d. 27 m

Roller Coaster is on the very bottom

Answer 1

Let N will be reaction. Then we have N - mg = mv²/r.

By condition N = 5mg; 5mg - mg = mv²/r. From here r = v²/4g = (15m/s)²/(4·9.8m/s²) ≈ 5.7 m.

Answer is a., radius r = 5.6 m