AP Physics 2: Algebra-Based FRQ Room

Airflow over an Airfoil Experiment

A wind tunnel experiment investigates the pressure distribution on an airfoil. Sensors along the cho

Analyzing a High-Speed Water Jet

A garden hose with an initial inner diameter of $$2\;cm$$ is fitted with a nozzle that reduces the d

Analyzing Experimental Data on Fluid Flow

Researchers studied the flow of an incompressible fluid in a pipe by measuring the flow speed and co

Bernoulli’s Equation and Venturi Meter

A Venturi meter is installed in a pipe to measure fluid flow. The meter provides different pressure

Bernoulli's Equation Application

A horizontal pipe has a constriction such that the cross-sectional area at Section 2 is one-third of

Bernoulli's Equation in Pipe Flow

A pump forces water through a horizontal pipe that includes a constriction. At Point 1 (just after t

Buoyancy and Floating Objects

An object with a mass of 150 kg and a volume of 0.75 m³ is placed in a fluid with a density of 800 k

Buoyancy and Stability of a Floating Body

A rectangular boat with a flat bottom is floating in freshwater (density = 1000 kg/m³). The boat has

Buoyancy in Multi-fluid Systems

This problem examines buoyancy when an object is in contact with two immiscible fluids, requiring de

Buoyant Force and Submerged Volume Analysis

An object with a mass of 150 kg and a volume of 0.75 m³ is observed to float in ethyl alcohol (densi

Calculating Flow Speed from a Known Pressure Drop

In a horizontal section of a water pipe (density = $$1000\;kg/m^{3}$$), a researcher measures a pres

Comparative Analysis of Pressure in Open versus Closed Fluid Systems

Two identical containers are filled with the same fluid. Container A is open to the atmosphere, whil

Continuity Equation in a Constricted Pipe

A horizontal pipe carries water (density $$1000\;kg/m^3$$) at a flow speed of $$6\;m/s$$. At one sec

Continuity Equation in a Non-Uniform Pipe

A researcher is analyzing water flow in a circular pipe whose diameter changes along its length. At

Continuity Equation in Pipe Flow

A circular pipe with a varying diameter carries water in a steady flow. At one section of the pipe,

Design Considerations for Submerged Structures

An engineer is designing a submerged structure that must resist external fluid pressure. (a) Derive

Designing a Multi-Variable Experiment on Fluid Properties

A research team is designing an experiment to investigate how fluid density, viscosity, and flow spe

Designing a Water Fountain: Pressure and Flow

A landscape architect is designing a water fountain and needs the water jet to reach a maximum heigh

Determining Fluid Density Experimentally

In a laboratory experiment, a student measures the mass and volume of an unknown fluid. The measurem

Dynamic Pressure in a Wind Tunnel

In a wind tunnel experiment, air flows at a speed of $$15\,m/s$$. Given that the density of air is $

Effect of Elevation Changes on Fluid Flow Speed and Pressure

A researcher investigates how a vertical drop in a pipeline affects fluid kinetic energy and pressur

Evaluating Fluid Pressure under Variable Density Conditions

In an experimental setup, the fluid density varies with depth according to $$\rho(y) = \rho_0 + k *

Flow Dynamics in a Non-Uniform Pipe System

Water flows through a pipe system that varies in cross-sectional area along its length. A provided g

Flow Rate Analysis Using a Venturi Meter

A venturi meter is installed in a pipe to measure water flow. The meter has an inlet diameter of $$D

Flow Through Irregular Channels

An experiment is carried out to measure water flow in an irregular channel where the cross-sectional

Flow through Varying Pipe Diameters

Water flows through a horizontal pipe that narrows. At Section 1, the pipe has a radius of 2 cm and

Fluid Exit Velocity: An Orifice Flow Experiment

A group of students conducts an experiment to measure the speed of water exiting a small orifice at

Fluid Pressure in a Rotating System

In a rotating cylindrical container, a fluid forms a parabolic free surface due to the centrifugal e

Fluid Pressure on a Dam Wall

A civil engineer is evaluating the force exerted on a vertical dam wall by the water in a reservoir.

