What is AP Physics 1 unit 3?
Unit 3 introduces conservation as a core physics principle. Instead of applying Newton's second law to every instant of motion, you can track energy across a system to predict speeds, heights, and force effects with far less algebra. The unit builds from kinetic energy through work, potential energy, and full conservation analysis, finishing with power as the rate of energy change.
Unit 3 is about how energy is stored, transferred, and conserved in physical systems. Work is the mechanism that changes a system's energy, potential energy is stored energy tied to position within a system, and conservation of energy lets you relate initial and final states without solving for every intermediate step.
Energy as a scalar
Kinetic energy K = 1/2 mv^2 and potential energy are both scalar quantities measured in joules. Because they are scalars, you add them algebraically rather than as vectors, which simplifies multi-object and multi-force problems significantly.
Work as energy transfer
Work W = Fd cos theta is the energy a force transfers into or out of a system. Only the force component parallel to displacement does work. Conservative forces like gravity and ideal springs do path-independent work; nonconservative forces like kinetic friction do path-dependent work and dissipate mechanical energy.
System boundaries matter
Whether mechanical energy is conserved depends entirely on how you define your system. If friction acts inside the system boundary, mechanical energy decreases. If you expand the system to include thermal energy, total energy is still conserved. Choosing your system carefully is a core AP skill.
Conservation of energy is a universal bookkeeping toolEnergy is conserved in every interaction. In a system where only conservative forces act internally and no work crosses the boundary, total mechanical energy E_mech = K + U stays constant. When nonconservative forces act, the change in mechanical energy equals the work done by those forces. This principle connects Unit 3 directly to oscillations in Unit 7, rotating systems in Unit 6, and fluid dynamics in Unit 8.
Unit 3 review notes
3.1
Translational Kinetic Energy
Translational kinetic energy is the energy an object has due to its translational motion. It depends on both mass and speed, but speed is squared, so doubling speed quadruples kinetic energy while doubling mass only doubles it. Because kinetic energy is a scalar, it is always zero or positive and has no directional component.
- Formula: K = 1/2 mv^2, where m is mass in kg and v is speed in m/s; result is in joules.
- Scalar quantity: Kinetic energy has magnitude only. Two objects moving in opposite directions at the same speed have the same kinetic energy.
- Frame-of-reference dependence: Different observers in different inertial frames measure different speeds for the same object and therefore calculate different values of K. There is no single correct value independent of frame.
- Speed vs velocity: K depends on the magnitude of velocity (speed), not its direction, so only the speed term v enters the formula.
A 2 kg cart moves at 3 m/s. What is its kinetic energy? If the cart's speed doubles to 6 m/s, by what factor does K change?
| Quantity | Doubles mass (2m) | Doubles speed (2v) |
|---|
| Effect on K | K doubles | K quadruples |
| New K expression | 2 * (1/2 mv^2) | 1/2 m(2v)^2 = 4 * (1/2 mv^2) |
3.2
Work
Work is the scalar measure of energy transferred into or out of a system by a force acting over a displacement. Only the component of force parallel to the displacement contributes. Work can be positive (force and displacement in the same direction), negative (force opposes displacement), or zero (force perpendicular to displacement, as with normal force on horizontal motion). The work-energy theorem states that the net work done on an object equals its change in kinetic energy.
- W = Fd cos theta: Work equals force magnitude times displacement magnitude times the cosine of the angle between them. Units are joules.
- Work-energy theorem: Delta K = sum of all work done on the object. Net positive work increases kinetic energy; net negative work decreases it.
- Conservative force: A force whose work is path-independent and depends only on initial and final positions. Gravity and ideal springs are conservative. Work done over a closed path is zero.
- Nonconservative force: A force whose work depends on the path taken. Kinetic friction and air resistance are nonconservative; they convert mechanical energy to thermal energy.
- Force-displacement graph: For a variable force, the work done equals the area under the F-parallel vs displacement curve.
A 10 N force is applied at 60 degrees to the horizontal as a box moves 4 m horizontally. How much work does the force do? Is this positive or negative work?
| Force type | Path dependence | Example | Potential energy? |
|---|
| Conservative | Path-independent | Gravity, ideal spring | Yes |
| Nonconservative | Path-dependent | Kinetic friction, air resistance | No |
3.3
Potential Energy
Potential energy is stored energy that belongs to a system of two or more objects interacting through conservative forces. It is a scalar associated with the configuration (positions) of objects within the system, not with any single object alone. The choice of zero potential energy is arbitrary and set by the observer to simplify analysis; only changes in potential energy are physically meaningful.
