Question

A 515kg roller coaster is at the bottom of a loop with a radius of 10m. If the speed at the bottom of the loop is 20m/s, what is the force of the track pushing up on the vehicle at this point?

Answer 1

v = 20 m/s

R = 10 m

m = 515 kg

$N - mg = ma_c \\ a_c = \frac{v^2}{R} \\ N = m(\frac{v^2}{R} + g) \\ = 515(\frac{400}{10}+10) \\ = 515 \times 50 \\ = 25750 \;N$

Answer: 25750 N