Force on a Dam from Hydrostatic Pressure

A dam holds back a body of water. The vertical, rectangular face of the dam is 10 m high and 20 m wi

Graphical Analysis of Flow Speed Variation

A researcher has collected experimental data on the relationship between a pipe's cross-sectional ar

Hydrostatic Pressure in a Cement Column

A researcher seeks to determine the pressure exerted on the ground by a vertical cement column. The

Hydrostatic Pressure in a Liquid Column

Consider an open tank filled with a liquid of density $$\rho$$. The hydrostatic pressure at a depth

Impact of Fluid Density on Buoyancy Forces

A block of wood with a volume of 1.0 m³ and a density of 600 kg/m³ floats in freshwater (density 100

Investigating Flow Speeds in a Constricted Pipe

A researcher sets up an experiment to study the relationship between pipe cross-sectional area and f

Investigating Pressure-Volume Relationships in Sealed Systems

Design an experiment to investigate the relationship between pressure and volume in a sealed contain

Manometer Pressure Measurements

An experiment uses a U-tube manometer filled with water to measure pressure differences in a fluid s

Net Force on a Submerged Curved Surface

Consider a dome-shaped, curved window that is fully submerged in water. The pressure on the surface

Non-uniform Flow Channel Velocity Measurement Error

A student designs an experiment to measure the velocity of water in an open channel that has section

Non-uniform Flow Through Constricted Channel Error

A student constructs an apparatus to measure fluid velocity in a channel that narrows and changes sh

Oil-Water Separation in Multi-Phase Fluid Systems

An experiment is conducted in a container to investigate oil-water separation based on density diffe

Pipeline Flow Optimization in a Water Treatment Facility

A water treatment facility operates a pipeline that has three sections with varying diameters. The f

Pressure Distribution in an Accelerating Container

A rectangular container filled with water (density $$1000\;kg/m^3$$) is accelerated horizontally at

Pressure Exerted by Fluid Column

A researcher investigates the variation of pressure with depth in a fluid contained within a transpa

Pressure Variation in a Swimming Pool

Consider a swimming pool with a uniform depth of 2.5 m filled with water (density $$\rho = 1000 \; k

River Flow Dynamics Study

A team of engineers conducts a field study to measure the flow characteristics of a river. They reco

Submerged Object Pressure Analysis

A researcher examines the variation of hydrostatic pressure on an object fully submerged in water.

Surface Pressure Analysis of a Column

A vertical column of cement has a base area of $$0.5\,m^2$$, a height of $$2\,m$$, and a density of

Temporal Flow Rate Analysis from an Experimental Graph

A student records the flow speed of water through a pipe over a 30-second interval. The graph shows

Testing Bernoulli's Principle in a Venturi Tube

A researcher is using a Venturi tube to study fluid velocities in water (density = $$1000\;kg/m^{3}$

The Siphon Effect and Limitations

A garden siphon is used to transfer water from one container to another that is placed at a lower el

Variable Buoyancy: Measuring Submerged Fraction of an Object

Design an experiment to measure how the submerged volume fraction of an object changes in fluids wit

Visualization of Laminar Flow in Pipes

In an experiment designed to visualize the velocity profile of a fluid in a pipe, sensors are placed

Adiabatic vs. Isothermal Process Comparison

A gas transitions between the same initial and final states via two different processes: an adiabati

Analysis of a Composite Thermodynamic Cycle

A gas undergoes a composite cycle consisting of an isobaric expansion, an adiabatic compression, and

Analysis of Conduction, Convection, and Radiation in Heat Transfer Experiment

An experiment is designed to study different modes of heat transfer. In one part of the experiment,

Analysis of Thermodynamic Processes on a P–V Diagram

A researcher examines four thermodynamic processes (isothermal, adiabatic, isobaric, and isochoric)

Analyzing Gas Mixtures with Dalton's Law

In a container, two different ideal gases are mixed together. Dalton's Law of Partial Pressures stat

Analyzing Temperature Effects on Molecular Speeds

A media report claims that to double the root mean square (rms) speed of gas molecules, the temperat

Comparing Real and Ideal Gas Behavior

Discuss the limitations of the Ideal Gas Law and explain the necessary corrections for real gases us

Comparison of Isothermal and Adiabatic Processes

A gas transitions between the same initial and final states via two different paths: one is isotherm

Conduction Across Layered Materials

A claim is made that the rate of heat transfer through a composite wall can be accurately described

Conduction, Specific Heat, and Temperature Change

A metal rod of mass 2 kg and specific heat capacity 400 J/(kg·K) is heated by supplying 8000 J of en