- Gravitational PE near Earth: Delta U_g = mg Delta y, where y is measured upward from the chosen reference level. The object-Earth system stores this energy.
- Elastic PE of a spring: U_s = 1/2 k(Delta x)^2, where k is the spring constant and Delta x is the stretch or compression from equilibrium. Always positive or zero.
- Zero PE reference: You choose where U = 0. Setting the reference at the lowest point of a problem often simplifies algebra, but the physics is the same regardless of choice.
- Object-Earth system: Gravitational potential energy is a property of the object-Earth system, not of the object alone. This framing is important for system-boundary reasoning.
- Conservative forces only: Potential energy can only be defined for conservative forces. There is no potential energy associated with friction or air resistance.
A spring with k = 200 N/m is compressed 0.15 m. What is the elastic potential energy stored in the spring-object system?
| Type | Formula | System | Depends on |
|---|
| Gravitational (near Earth) | Delta U_g = mg Delta y | Object-Earth | Height change |
| Elastic (ideal spring) | U_s = 1/2 k(Delta x)^2 | Object-spring | Compression or stretch from equilibrium |
3.4
Conservation of Energy
Mechanical energy is the sum of a system's kinetic and potential energies: E_mech = K + U. If only conservative forces act within a system and no work crosses the system boundary, E_mech is constant. When nonconservative forces like friction act inside the system, mechanical energy decreases by the magnitude of work done by those forces, and that energy appears as thermal energy or sound. Defining the system boundary determines whether energy is conserved or transferred.
- Mechanical energy: E_mech = K + U. Includes all kinetic and potential energies of objects within the system.
- Conservation condition: If net work by nonconservative forces is zero and no energy crosses the boundary, Delta E_mech = 0, so K_i + U_i = K_f + U_f.
- Nonconservative work: W_nc = Delta E_mech. Friction does negative work on the system, reducing mechanical energy by converting it to thermal energy.
- System boundary selection: Expanding the system to include the surface and object together means friction becomes an internal interaction; total energy including thermal energy is still conserved.
- Energy dissipation: Kinetic friction converts mechanical energy to thermal energy. This energy is not lost from the universe but is no longer available as mechanical energy.
A 0.5 kg ball is released from rest at a height of 2 m above the ground. Using conservation of energy and ignoring air resistance, what is its speed just before it hits the ground?
| System type | Nonconservative forces inside? | E_mech behavior | Equation form |
|---|
| Isolated, conservative only | No | Constant | K_i + U_i = K_f + U_f |
| With friction or drag | Yes | Decreases | K_i + U_i + W_nc = K_f + U_f |
3.5
Power
Power is the rate at which energy is transferred or converted. Average power equals total energy change divided by elapsed time. Instantaneous power delivered by a constant force equals the component of that force parallel to the object's velocity multiplied by the speed. The SI unit of power is the watt, equal to one joule per second.
- Average power: P_avg = Delta E / Delta t = W / Delta t. Use this when you know total energy change and total time.
- Instantaneous power: P_inst = F_parallel * v = Fv cos theta. Use this when you know force and speed at a specific moment.
- Watt: The SI unit of power: 1 W = 1 J/s. Power can be positive (energy into system) or negative (energy out of system).
- Sign of power: Positive power means energy is being transferred into the system or object; negative power means energy is being removed.
A motor lifts a 50 kg crate 8 m in 10 seconds at constant speed. What is the average power output of the motor?
| Formula | When to use | Variables needed |
|---|
| P_avg = Delta E / Delta t | Total energy change over a time interval | Energy change, time |
| P_avg = W / Delta t | Work done over a time interval | Work, time |
| P_inst = Fv cos theta | Force and speed at one instant | Force magnitude, speed, angle |
Practice AP Physics 1 unit 3 questions
Try stimulus-based AP practice questions and written prompts after you review the notes.
A sled of mass 20 kg is pulled across a rough horizontal surface at a constant speed by a rope angled at 60∘ above the horizontal, as shown in the figure. The tension in the rope is 50 N.
