Energy
Energy: Work, Power, and Conservation
Energy questions test whether you can track energy between forms and apply conservation. Work is done when a force causes displacement in the direction of the force; a force perpendicular to motion (like the normal force on a level floor, or tension in a string on a circling object) does zero work. The work-energy theorem states that net work equals the change in kinetic energy.
Know the standard forms: kinetic energy (½mv²), gravitational potential energy near Earth (mgh), elastic potential energy in a spring (½kx²), and internal energy from friction. Power is the rate of doing work, or force times velocity when the force is along the motion.
Conservation of energy is the workhorse. In the absence of friction, total mechanical energy is constant, so a pendulum or roller coaster trades potential and kinetic energy. With friction, mechanical energy decreases and the "lost" energy appears as thermal energy; the total energy is still conserved. Efficiency compares useful output energy to total input energy and is always less than 100% in real systems.
Worked example: A 2.0 kg block slides from rest down a frictionless 5.0 m ramp inclined at 30°. The height dropped is 5.0·sin30° = 2.5 m. Setting mgh = ½mv² gives v = √(2gh) = √(2·9.8·2.5) ≈ 7.0 m/s. Notice mass cancels-a useful check.
Traps: forgetting that work requires a component of force along displacement; assuming energy is "used up" rather than transformed; using total distance instead of vertical height for gravitational potential energy; and ignoring the work done against friction when computing final speed.
Rule of thumb: identify initial and final states, write the energy balance (initial mechanical + work in = final mechanical + thermal), and cancel the mass whenever it appears on both sides.