Contained Gas Pressure and the Ideal Gas Law

Investigate the pressure exerted by a gas confined in a cylindrical container. Summarize how the Ide

Conversion between Energy and Work in Cyclic Processes

In a cyclic thermodynamic process, the system converts energy between heat and work. (a) Explain ho

Designing a Convection Experiment

Develop an experimental proposal to investigate how fluid temperature affects the rate of convective

Designing an Experiment on Gas Pressure and Temperature

Design an experiment to verify the Ideal Gas Law using a sealed syringe. The aim is to observe the r

Designing an Experiment on Thermal Conductivity Variation with Material

A laboratory experiment is conducted to compare the thermal conductivity of different materials usin

Designing an Experiment to Measure Thermal Conductivity

Outline an experimental design to measure the thermal conductivity (k) of an unknown material using

Determining Heat Engine Efficiency

A cyclic heat engine operates with the following heat transfers during each cycle: it absorbs 1000 J

Effect of Molecular Mass on RMS Velocity

Examine how the molecular mass of a gas affects its root mean square velocity, given by the equation

Effect of Temperature on RMS Velocity

Given that $$v_{rms} = \sqrt{\frac{3k_B T}{m}}$$ for an ideal gas, (a) Explain the functional depend

Entropy Change and the Second Law of Thermodynamics

During a reversible isothermal expansion of an ideal gas, the entropy change is described by the equ

Error Analysis in Pressure and Temperature Measurements

In an experiment, several measurements of a gas's pressure and temperature were recorded along with

Gas Particle Collisions and Pressure Derivation

The kinetic theory of gases explains that the pressure exerted by a gas is due to the collisions of

Gas Pressure in Constant Volume Experiment

In a constant-volume experiment, a sealed container is heated and the resulting pressure is measured

Heat Engine Efficiency and Work Output

A heat engine undergoes a cyclic process where it absorbs 800 J of heat from a high-temperature sour

Heat Engine Work Cycle Analysis

A heat engine operates by drawing $$Q_H = 800\,J$$ of heat from a high-temperature source and discar

Heat Engines: Efficiency and Work Calculations

A heat engine operates in a cycle, drawing 800 J of heat from a high-temperature source and rejectin

Heat Transfer Conduction/Convection Experiment Error

A student investigates heat transfer through a metal rod by heating one end and measuring temperatur

Heating a Gas: Conduction vs. Convection

Heat can be transferred via different mechanisms. In the context of a gas being heated, consider the

Ideal Gas: Container Pressure and Force

Consider a cylindrical container of gas with a radius $$r = 0.15\;m$$ and height $$h = 0.30\;m$$ tha

Influence of Molar Mass on Molecular Speeds

A researcher compares the root-mean-square speeds of molecules from two different gases under identi

Investigating Pressure-Temperature Relationship in a Closed Gas Container

In a constant-volume container, the pressure of a confined gas changes as the temperature varies. De

Isothermal Process Work Calculation

An ideal gas undergoes an isothermal expansion at a constant temperature of 350 K. The gas expands f

Kinetic Energy and Temperature Relationship

An experiment on an ideal gas was conducted to measure the average molecular kinetic energy and temp

Maxwell-Boltzmann Distribution Analysis Experiment Error

A student conducts an experiment to validate the Maxwell-Boltzmann distribution by measuring the fli

Modes of Heat Transfer: Conduction, Convection, and Radiation

A copper rod of length $$L$$ and cross-sectional area $$A$$ experiences a temperature difference $$\

Multi-Cycle Heat Engine Performance Analysis

A heat engine operates in cycles. In each cycle, it absorbs 1000 J of heat, performs 400 J of work,

Pressure and Force in Confined Gas Systems

A researcher measures the pressure of a confined gas inside a container with a flexible lid. The int

Pressure Changes in a Sealed Rigid Container

A sealed, rigid container (i.e., constant volume) contains an ideal gas. (a) Derive the relationsh

Pressure Force in a Confined Gas

A cylindrical container of radius 15 cm and height 30 cm contains 0.6 mole of an ideal gas at 433 K.