QuestionWhich of the following is most nearly the work done by friction on the sled as it moves a horizontal distance of 10 m?
−500 J
−433 J
−250 J
A block of mass m slides to the right with initial speed v0 across a rough horizontal surface with coefficient of kinetic friction μk, as shown in the figure.
QuestionWhich of the following correctly describes the change in total mechanical energy of the system defined as the block only, and why?
It decreases because the external force of friction does negative work on the block.
It decreases because friction is an internal force that converts mechanical energy to thermal energy within the system.
It remains constant because the work done by friction equals the work done by the applied force on the block.
It decreases because friction removes energy from the block and transfers it to the surroundings as heat.
4. In Scenario 1, a student pushes a cart of mass m=2.0 kg up a straight incline that makes an angle θ=30∘ above the horizontal, as shown in Figure 1. The cart starts from rest and moves a distance d=4.0 m along the incline while the student applies a constant force of magnitude F1=18 N parallel to the incline. The coefficient of kinetic friction between the cart and the incline is μk=0.20. The cart remains in contact with the incline.
In Scenario 2, the student repeats the experiment on the same incline with the same cart and the same friction conditions, but applies a different constant force of magnitude F2=22 N parallel to the incline. The cart again starts from rest and moves the same distance d=4.0 m along the incline.
Figure 1. Cart pushed up a 30° incline; displacement along the incline is 4.0 m. Forces on the cart are shown: applied force parallel up the incline, kinetic friction parallel down the incline, weight vertically downward, and normal force perpendicular to the incline.
• v1>v2
• v1<v2
• v1=v2
Justify your answer in terms of the work done by ALL forces acting on the cart over the distance d in each scenario. Use qualitative reasoning beyond referencing equations.
1. A student investigates the motion of a block and spring on an incline, as shown in Figure 1. A block of mass m=2.0 kg starts from rest at the bottom of a rigid incline that makes an angle θ=30∘ with the horizontal. The block is attached to an ideal spring of spring constant k=400 N/m that is initially stretched by xi=0.30 m relative to its equilibrium length. The block is released from rest at t=0. The coefficient of kinetic friction between the block and the incline is μk=0.20. Take the gravitational field to be g=9.8 m/s2.
Figure 1. Block–spring system on a 30° incline. The block starts from rest at the bottom end of the incline with the spring initially stretched by 0.30 m relative to equilibrium length; positive x is up the incline.
Figure 2. Axes for graphing translational kinetic energy K of the block versus time t, with marked times t₁ and t₂.
i. On the axes shown in Figure 2, sketch a graph of the translational kinetic energy K of the block as a function of time t from t=0 until t>t2.
ii. Derive an expression for the speed v1 of the block at time t=t1 (when the spring is at equilibrium length) in terms of m, k, xi, μk, θ, g, and physical constants, as appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the reference information.
iii. Derive an expression for the total distance d the block travels along the incline from t=0 to t=t2 in terms of m, k, xi, μk, θ, g, and physical constants, as appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the reference information.
Increases
Decreases
Remains constant
Justify your response by identifying energy transfers into or out of the system and describing the role of friction.
3. Students are investigating the relationship between the compression of a spring and the speed of a cart.
Figure 1. Cart launched by a compressed spring; speed measured by two photogates separated by 0.20 m.
Figure 2. Cart on a level track pulled by a hanging mass over a low-friction pulley; vertical drop distance y indicated.
Spring compression x (m) | Cart speed v (m/s) |
|---|
0.08 | 0.79 |
0.10 | 0.98 |
0.12 | 1.19 |
0.14 | 1.39 |
0.16 | 1.59 |
The students correctly determine that, if nonconservative work is negligible, conservation of mechanical energy leads to the relationship v2=mkx2.
The students create a graph with x2 plotted on the horizontal axis.
i. Indicate what measured or calculated quantity could be plotted on the vertical axis to yield a linear graph whose slope can be used to calculate an experimental value for the spring constant k.
Vertical axis: Horizontal axis: x2
ii. On the blank grid provided, create a graph of the quantities indicated in part C(i) that can be used to determine k.
• Use Table 2 to record the data points or calculated quantities that you will plot.
• Clearly label the vertical axis, including units as appropriate.
• Plot the points you recorded in Table 2.
iii. Draw a straight best-fit line for the data graphed in part C(ii).