Systems, Non-Conservative Forces & Energy Bookkeeping
- Define a system boundary and explain how it determines whether a force does work or stores potential energy
- Apply the work–energy theorem when friction or an applied force is present
- Track energy through a multi-stage problem where mechanical energy is not conserved
Potential energy belongs to a system, never to an object
A ball alone has no gravitational potential energy. The ball–Earth system does, because potential energy is stored in the interaction between two objects. This is not pedantry — it decides which equation you write. If Earth is inside your system, gravity is an internal force and you account for it as ΔU. If Earth is outside, gravity is an external force and you account for it as work done on the system. Doing both is double-counting; doing neither loses the term entirely.
Conservative vs. non-conservative
A force is conservative if the work it does depends only on the start and end points, not the path — gravity and ideal springs qualify, which is exactly why each has a potential-energy function. Friction and air resistance are non-conservative: drag a block in a circle back to its start and friction has done negative work the whole way, so the path length matters. There is no such thing as "friction potential energy"; that work becomes thermal energy and does not come back.
Friction generates heat proportional to path length
The thermal energy produced by kinetic friction is ΔE_thermal = f_k · d, where d is the distance traveled along the surface, not the displacement. A block that slides 3 m forward and 3 m back has zero displacement but has generated friction heating over 6 m. Note also that this energy is shared between the block and the surface, which is why the exam phrases it as energy "dissipated by friction" rather than work done on the block.
A 2.0 kg block is launched at 8.0 m/s along a level surface with coefficient of kinetic friction 0.20. How far does it slide before stopping? (g = 10 m/s²)
- 1.Initial kinetic energy: K = ½mv² = ½(2.0)(8.0)² = 64 J.
- 2.Friction force: f_k = μ_k N = μ_k mg = (0.20)(2.0)(10) = 4.0 N.
- 3.All the kinetic energy goes to thermal energy: 64 J = f_k · d = 4.0 N × d.
- 4.Solve: d = 64 ÷ 4.0 = 16 m.
When to reach for energy instead of forces
Energy methods are the better tool whenever a problem gives you speeds and positions but not time, or whenever the force is not constant so the kinematic equations do not apply. A ball rolling down a curved, frictionless ramp of unknown shape is unsolvable with Newton's laws at the AP level, but trivial with energy: the drop in height sets the speed regardless of the path. Conversely, if the question asks about a force or an acceleration at one instant, forces are the faster route.
Work is a scalar and it can be negative. Friction and any force with a component opposite the motion do negative work. And a force perpendicular to the motion does zero work — which is why the normal force, the tension on an orbiting satellite, and the centripetal force in uniform circular motion never change kinetic energy.
A person carries a 10 kg box horizontally across a room at constant speed. How much work does the person do on the box against gravity?
A block slides down a rough incline. Which statement is correct?
A 1.0 kg ball is dropped from 5.0 m and lands at 8.0 m/s. How much energy was dissipated by air resistance? (g = 10 m/s²)
On a free-response, state your system and your zero of potential energy in words before writing any equation. Both are rubric points on energy questions, and choosing the ground as U = 0 makes almost every problem arithmetically cleaner.
Answer the 3 checkpoints as you read.
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