Conservation of energy
▶︎ Watch it animatedinteractive step-through · ~3 min · optionalConservation of energy says the total K + U stays fixed when only conservative forces do work, so as one rises the other falls and nothing is used up. Draw the total energy as a flat line across an energy curve U(x): the kinetic energy is the gap up to that line, K = E - U, and the object turns around where the line meets the curve, where K = 0.
Energy conservation slips in three places. Students use K + U = constant even when friction or drag acts, though mechanical energy then drops by the non-conservative work, E_f = E_i + W_nc. They misread the turning points on a U(x) graph, where the object turns as the energy line meets the curve and U = E, not at the flat bottom of the well. And they treat energy as used up as an object slows, when with only conservative forces it merely trades between K and U, fastest where U is lowest.
The work
3 ways in · any order
Lesson
Conservation of energy
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How the total mechanical energy K + U stays fixed when only conservative forces do work, so it drops by the non-conservative work when friction or drag act, E_f = E_i + W_nc; how to read turning points off a U(x) graph, where the energy line meets the curve and K = E - U falls to zero; and why energy is a running total that trades between K and U rather than being used up. Worked examples handle conservation with and without friction, reading turning points and the allowed region, and finding speed from K = E - U. Closes with a ten-scenario skill check on all three traps.
Diagnostic
10-item topic check
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Ten items on the main mistakes for Topic 3.4: applying K + U = constant when friction or drag is present, misreading the turning points on a U(x) graph, and treating energy as used up as an object slows instead of trading between K and U. Take it cold to find what is shaky, or after the lesson to confirm it is not.
Targeted Practice
Drill a single misconception
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Pick one of the mistakes you've missed and drill it on its own. The round is adaptive: two correct in a row clears it and you move on.