Conservation of energy means the total stays constant as it converts between forms. Drag the slider below to set the ball's release height in a frictionless valley, and watch its potential and kinetic energy trade off — while the total, and the speed at the bottom, follow from the drop.
Think of two tanks the ball is always emptying into each other: a “height” tank holding potential energy (PE = m·g·h) and a “speed” tank holding kinetic energy (KE = ½·m·v²). As the ball slides down the frictionless valley, the height tank drains into the speed tank; as it climbs the far side, the pour reverses. The Total energy readout never budges because nothing is added or lost — energy is only converted, never used up.
The single slider sets the release height, and that one choice fixes the motion. Drop the ball and the KE and PE bars visibly trade off: at the top it is all PE and zero KE, so the Speed reads nothing; at the lowest point it is all KE, and the Speed peaks at v = sqrt(2·g·h). Because that relationship is a square root, quadrupling the release height only doubles the bottom speed. Watch the ball rise on the opposite side to exactly the same height it left — energy conservation forbids it from climbing any higher.
Notice what the slider does not include: mass. Setting m·g·h = ½·m·v² cancels the m on both sides, so a heavy ball and a light one hit the same bottom speed from the same drop. Real tracks bleed a little energy to heat each pass, but the ideal case runs forever. Put numbers to the peak with the kinetic energy calculator, or step into another hands-on physics sandbox next.
In a frictionless system the total mechanical energy stays constant — energy only converts between forms. As the ball descends, potential energy (mgh) turns into kinetic energy (½mv²), and back again as it rises.
v = sqrt(2gh), where h is the release height, because all the potential energy has become kinetic energy. Since it is a square root, quadrupling the height only doubles the bottom speed.
No. Setting mgh = ½mv² cancels the mass, so the bottom speed depends only on the release height and gravity, not on the ball's mass — a heavy and a light ball arrive at the same speed.
Because energy is conserved. It can turn all its potential energy into kinetic energy and back, but never gain any, so it can only return to the same height. Real friction makes it stop a little lower each pass, the energy going to heat.