Pressure Sensor Calibration Error in Gas Experiment

In an experiment intended to verify the Ideal Gas Law, a student uses a pressure sensor to record th

Radiative Heat Transfer Experiment Error

In an experiment designed to quantify radiative heat transfer, a student sets up a hot plate surroun

Real Gas Behavior vs. Ideal Gas Law: Experiment Design to Evaluate Deviations

While the ideal gas law (PV = nRT) works well for many gases, real gases deviate from this behavior

Thermodynamic Analysis of an Ice Melting Process

When heat is added to a substance at its melting point, the phase change occurs without a change in

Thermodynamic Process Data Analysis: Evaluating P–V and T–S Diagrams

Graphs such as P–V and T–S diagrams provide insight into the energy changes in a system during therm

Thermodynamics and Mechanical Work in an Automobile Engine

An internal combustion engine converts the chemical energy of fuel into mechanical work. Consider th

Work Done in a Non-Constant Pressure Process

An ideal gas is compressed in a cylinder by a piston, and the pressure inside the cylinder varies wi

Work Done in Isobaric and Isochoric Processes on a PV Diagram

A gas confined in a piston-cylinder assembly undergoes two distinct processes as shown on the PV dia

Analysis of an Electric Dipole Field

An electric dipole consists of two charges, \(+q\) and \(-q\), separated by a distance \(d\). (a) D

Application of Coulomb's Law

Coulomb’s Law states that the magnitude of the electric force between two point charges is given by

Balancing Gravitational and Electric Forces in a Uniform Field

A small object of mass 5.0 g is placed 2.0 cm above a large, positively charged horizontal plate tha

Capacitor Design Challenge

A parallel-plate capacitor is constructed with two metal plates separated by a distance of 0.2 mm in

Charge Induction in Connected Conducting Spheres

In an induction experiment, two neutral conducting spheres are brought into contact while a charged

Charge Quantization and Experimental Uncertainty

In a series of experiments, students measured the net charge on several isolated metallic spheres us

Charge Quantization Experiment Analysis

An experiment measures the charge on small spheres, and the measured values (in Coulombs) are found

Charge Redistribution Experiment

An experiment is designed to verify the conservation of charge during collisions between conducting

Coulomb's Law and Electric Field Vector Addition in an Equilateral Triangle

Three point charges are placed at the vertices of an equilateral triangle with a side length of $$0.

Determining Coulomb's Constant Experiment

A series of measurements is conducted to determine Coulomb’s constant $$k$$ by measuring the force b

Determining Coulomb's Constant Experiment

A researcher conducts an experiment to determine Coulomb's constant by suspending two small charged

Diagram Analysis: Electric Field Lines and Equipotentials in a Dipole

The following diagram represents an electric dipole configuration. It shows two charges located on t

Distance Dependence in Coulomb's Law

Coulomb's Law quantitatively describes the force between two point charges as inversely proportional

Electric Field Variation with Distance

A researcher measures the strength of the electric field produced by a point charge of $$+2.0 \times

Electric Potential Variation Analysis

A series of electric potential measurements were taken at three different positions (A, B, and C) in

Energy Conservation in a Capacitor Discharge

A capacitor with a capacitance of 20 μF is initially charged to 200 V and then discharged through a

Energy Stored in a Capacitor: Discharge Process Oversight

An experiment is conducted to measure the energy stored in a charged capacitor. The capacitor is cha

Graphical Analysis of Electric Potential Energy

A graph is provided showing the electrical potential energy U of a test charge as a function of its

Investigating Capacitor Energy Storage Versus Separation Distance

Design an experiment to measure how the energy stored in a parallel-plate capacitor changes as the d

Measuring Electric Potential Variations from a Point Charge

Develop an experimental design to measure the electric potential at various distances from a fixed p

Net Electric Force on a Central Charge in a Square Configuration

Four equal positive point charges are fixed at the vertices of a square, and a negative point charge

Net Force in Linear Charge Arrangement

A researcher arranges three point charges along the x-axis as follows: $$q_1 = +2.0 \; nC$$ at $$x =

Parallel-Plate Capacitor Design

A researcher aims to design a parallel-plate capacitor in vacuum. The desired capacitance is $$15 \;

Potential Difference in a Parallel-Plate Capacitor

A parallel-plate capacitor has plates of area A = 0.05 m² separated by a distance d = 0.001 m and is

Potential Energy Change in a Uniform Field

In a controlled experiment, a charged particle initially at rest moves through a uniform electric fi

RC Circuit: Charging a Capacitor

A capacitor with a capacitance of $$100\,\mu F$$ is connected in series with a resistor of $$10\,k\O

Superposition of Forces in a Square Configuration

Four equal positive point charges are placed at the vertices of a square. A negative charge is place

Uniform Electric Field Balance Experiment

A large, positively charged horizontal plate produces a uniform electric field of magnitude $$E = 1.

