Work and the Work-Energy Theorem
When a force pushes an object through some distance, energy changes form. If the force pushes along the motion, kinetic energy goes up. If it pushes against the motion, kinetic energy goes down. The amount that transfers is the work done by that force, written as $W = Fd\cos\theta$. That cosine is where most of the trouble starts. It is also where the work-energy theorem, $W_{\text{net}} = \Delta K$, comes into play.
Three traps wait in this topic. The first treats every push as work, even when it points sideways to the motion. The second insists that pushing on a wall for ten minutes must produce some work, since the muscles are tired. The third drops the cosine and treats $W = Fd$ as the universal formula, even when the force is at $30^\circ$ or $60^\circ$ to the motion. The lesson is built around catching all three.
The work
3 ways in · any order
Lesson
Work and the Work-Energy Theorem
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Read the lesson, then run a ten-scenario applet that drills the cosine, the sign of work, and the work-energy theorem on a frictionless block. Progress saves automatically.
Diagnostic
10-item topic check
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Ten multiple-choice items targeting perpendicular-zero-work, the muscle-effort trap, and the dropped cosine. About fifteen minutes. The result lights up exactly which misconceptions to drill next.
Targeted Practice
Drill a single misconception
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Pick one of the failure modes you've missed and grind it on its own. The round is adaptive: two correct in a row clears the misconception and you move on.