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Flashcards · AP® Physics C: Mechanics · Unit 3

Unit 3: Work, Energy, and Power flashcards

40 cards on topics 3.1 to 3.5. Pick a topic or study the whole unit.

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3.1 Translational Kinetic Energy

What is translational kinetic energy?
K = ½mv², the energy of motion from place to place, where v is the speed (of the center of mass for a system). Unit: the joule, 1 J = 1 kg·m²/s².
Can kinetic energy be negative or have a direction?
No. K is a scalar and K ≥ 0. It depends on speed only, never on direction. A change ΔK can be positive or negative.
How does K change if speed doubles?
It quadruples, because K ∝ v² at fixed mass. If K is multiplied by 4 at fixed mass, the speed doubles.
How do you find K from velocity components?
Square and add the components: v² = v_x² + v_y² + v_z², then K = ½mv². Never add components as plain numbers.
How do you find ΔK correctly?
ΔK = K_f − K_i = ½mv_f² − ½mv_i². It is not ½m(Δv)².
What is the rate of change of kinetic energy?
dK/dt = m v_x a_x in one dimension, and m v·a in general. Positive means K is rising; negative means it is falling.
What is K at the top of a projectile's path?
Not zero. The horizontal velocity remains, so K_top = ½mv_x². A K–t graph for a projectile is U-shaped with this minimum.
Does kinetic energy depend on the reference frame?
Yes. Observers moving relative to each other measure different speeds and so different K. In a frame moving at u, K′ = ½m|v − u|².

3.2 Work

What is work?
Energy transferred into (W positive) or out of (W negative) a system by a force acting while its point of application moves. Work is a scalar measured in joules, 1 J = 1 N·m.
How do you calculate work by a constant force?
W = F · d = Fd cos θ, where θ is the angle between F and d. Only the force component parallel to the displacement does work. In components, W = F_xd_x + F_yd_y + F_zd_z.
How do you calculate work by a force that varies along the path?
W = ∫ₐᵇ F · dr; in one dimension W = ∫ F_x dx. This is the signed area under the force–position graph.
What does the work–energy theorem state?
W_net = ΔK = ½mv_f² − ½mv_i², where W_net is the total work by all forces on the object.
What is the work done by an ideal spring?
W_s = −½k(x_f² − x_i²), with x measured from the relaxed length. It is negative when the spring is stretched or compressed further.
Does the centripetal force do work?
No. It is perpendicular to the velocity at every instant, so W = 0 and the speed does not change.
What is the difference between conservative and nonconservative forces?
Work by a conservative force (gravity, ideal spring) depends only on start and end positions and is zero round a closed path. Work by a nonconservative force (kinetic friction, air resistance) depends on the path.
F_x = 4.0x³ (N, x in m). How much work does it do from x = 0 to 1.0 m?
W = ∫₀¹ 4.0x³ dx = [x⁴]₀¹ = 1.0 J.

3.3 Potential Energy

What is potential energy?
A scalar energy stored in the arrangement of a system of two or more interacting objects. It exists only for conservative interactions. Only changes in U are physical; you choose where U = 0.
How is potential energy related to a conservative force?
ΔU = −W_c = −∫F_c · dr. In one dimension, F_x = −dU/dx: the force is minus the slope of the U(x) graph and points toward lower U.
How do you find and classify equilibrium positions on a U(x) graph?
Equilibrium is where dU/dx = 0. A minimum (d²U/dx² positive) is stable; a maximum (d²U/dx² negative) is unstable. Equilibrium is not where U = 0.
What is the potential energy of an ideal spring?
U_s = ½k(Δx)², with U = 0 at the relaxed length. For a nonideal spring, integrate the actual force instead.
What is the gravitational potential energy of two spheres?
U_g = −Gm₁m₂/r, with U = 0 at infinite separation. It is negative and rises toward zero as r increases.
When can you use ΔU_g = mgΔy?
Near a planet's surface, when Δy is much smaller than the planet's radius so g is nearly constant. For large heights use −Gm₁m₂/r.
How do you find the potential energy of three or more objects?
Add the potential energy of every pair once: U = U₁₂ + U₁₃ + U₂₃ + …. Do not count a pair twice.
Does an object have potential energy?
Strictly, a system does. Gravitational potential energy belongs to the object–Earth system, not the object alone.

3.4 Conservation of Energy

What is mechanical energy, and when is it conserved?
E_mech = K + U. It is conserved when no external work is done and no friction acts inside the system: K_i + U_i = K_f + U_f.
What is the general energy equation for any system?
ΔK + ΔU + ΔE_th = W_ext. Energy is always conserved; a change in one form is balanced by other forms or by energy crossing the boundary as work.
Why must you choose the system before writing energy terms?
A single object can only have kinetic energy. Potential energy needs a system of interacting objects. Include Earth and use U_g, or leave Earth out and count gravity's work, but not both.
How do you find speed from a potential energy graph?
v(x) = √[2(E − U(x))/m]. The object can only be where U(x) ≤ E. Turning points are where U(x) = E, so K = 0 there.
What is escape speed from a planet's surface?
v_esc = √(2GM/R), from ½mv² − GMm/R = 0 using U_g = −GMm/r.
How much thermal energy does sliding friction produce?
ΔE_th = ∫ f_k ds, which is f_k d for constant friction over path length d. Integrate when μ_k varies along the path.
Does friction break conservation of energy?
No. Total energy is conserved; kinetic friction converts mechanical energy into thermal energy and sound, so mechanical energy is not conserved.
A 0.20 kg object has E = 1.0 J at a point where U = 0.64 J. What is its speed?
K = 1.0 − 0.64 = 0.36 J, so v = √(2 × 0.36 ÷ 0.20) = √3.6 ≈ 1.9 m/s.

3.5 Power

What is power?
The rate at which energy is transferred or converted. Average power P_avg = ΔE/Δt = W/Δt. Instantaneous power P = dW/dt. Unit: the watt, 1 W = 1 J/s.
How do you find the power delivered by a force on a moving object?
P = F · v = Fv cos θ: only the force component along the velocity counts. In components, P = F_xv_x + F_yv_y + F_zv_z.
How is net power related to kinetic energy?
P_net = F_net · v = dK/dt. Positive net power means speeding up; negative means slowing down.
How do you find work from a power–time graph?
W = ∫P dt, the area under the P–t graph.
What is the speed of an object pushed from rest at constant power?
If only that force does work, K = Pt, so v = √(2Pt/m). The force F = P/v falls as v rises, and the model fails near v = 0.
Is a kilowatt-hour a unit of power?
No. It is a unit of energy: 1 kWh = 3.6 × 10⁶ J.
Can you find average power from average force times average velocity?
Not when both vary. Use P_avg = W/Δt instead.
Which forces deliver zero power?
Forces perpendicular to the velocity, such as the normal force on level ground or the tension in uniform circular motion.

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