AP Physics 2

UNIT 8: Fluids

States of Matter & Fluids

• Solid: Fixed shape and volume.

• Liquid: Fixed volume, no fixed shape.

• Gas: No fixed shape or volume.

• Fluid: A substance without a fixed shape (liquids and gases).

Density

• Definition: Mass per unit volume.

• Formula: $\rho=\frac{m}{V}$

  • $\rho$ : density (lowercase Greek letter rho)

  • $m$ : mass

  • $V$ : volume

Pressure

• Definition: Force perpendicular to a surface divided by the area it acts upon.

• Formula: $P=\frac{F}{A}$

• Nature: Scalar (magnitude only).

• Units: Pascals (Pa) = N/m²

Absolute and Gauge Pressure

• Absolute Pressure (P_abs): Total pressure at a point in a fluid.

  • $Pabs=Po+\rho gh$

    • P₀ : Pressure at the top of the fluid.

    • $pgh$ : Gauge Pressure (pressure due to fluid weight).

• Gauge Pressure ($pgh$ ): Pressure due to the weight of the vertical column of fluid above a point.

  • Does not depend on the cross-sectional area of the fluid.

Buoyant Force

• Definition: The sum of all forces applied by the surrounding fluid on an object.

• Direction: Always upward.

• Magnitude: Equal to the weight of the fluid displaced by the object.

• Formula: $FB=mg=\rho Vg$

Object Behavior in Fluid

• If \rho obj<\rho f , object accelerates upward.

• Floating Object: Vobj > Vf

• Submerged Object: Vobj = Vf

Ideal Fluid Flow Conditions

1. Nonviscous: No internal friction.

2. Incompressible: Constant density.

3. Steady (Laminar): Regular and consistent flow.

4. Irrotational: Zero net angular velocity.

• Pressure difference causes fluid flow.

Volumetric Flow Rate & Continuity Equation

• Volumetric Flow Rate ($Q=Av$ ):

  • A : cross-sectional area

  • $v$ : speed of fluid flow

• Continuity Equation: $A1v1=A2v2$

  • The volumetric flow rate is constant.

  • If area decreases, fluid speed increases.

Bernoulli's Equation

• Description: Conservation of mechanical energy for ideal fluid flow.

• Equation: $P1+\frac12\rho v1^2+pgh1=k$

Bernoulli's Principle

• Concept: Relates fluid speed and pressure.

• If height difference is negligible, if fluid speed increases, fluid pressure decreases.

Torricelli's Theorem

• Application: Speed of ideal fluid exiting a small hole from a large, open reservoir.

• Formula: $v=\sqrt{2gh}$

  • h : depth of the fluid from the top surface to the hole.

UNIT 9: Thermodynamics

Ideal Gases & The Ideal Gas Law

Ideal Gas Assumptions

• Particles don't interact (no intermolecular forces).

• Particles don't take up volume (their individual volume is negligible compared to container volume).

Describing Ideal Gases (Variables)

• Volume (V): Volume of the container.

• Pressure (P): Force exerted by gas particles on container walls per unit area.

• Temperature (T): Measured in Kelvin (absolute scale), related to particle kinetic energy.

• Number of moles (n): Amount of gas present.

• Number of molecules (N): he number of molecules in the gas.

• Constant for Molar Ideal Gas Law (R):

  • Pressure in Pa and Volume in m³: $R=8.31\left(\frac{J}{K\cdot mol}\right)$

  • Pressure in atm and Volume in L: $R=0.0821\left(\frac{\left(L\cdot atm\right)}{K\cdot mol}\right)$

• Boltzmann's constant (k_B): $k_B=1.38\times 10^{-23} \dfrac{J}{K}$

  • Unit for Pressure is Pa and for Volume it’s m³

Relationships Between Variables

• Volume and Pressure: Inverse relationship. As V decreases, P increases .

• Volume and Temperature: Direct relationship. As V decreases, T decreases.

• Volume and Moles (and Molecules): Direct relationship. As V increases, n or N increases.

Formulas

• Molar: $PV=nRT$

• Molecular: $PV=N\left(kB\right)T$

UNIT 10: Electric Force, Field, and Potential

UNIT 11: Electric Circuits

UNIT 12: Magnetism and Electromagnetism

UNIT 13: Geometric Optics

UNIT 14: Waves, Sound, and Physical Optics

UNIT 15: Modern Physics