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Flashcards · AP® Physics 1: Algebra-Based · Unit 3

Unit 3: Work, Energy, and Power flashcards

35 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 an object has because its center of mass moves. Units: J = kg·m²/s². It is a scalar, never negative, and zero only at rest.
A runner triples her speed. By what factor does her kinetic energy change?
It multiplies by 9, because K ∝ v². Doubling speed gives 4 times the kinetic energy, not twice.
How do you find a change in kinetic energy?
ΔK = ½mv² − ½mv₀². Subtract the two kinetic energies; do not write ½m(Δv)².
A 0.10 kg ball hits a wall at +5.0 m/s and rebounds at −5.0 m/s. What is ΔK?
Zero. Kinetic energy depends on speed, not direction, and the speed is unchanged (although the velocity changed).
What graph of kinetic energy data gives a straight line, and what is its slope?
K against v² is a straight line through the origin with slope ½m, so mass = 2 × slope. K against v is a parabola.
How do you find the total kinetic energy of several objects?
Add each object's ½mv² as a plain positive number. Kinetic energies of objects moving in opposite directions do not cancel.
Do all observers measure the same kinetic energy for an object?
No. Speed depends on the frame, so observers in different frames measure different kinetic energies. Each is correct in their own frame; do not mix frames.

3.2 Work

How do you calculate the work done by a constant force?
W = F∥d = Fd cos θ, where θ is the angle between the force and the displacement. Only the component parallel to the displacement does work. W in J.
What is the work-energy theorem?
The change in an object's kinetic energy equals the net work done on it by all forces: ΔK = ΣW = W_net.
What is the difference between conservative and nonconservative forces?
Conservative forces (gravity, ideal springs) do work that depends only on start and end positions, zero for a round trip, and have a potential energy. Nonconservative forces (friction, air resistance) do path-dependent work.
How do you find the work done by a force that varies with position?
Find the area under the F_x–x graph; area below the axis is negative work. A force rising from 0 to 12 N over 0.30 m does ½ × 0.30 × 12 = 1.8 J.
How much energy does friction dissipate?
Friction force × path length (not displacement). It becomes thermal energy and sound. Friction on a sliding object does negative work.
Does gravity do more work on an object sliding down a longer ramp?
No. Work done by gravity depends only on the height change: W_g = −mgh for rising by h, whatever the path.
How does stopping distance depend on initial speed for a constant friction force?
d = mv₀² / (2F_f), so d ∝ v₀². Doubling the speed gives four times the stopping distance.

3.3 Potential Energy

What is potential energy, and which objects have it?
Energy stored in the arrangement of a system whose objects interact through conservative forces. A single object cannot have it: name the system, such as ball–Earth or block–spring.
How much energy is stored in an ideal spring?
U_s = ½kΔx², with Δx the change from the relaxed length in metres. It is never negative. Doubling Δx gives four times the energy.
What is the gravitational potential energy of two spheres?
U_g = −Gm₁m₂ / r, with r centre to centre and U = 0 at infinite separation. It is always negative; tripling r makes it one third as negative, so larger.
When can you use ΔU_g = mgΔy?
Near a planet's surface, when Δy is much smaller than the planet's radius so the field is constant. For satellites use the general form −Gm₁m₂ / r.
How is the change in potential energy linked to work done by a conservative force?
ΔU = −W_conservative, where the force acts between objects inside the system.
Where is the zero of potential energy?
Wherever you choose: pick the most convenient zero and state it. Only changes in U matter, and the system can have negative U below the zero.
How do you find the potential energy of three interacting objects?
Add the potential energy of every pair: A, B and C have three pairs (AB, BC, AC).

3.4 Conservation of Energy

When is the mechanical energy of a system constant?
When no outside force does work and there is no friction or air resistance inside: K_i + U_i = K_f + U_f, with E_mech = K + U.
How do you write energy conservation when friction acts inside the system?
K_i + U_i = K_f + U_f + ΔE_thermal. Mechanical energy is dissipated as thermal energy and sound; total energy is still conserved.
How fast is an object moving after falling a height h from rest on a smooth path?
v = √(2gh), independent of mass. A stone dropped 5.0 m reaches √(2 × 9.8 × 5.0) ≈ 9.9 m/s.
Why does choosing the system matter in energy problems?
With Earth inside, gravity's effect is ΔU_g. With the ball alone, gravity is an outside force doing work, so the ball's energy changes. Never count both ΔU_g and W_g.
A spring launcher's compression is doubled. How high does the launched object go?
Four times as high, since ½kΔx² = mgh gives h ∝ Δx² (no friction).
A 0.50 kg block is pushed against a spring (k = 200 N/m), compressing it 0.10 m on a smooth floor. How fast does it leave?
½kΔx² = ½ × 200 × 0.10² = 1.0 J = ½mv², so v = √(2 × 1.0 / 0.50) = 2.0 m/s.
What is the general energy rule for any system?
ΔE_system = W_outside: the system's energy changes only by work done by forces from outside. Inside, energy only changes form.

3.5 Power

What is power?
The rate at which energy is transferred or converted: P_avg = ΔE / Δt = W / Δt. Unit: watt, 1 W = 1 J/s.
How do you find the instantaneous power of a constant force?
P = F∥v = Fv cos θ, with θ the angle between force and velocity. A constant force on a speeding-up object delivers increasing power.
A 200 N force acts at 60° to the velocity of a cart moving at 3.0 m/s. What is its power?
P = Fv cos θ = 200 × 3.0 × cos 60° = 300 W.
How do you read power and energy from graphs?
Slope of an energy–time graph = power. Area under a power–time graph = energy transferred (below the axis means energy out).
What limits a vehicle's top speed on level ground?
At constant velocity the driving force equals the resistive force, so v_max = P_max / F_resistive.
What is a kilowatt-hour?
A unit of energy, not power: 1 kWh = 1000 W × 3600 s = 3.6 × 10⁶ J.
What is the power of a force perpendicular to the velocity, or against it?
Perpendicular: zero power. Against the velocity (such as friction on a sliding object): negative power, taking energy out of the object.

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