Uniform Electric Field Equilibrium Experiment

An experiment is set up in which a large, positively charged plate generates a uniform electric fiel

Uniform Electric Field from a Charged Plate

A large horizontal plate carries a uniform positive surface charge density σ = 2.0 × 10⁻⁶ C/m².

Work and Electrical Potential Energy in a Uniform Electric Field

A positive charge q = 1.0 × 10⁻⁶ C is moved a distance d = 0.05 m in the direction of a uniform elec

Analysis of a Simple Series Circuit

This FRQ examines a simple series circuit. Consider an ideal battery with an electromotive force (EM

Analyzing Ammeter and Voltmeter Measurements

A circuit is constructed with a battery and a resistor. An ammeter and a voltmeter are connected to

Analyzing Power Dissipation in a Resistor Network

Consider a resistor network connected to a $$12~V$$ battery.

Analyzing Power Efficiency in a Circuit with Multiple Loads

A circuit with multiple load components draws power from a battery. The following table presents mea

Applying Kirchhoff’s Laws in Multi-Loop Circuits

A circuit consists of two loops sharing a common resistor. The components of this circuit are provid

Battery Internal Resistance and Power Delivery

A battery modeled as an ideal EMF source of 12 V in series with an internal resistance of 2 Ω is con

Capacitor Charging and Discharging in RC Circuits

An experiment claims that when a charged capacitor discharges through a resistor, the voltage across

Capacitor Charging in an RC Circuit

In an RC circuit, a capacitor is charged through a resistor by a 12 V battery. The voltage across th

Capacitors in Series and Parallel: Equivalent Capacitance Analysis

An experiment is performed using two identical capacitors each with capacitance $$C = 5\;F$$. They a

Charging Behavior of an RC Circuit

A capacitor with capacitance $$C = 5 \text{ F}$$ is charged through a resistor of $$R = 3 \Omega$$ b

Circuit Design for Energy Efficiency

An engineer designs two circuits using the same 12 V battery but with different resistor network con

Critically Evaluating the Role of Wire Material in Circuit Performance

A claim has been made that using wires made of materials with low resistivity, such as copper, enhan

Current Flow Analysis in a Simple Battery Circuit

A researcher claims that a circuit composed of a 12 V battery and various resistors produces a conti

Design of a Capacitor Bank for Energy Storage

A capacitor bank is required to store at least $$50~J$$ of energy at a working voltage of $$12~V$$.

Determining Capacitance Changes Due to Physical Adjustments

A parallel-plate capacitor has plate area A, plate separation d, and a dielectric constant k. Answer

Determining Resistivity through Experimental Measurements

A researcher studies a uniform wire made of an unknown material. The wire has a length of 2 m and a

Effect of a Discharged Capacitor on Parallel Resistor Branches in an RC Circuit

In an experiment, an initially uncharged (discharged) capacitor is connected in parallel with two re

Effect of Capacitance Variation on Steady-State Voltage

A capacitor is initially charged to $$15 \text{ V}$$. Two scenarios are considered when its physical

Effect of Resistor Arrangement on Circuit Current Distribution

A circuit consists of a 12 V battery connected to a resistor network featuring both series and paral

Effects of Altering Capacitance in a Charged Capacitor Circuit

A capacitor is first charged in a circuit with a battery connected, and then the battery is disconne

Energy Storage Analysis in Capacitors

A capacitor stores energy according to the formula $$E = \frac{1}{2} C V^2$$. Consider a capacitor w

Equivalent Capacitance of Mixed Capacitor Networks

Three capacitors are connected in a network. Capacitor $$C_1 = 4\,\mu F$$ is connected in series wit

Evaluating the Equivalent Capacitance of a Parallel Capacitor Array with a Battery

A student conducts an experiment to determine the equivalent capacitance of two capacitors connected

Experimental Design: Effect of Resistor Arrangements on Circuit Behavior

Design an experiment to investigate how different resistor configurations (series vs. parallel) affe

Experimental Determination of Resistor Resistance Using Ohm's Law

Devise a procedure to determine the resistance of an unknown resistor using a battery, an ammeter, a

