Physics Exam 3 Study Guide: Waves, Thermodynamics, Fluids, and Kinetic Theory

Waves and Simple Harmonic Motion

Transverse Waves

Transverse waves are waves in which the oscillation is perpendicular to the direction of wave propagation. Common examples include waves on a string and electromagnetic waves.

• Wave Properties: Amplitude, wavelength, frequency, and velocity.

• Wave Velocity Equation: For a stretched string, the velocity $v$ is given by $v = \sqrt{\frac{T}{\mu}}$, where $T$ is the tension and $\mu$ is the mass per unit length.

• Graphical Analysis: Velocity vs. tension plots help visualize how increasing tension increases wave speed.

• Example: If the tension in a string doubles, the wave speed increases by a factor of $\sqrt{2}$.

Simple Harmonic Motion (SHM)

SHM describes periodic motion where the restoring force is proportional to displacement and directed toward equilibrium.

• Key Quantities: Period ($T$), frequency ($f$), amplitude ($A$), velocity ($v$).

• Period of a Mass-Spring System: $T = 2\pi \sqrt{\frac{m}{k}}$

• Period of a Pendulum: $T = 2\pi \sqrt{\frac{L}{g}}$

• Relationship: If mass doubles, period increases by $\sqrt{2}$; if amplitude doubles, period remains unchanged.

• Example: Doubling the spring constant halves the period.

Fluids and Buoyancy

Buoyant Force

Buoyant force ($F_b$) is the upward force exerted by a fluid on an immersed object, equal to the weight of the displaced fluid.

• Archimedes' Principle: $F_b = \rho_{fluid} V_{displaced} g$

• Time-Dependent Buoyancy: As an object is lowered into a fluid, $F_b$ increases until fully submerged.

• Example: A plot of $F_b$ vs. time shows a rise as the object enters the fluid, then levels off when fully submerged.

Fluid Flow and Continuity

Fluid dynamics studies the movement of liquids and gases. The continuity equation relates the speed and cross-sectional area of a pipe.

• Continuity Equation: $A_1 v_1 = A_2 v_2$

• Application: If a pipe narrows, the fluid speed increases in the narrower section.

• Example: Water flows faster through a narrow pipe than a wide one, assuming incompressible flow.

Density and Floating Objects

Whether an object floats or sinks depends on its density relative to the fluid.

• Density Formula: $\rho = \frac{m}{V}$

• Floating Condition: If $\rho_{object} < \rho_{fluid}$, the object floats; otherwise, it sinks.

• Example: A ball with lower density than water will float; statements about its position can be evaluated using density values.

Thermodynamics and Heat

Specific Heat Capacity

Specific heat capacity ($c$) is the amount of heat required to raise the temperature of 1 kg of a substance by 1°C.

• Equation: $Q = mc\Delta T$

• Application: Given mass, energy, and temperature change, $c$ can be calculated.

• Example: If 500 J raises 2 kg of material by 5°C, $c = \frac{500}{2 \times 5} = 50$ J/kg·°C.

Heat Transfer and Proportionality

Heat transfer depends on mass, specific heat, and temperature change.

• Proportionality: $\Delta T = \frac{Q}{mc}$

• Comparisons: For equal heat input, a substance with lower specific heat will experience a greater temperature rise.

Phase Changes and Heating Curves

Heating curves show temperature changes as a substance absorbs heat, including phase transitions (melting, boiling).

• Key Points: Temperature remains constant during phase changes; energy goes into changing phase, not temperature.

• Example: Ice to steam heating curve: flat regions at melting and boiling points.

Kinetic Theory and Ideal Gases

Ideal Gas Law

The ideal gas law relates pressure, volume, temperature, and number of moles.

• Equation: $PV = nRT$

• Application: Used to compare properties of different gases under the same conditions.

Kinetic Energy and Temperature

Temperature is a measure of the average kinetic energy of molecules in a substance.

• Average Kinetic Energy: $KE_{avg} = \frac{3}{2}k_B T$

• Root Mean Square Speed: $v_{rms} = \sqrt{\frac{3k_B T}{m}}$

• Comparisons: For two gases at the same temperature, lighter molecules move faster.

• Example: If temperature doubles, $v_{rms}$ increases by $\sqrt{2}$.

Mole Calculations

The number of moles in a substance can be calculated from mass and molar mass.

• Equation: $n = \frac{m}{M}$, where $m$ is mass and $M$ is molar mass.

• Application: Given mass, atomic weight, and density, calculate moles present.

Tables

Comparison of Key Physical Quantities

Quantity	Formula	Units
Buoyant Force	$F_b = \rho_{fluid} V_{displaced} g$	N (Newtons)
Specific Heat	$Q = mc\Delta T$	J/kg·°C
Density	$\rho = \frac{m}{V}$	kg/m³
Ideal Gas Law	$PV = nRT$	Pa·m³
Root Mean Square Speed	$v_{rms} = \sqrt{\frac{3k_B T}{m}}$	m/s
Period (Pendulum)	$T = 2\pi \sqrt{\frac{L}{g}}$	s (seconds)

Additional info:

• Some questions reference textbook-style diagrams (e.g., heating curves, fluid flow) and may require interpretation of graphical data.

• Atomic mass and molecular speed questions relate to kinetic theory and the behavior of gases.

• Proportionality and analogy questions test understanding of how physical quantities change with variables.