Mechanical energy (ME) is the total energy associated with an object's motion and position within a system. It's the sum of all kinetic and potential energies:
For a system with both gravitational and elastic PE:
Mechanical energy is a snapshot of how much energy is available for motion or stored in position. It's the quantity that conservation of energy tracks.
When only conservative forces do work on a system, mechanical energy is conserved — the total ME at any point equals the total ME at any other point:
This is extraordinarily powerful. You don't need to know the forces at every instant, the acceleration at every moment, or anything about the path taken. You only need the initial and final states. Set them equal and solve.
Set initial conditions for an object rolling off a ramp. Watch the energy bars show how KE, PE, and thermal energy account for every Joule — the totals always balance.
Set friction to 0 — ME is perfectly conserved. Add friction — ME decreases but total energy (ME + E_thermal) stays constant. The bars always account for every Joule.
A 2 kg ball starts at rest at the top of a 5 m tall frictionless ramp. What is its speed at the bottom? (g = 10 m/s²)
Friction and air resistance convert mechanical energy to thermal energy. The ME at the end is less than at the start — but the missing energy didn't disappear. It became heat in the surfaces.
E_thermal is the energy dissipated by friction. For kinetic friction over a distance d: E_thermal = f_k × d = μ_k × F_N × d. It's always positive — friction always removes energy from the mechanical system.
A 3 kg block slides from rest down a 4 m ramp inclined at 30°. The coefficient of kinetic friction is 0.2. What is its speed at the bottom? (g = 10 m/s²)
Energy bar charts — sometimes called LOL diagrams — are a visual representation of energy at two points in a problem, with a "work" column in the middle showing any external energy transfer. They're an AP exam staple and worth partial credit on FRQs even when the algebra goes wrong.
Each bar's height represents the amount of that energy type. The total height of all bars must be equal at each state (accounting for any external work between them). Drawing these before writing equations helps you see exactly what's happening before you do the math.
Build a LOL (energy bar chart) diagram. Set the initial energies and any external work, then adjust how the final ME splits between KE and PE.
The most complete and general form of energy conservation in AP Physics 1 is:
The change in a system's total energy equals the net work done on it by external forces. This single equation covers every case:
A 5 kg box starts at rest on a platform 3 m high. It slides down a ramp (μ_k = 0.25, ramp length 5 m, normal force = 40 N) then is pushed by a 20 N horizontal force for 4 m on a frictionless floor. Find its final speed.