Work, energy and power
Head-on collision
Section titled “Head-on collision”Momentum is always conserved in a collision. Energy is a different story: in a perfectly elastic collision the kinetic energy is also conserved, in a perfectly inelastic one the two bodies stick together and as much energy as possible is lost to heat and deformation. The coefficient of restitution dials between the two. Watch the dissipated bar in the energy panel jump at the moment of impact.
Momentum conservation and the definition of (separation speed over approach speed) give
The kinetic energy lost is .
The impact is an impulse solved at the velocity level with Newton’s restitution rule. The energy it removes is computed exactly from the impulse and credited to the dissipation ledger, so the energy panel balances to 1e-10.
Bob in a vertical circle
Section titled “Bob in a vertical circle”Swing a bob on a string in a vertical circle. At the top the string can only pull, never push, so if the bob is too slow the string goes slack and the bob falls inward instead of completing the circle. There is a minimum speed at the bottom that just makes it over the top. Set the speed slider a little below it and watch the event log.
At the top, . The string stays taut while . Energy conservation between bottom and top, , gives the minimum
Tension at the bottom is .
The string is a rope constraint, so it cannot push. When the required tension would be negative the engine lets the
rope go slack and emits a rope_slack event. Validated: the event appears when launched at 95 % of the critical speed
and not at 105 %.