An air-hockey puck glides across its table on a cushion of air. A packing box slides across a carpet.
Both move along a flat surface. One of them keeps its mechanical energy. The other loses it fast.
Every conservation solve opens with one gatekeeper question: is mechanical energy approximately conserved here?
Well, the check is a scan of the scenario for three things: friction, air resistance, and collisions.
The air-hockey puck: the air cushion holds it clear of the surface beneath, so friction is negligible; at its gentle speed, air resistance barely acts; nothing hits anything. Conserved.
The packing box: the same flat-surface scene with one change. Carpet grips. Friction is large. Not conserved.
A pendulum swinging gently, air resistance negligible: no sliding surfaces, nothing collides. Conserved, approximately.
Two bumper cars meet: a collision costs kinetic energy in the moment of impact, so mechanical energy is not conserved through the hit.
The word approximately is honest bookkeeping: small spoilers always exist, and the verdict says they do not matter HERE, for this stretch of motion.
A marble rolls along a smooth, level glass channel; friction and air resistance are negligible. Is its mechanical energy approximately conserved?
Scan the scenario: friction negligible, air resistance negligible, and the marble hits nothing.
No spoiler matters here.
Yes: the marble's mechanical energy is approximately conserved.
A skydiver falls at a steady speed through the air. Is her mechanical energy approximately conserved?
The steady fall looks calm, but scan it: her GPE falls the whole time while her KE stays fixed, and the scenario is full of air.
Air resistance is large here; it is exactly what holds the speed steady.
No: her mechanical energy is not conserved; air resistance matters.
One cue to carry into the drill: a cushion of air holds a glider clear of the surface beneath it, so sliding friction there is negligible, even while a fan keeps the cushion blowing.
A hovercraft toy skims across a gym floor on its cushion of air at a gentle pace. Is its mechanical energy approximately conserved?
A packing crate slides across rough concrete. Is its mechanical energy approximately conserved?
A pendulum in a science room swings gently, with negligible air resistance. Is its mechanical energy approximately conserved?
An ice skater glides in a straight line across smooth rink ice, friction negligible. Is her mechanical energy approximately conserved?
A skydiver falls at a steady speed through the air. Is her mechanical energy approximately conserved?
Two shopping carts roll into each other and latch together. Is their mechanical energy approximately conserved through the impact?
In which scenario is the sled's mechanical energy approximately conserved?
A marble run has four sections. On which section is the marble's mechanical energy NOT approximately conserved?
A hockey puck crosses smooth rink ice, friction negligible, then slides onto a stretch of bare concrete. On which stretch is its mechanical energy approximately conserved?