Total mechanical energy stays constant when only conservative forces do work.
When only conservative forces act, T+V stays constant: ½mv₁²+mgh₁=½mv₂²+mgh₂. With friction, E₁+W_nc=E₂. It simplifies problems that would need integration of forces.
A ball dropped from 5 m hits the ground at √(2gh)≈9.9 m/s.
Energy conservation gives direct speed and height answers without solving the motion, and it shows where energy is lost to friction.
Total mechanical energy stays constant when only conservative forces do work.
Energy conservation gives direct speed and height answers without solving the motion, and it shows where energy is lost to friction.
When only conservative forces do work, such as gravity and ideal springs. If friction or drag does work, include its loss as heat or other energy.
They reduce efficiency, produce heat and waste energy, so engineers account for them in brakes, drivetrains and bearings.
Typical applications include predicting the speed of a roller coaster at the bottom of a drop, checking how far a pendulum swings after a release and estimating the speed of a skier at the bottom of a slope.
Study "Potential energy" first (topic 28 of 106 in Engineering Mechanics). It covers the groundwork this topic builds on.
Choose two states to compare. Energy is not directional. Roller coasters and pendulums.
A ball dropped from 5 m hits the ground at √(2gh)≈9.9 m/s.
The next topic is "Power", which builds directly on this one.
It is classed as Beginner in Engineering Mechanics (topic 29 of 106). It is an entry-level topic. It relies only on basic school mathematics and the ideas introduced earlier in this discipline.
Want to practise? Open the interactive course for quick checks, quizzes, simulations and progress tracking.