AP Physics 2 connects fluid behavior, thermal systems, waves, optics, electric circuits, and modern physics into one algebra-based course. This cheat sheet focuses on the high-value relationships students use most often in fluids, thermodynamics, and modern physics. It helps students quickly compare equations, identify assumptions, and choose the right conservation law during problem solving.
The core ideas include pressure from fluids, buoyant force, conservation of mass in flow, and energy conservation in moving fluids. Thermodynamics centers on heat transfer, internal energy, work, entropy, and the efficiency limits of engines. Modern physics uses quantized energy, photons, wave-particle behavior, atomic transitions, and nuclear energy changes.
Key Facts
- Fluid pressure at depth is , where is surface pressure and is depth below the surface.
- Buoyant force equals the weight of displaced fluid, so .
- For ideal incompressible flow, the continuity equation is .
- Bernoulli’s equation for steady ideal flow is along a streamline.
- The first law of thermodynamics is , where is work done by the system.
- Thermal efficiency for a heat engine is , and the maximum Carnot efficiency is using kelvin temperatures.
- Photon energy is quantized by , where is Planck’s constant.
- Mass-energy equivalence is , and nuclear energy changes can be found from .
Vocabulary
- Gauge pressure
- Gauge pressure is the pressure above atmospheric pressure, often written as for a fluid at rest.
- Buoyant force
- Buoyant force is the upward force on an object in a fluid caused by pressure increasing with depth.
- Ideal fluid
- An ideal fluid is incompressible, nonviscous, and flows steadily without turbulence.
- Entropy
- Entropy is a measure of energy dispersal or microscopic disorder, and for a reversible process .
- Photon
- A photon is a quantum of electromagnetic radiation with energy .
- Binding energy
- Binding energy is the energy required to separate a nucleus into its individual protons and neutrons.
Common Mistakes to Avoid
- Using Celsius in thermodynamic efficiency formulas is wrong because requires absolute temperature in kelvin.
- Confusing object volume with displaced volume is wrong because buoyant force depends on , not always the object’s full volume.
- Assuming higher fluid speed means higher pressure is wrong for ideal horizontal flow because Bernoulli’s equation shows larger corresponds to smaller when height is unchanged.
- Treating heat as a substance stored in an object is wrong because heat is energy transferred due to a temperature difference, while internal energy is energy contained in the system.
- Using with wavelength directly is wrong unless frequency is known, since wavelength must be converted using for light in vacuum.
Practice Questions
- 1 A diver is below the surface of fresh water. Using and , find the gauge pressure .
- 2 Water flows through a pipe that narrows from area to . If , find using .
- 3 A heat engine absorbs from a hot reservoir and exhausts to a cold reservoir. Find the work output and efficiency .
- 4 Explain why a floating object can have zero net force even though gravity acts downward on it.
Understanding AP Physics 2 Fluids, Thermo, and Modern Physics
Fluid problems become much clearer when you first decide whether the fluid is resting or moving. A resting liquid pushes in every direction, not just downward. This explains why a dam is thicker near its base and why a diver feels pressure on the sides of their body.
Gauge pressure measures the extra pressure caused by the fluid, while absolute pressure includes the pressure of the air above it. Keep those ideas separate. For floating objects, compare average object density with fluid density.
An object can be made of dense material yet float if its shape creates enough volume to displace water. A steel ship works this way.
In flow problems, check whether the question describes one smooth stream of incompressible fluid. Real fluids have viscosity, turbulence, and energy loss, so ideal flow models are approximations.
Thermodynamics tracks energy as it moves between a system and its surroundings. The hardest part is often defining the system clearly. It might be gas in a cylinder, water in a cup, or air inside a refrigerator.
Heat is energy transferred because of a temperature difference. Work is energy transferred when a force causes motion, such as a gas pushing a piston outward. Internal energy refers to microscopic kinetic and potential energy in a material.
A pressure versus volume graph gives useful physical meaning. The area under a process curve represents work done during that change.
Different paths between the same starting and ending states can involve different heat transfers and different amounts of work. This matters for engines, since an engine must repeat a cycle to produce useful work continuously.
No engine can turn all incoming thermal energy into work. Some energy must leave to a cooler place because random molecular motion naturally spreads energy out. Entropy helps describe this spreading and the number of possible microscopic arrangements.
In everyday life, this is why hot food cools, ice melts in a warm room, and refrigerators require electrical energy to move heat from a cold interior to a warmer kitchen. Temperature must be measured on the kelvin scale when comparing the theoretical limits of an engine. Celsius temperatures have the same size degrees, but their zero point does not represent the absence of thermal motion.
Be careful with efficiency statements. A high efficiency means less wasted input energy, not that the machine creates extra energy.
Modern physics shows where familiar classical ideas stop working. Light produces interference patterns like a wave, yet detectors record separate photon arrivals. Atomic electrons can occupy only certain energy states, so atoms absorb or emit light at specific wavelengths.
These spectral lines act like fingerprints in laboratory samples and distant stars. In photoelectric experiments, brighter light increases the number of released electrons when the frequency is high enough. Light below a threshold frequency cannot release electrons, even if it is very bright.
Nuclear questions require careful accounting of total charge and nucleon number before considering energy. Small mass differences can correspond to large energy changes because the speed of light squared is enormous.
Focus on conservation laws, units, diagrams, and stated assumptions before selecting an equation. That habit prevents many AP Physics 2 errors.