AP Physics C · Unit 3
Work, Energy and Power: every key term you need (+ practice quiz)
35 flashcard terms for AP Physics C Unit 3, written to match the course framework. Read them here, drill them as flashcards, or take the 22-question quiz. Free, no account needed.
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Work by a Constant Force W = F·d = Fd cosθ; the dot product of force and displacement; only the force component along the displacement does work.
Work as an Integral W = ∫F·dx; for a varying force, work is the area under the force-position graph; required when F depends on position.
Work by a Spring W = ∫(−kx)dx = −½kx²; work done by a spring force stretched from 0 to x; negative when stretching.
Kinetic Energy KE = ½mv²; the energy of motion; a scalar that depends on the square of speed and is always non-negative.
Work-Energy Theorem W_net = ΔKE = ½mv² − ½mv₀²; the net work done on an object equals its change in kinetic energy.
Potential Energy U; stored energy associated with a conservative force and configuration; only changes in U are physically meaningful.
Gravitational PE (near Earth) U = mgy; potential energy relative to a chosen reference height; increases with height.
Elastic (Spring) PE U = ½kx²; energy stored in a stretched or compressed spring; always positive and quadratic in displacement.
Conservative Force A force whose work is path-independent and whose round-trip work is zero; gravity and springs qualify, so a PE can be defined.
Non-Conservative Force A force like kinetic friction whose work depends on the path; it dissipates mechanical energy (often as heat).
Force from Potential Energy F = −dU/dx; the force is the negative gradient (slope) of the potential energy function.
Conservation of Mechanical Energy When only conservative forces act, KE + U = constant; energy converts between kinetic and potential forms.
Energy with Friction KE₀ + U₀ = KE_f + U_f + |W_friction|; friction removes mechanical energy equal to f_k times distance traveled.
Power P = dW/dt; the rate of doing work or transferring energy; measured in watts (1 W = 1 J/s).
Instantaneous Power P = F·v; the dot product of force and velocity; the rate at which a force delivers energy at an instant.
Average Power P_avg = W/Δt = ΔE/Δt; total energy transferred divided by the elapsed time.
Potential Energy Diagram A plot of U(x); slope gives −F, minima are stable equilibria, maxima are unstable, and flat regions are equilibrium.
Turning Points Positions where KE = 0 so U(x) = E; the object momentarily stops and reverses within a potential well.
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Stable Equilibrium A minimum of U where dU/dx = 0 and d²U/dx² > 0; a small displacement produces a restoring force.
Work by Gravity is Path-Independent W_grav = −mgΔy regardless of path taken; a defining feature of the conservative gravitational force.
Energy Units The joule (J = N·m = kg·m²/s²); the SI unit shared by work, kinetic energy, and potential energy.
Work by a Variable Force W = ∫F·dr along the path; the area under an F-x graph for one-dimensional motion.
Work-Energy Theorem Derivation ∫F dx = ∫m(dv/dt)dx = ∫mv dv = ½mv² − ½mv₀²; net work equals change in kinetic energy.
Force from Potential Energy F = −dU/dx; force points toward decreasing potential energy; in 3D F = −∇U.
Potential Energy from Force U(x) = −∫F dx + C; only differences in U are physical, so the reference point is arbitrary.
Equilibrium from U(x) Equilibrium where dU/dx = 0; stable if d²U/dx² > 0 (minimum), unstable if < 0 (maximum).
Energy Diagram Turning Points Where E = U(x) the kinetic energy vanishes and the particle reverses; regions with U > E are forbidden.
Conservative Force Test Work is path-independent and zero around any closed loop; equivalently F derives from a potential.
Non-Conservative Work W_nc = ΔK + ΔU; friction removes mechanical energy as thermal energy, dependent on path length.
Gravitational Potential (General) U = −GMm/r with U → 0 at infinity; escape speed from √(2GM/R) via energy conservation.
Instantaneous Power P = dW/dt = F·v; for a car at constant speed on a hill, P = (mg sinθ + f)v.
Spring Potential (Nonlinear) For F = −kx − bx³, U = ½kx² + ¼bx⁴; integrate the force to build the potential.
Small Oscillations About a Minimum Near a minimum, U ≈ U₀ + ½k_eff(x−x₀)² with k_eff = U″(x₀); motion is approximately simple harmonic.
Work by Gravity on Curved Path Depends only on Δh: W = −mgΔh regardless of the path shape, because gravity is conservative.
Energy vs Newton Approach Energy methods avoid vectors and time but cannot give the time or forces of constraint directly.
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