ACT Science: Kinetic and Potential Energy—Conservation and Conversions

Kinetic energy (KE) is energy of motion. KE=0.5mv² (where m=mass, v=velocity). Potential energy (PE) is stored energy. For gravity, PE=mgh (where m=mass, g=gravity, h=height). Total mechanical energy E=KE+PE. In a closed system with no friction, total mechanical energy is conserved: E_initial=E_final. As an object falls, PE converts to KE: the lower it falls, the less PE and more KE it has, but the sum stays constant. This principle explains roller coasters, pendulums, and collisions.

Example: A ball at rest on a 10-meter cliff has PE=mgh=m(10)(10)=100m (in joules, if g≈10 m/s²) and KE=0. Total=100m. Halfway down (5 meters), PE=50m, KE=50m. Total still 100m.

Scenario 1 (Free fall): An object (m=2 kg) falls from 20 m. Initial: PE=2(10)(20)=400 J, KE=0. Just before impact: PE=0, KE=400 J. Velocity at impact: 0.5(2)v²=400 → v²=400 → v=20 m/s. Scenario 2 (Pendulum): A pendulum swings from high (all PE) to low (maximum KE) and back (PE again). At the lowest point, KE is maximum. At the highest points, KE=0 and PE is maximum. Scenario 3 (Friction present): Real-world objects lose energy to friction. A ball rolling down a ramp reaches the bottom with less speed than predicted because some energy converts to heat. Without friction, total energy is constant. With friction, total energy decreases (converts to heat).

Always check: Does the system include friction? If yes, account for energy loss.

Situation 1: A 1-kg ball is thrown upward at 20 m/s from ground level. Find total mechanical energy. E=KE+PE=0.5(1)(20)²+0=200 J. (Initial PE=0 at ground level.) At the peak, all energy is PE: PE=mgh → 200=1(10)h → h=20 m. Situation 2: A 3-kg object at rest on a 15-m ledge falls. Find KE just before impact. Initial E=PE=3(10)(15)=450 J. At impact: KE=450 J. Find velocity: 0.5(3)v²=450 → v²=300 → v≈17.3 m/s. Situation 3: A 2-kg block slides down a frictionless ramp from 8 m height. Find speed at bottom. PE=2(10)(8)=160 J converts to KE. 0.5(2)v²=160 → v²=160 → v≈12.6 m/s. Complete all three daily until energy calculations are fast and accurate.

Verify with energy conservation: initial energy = final energy.

Energy conservation questions appear in 1-2 ACT Science passages. They are computational once you know KE and PE formulas. Investing 20 minutes in energy conservation yields 1-2 guaranteed points because the concept is straightforward and formulas are provided.

Master these formulas one day before the test. By test day, energy problems become routine calculations.