Vertical loop: energy and contact challenge

Adjust the release height h and loop radius R. Try to complete the loop with the smallest possible height.

Theoretical target: h = 2.5R
StateReady
h/R2.500
Speed0.00 m/s
N/m
Score1000
Press Start or the Space bar
Kinetic energy0%
Potential energy100%
Mechanical energy100%
Physical model

The particle starts from rest and friction is neglected. The ramp and loop are integrated with the same timestep. In the loop, v² = 2g[h − R(1 − cos θ)] and N/m = v²/R + g cos θ. The ideal threshold for completing the loop is h ≥ 5R/2.