Exploring the Influence of Circuit Component Placement on Measured Values

In an experiment to study circuit behavior, a student assembles various configurations using the sam

Graphical Analysis of Battery Discharge

A battery is discharged over time and its terminal voltage is recorded. The following graph shows th

Impact of Wire Dimensions on Resistance

In an experiment, two wires made of the same material but with different lengths and cross-sectional

Investigating Charge Leakage Effects in Capacitor Charging Experiment

A student studies the charging curve of a capacitor in an RC circuit by recording the voltage over t

Investigating Temperature Dependence of Resistance

Resistance in metallic conductors generally increases with temperature. Answer the following:

Investigating the Impact of Wire Geometry on Electrical Resistance

A claim is made that the resistance of a wire depends on its length and cross-sectional area as desc

Investigation of Non-Ohmic Behavior

A filament lamp exhibits non-ohmic behavior. The following graph shows its voltage versus current re

Measuring Electric Current and Voltage in a Simple Circuit

In a simple circuit consisting of a battery, a resistor, and connecting wires, you are asked to inve

Measuring Power Dissipation in Resistive Elements

Power dissipation in a resistor is an important factor for both performance and safety. Given the fo

Multiple Energy Sources in a Complex Circuit

Consider a complex circuit composed of two branches connected in parallel. The details for each bran

Power Dissipation Analysis in Resistive Networks

Consider a circuit powered by a $$24 \text{ V}$$ battery. The circuit consists of a series resistor

RC Circuit Capacitor Charging

A capacitor is connected in series with a resistor and a battery in an RC circuit. Answer the follow

Resistor Networks and Equivalent Resistance

A circuit contains three resistors arranged in a mixed series-parallel configuration. Resistors R1 =

Series and Parallel Resistor Networks

Consider a circuit that contains a 12 V battery connected to three resistors arranged such that resi

Transient Behavior in RC Circuit: Initial vs Steady-State

An RC circuit is constructed with a $$12~V$$ battery, and two branches: one branch contains a $$6~\O

AC Generator Induced EMF Analysis

Consider an alternating current generator where a coil of $$N$$ turns and area $$A$$ rotates in a un

Analysis of Motional EMF in a Moving Conductor

A metal rod of length $$\ell = 0.4 \; m$$ moves with a constant speed of $$v = 4 \; m/s$$ through a

Charged Particle Force Analysis

A proton with charge $$q = +1.6×10^{-19} C$$ enters a uniform magnetic field $$B = 0.3 T$$ with a sp

Charged Particle in a Non-Uniform Magnetic Field

A charged particle with charge $$q = 2 \times 10^{-6}$$ C moves along the x-axis at a constant speed

Comparing Magnetic Field Mapping Techniques

Design an experiment to compare two techniques for mapping magnetic field lines: one using iron fili

Comparing Magnetic Forces on Charges and Wires

This FRQ compares the magnetic force on an individual moving charge to the force on a current-carryi

Critical Angle for Maximal Magnetic Force

A researcher investigates the dependence of the magnetic force on a charged particle with the equati

Current-Carrying Wire in Variable Magnetic Field

A researcher studies a straight wire of length $$\ell$$ carrying a current $$I$$, placed in a magnet

Designing a Magnetic Levitation Experiment

A researcher aims to levitate a small object using a combination of current-carrying coils and perma

Determining Magnetic Force on a Moving Charge

A researcher sets up an experiment where a charged particle is projected horizontally into a region

Effect of Changing Magnetic Field Strength on Induced Current

A coil is subjected to a magnetic field that decreases linearly from $$B_0$$ to $$B_1$$ over a time

Energy Conversion in an Electromagnetic Generator

A simple electromagnetic generator consists of a rotating loop placed in a uniform magnetic field, r

Energy Transformation in a Moving Conductor Experiment

In an experiment, a conducting bar is made to slide through a uniform magnetic field, generating an

Evaluating Magnetic Flux Change in a Rotating Loop

A circular loop of wire is rotated in a uniform magnetic field. The change in orientation causes the

Experimental Design for Faraday's Law Validation

You are tasked with designing an experiment to validate Faraday's law of electromagnetic induction.

Experimental Investigation of Lenz's Law

A researcher sets up an experiment where the area of a coil is rapidly decreased while the coil is p

Faraday's Law and Rotating Loop

This FRQ requires applying Faraday's law to a rotating circular loop in a uniform magnetic field.

Faraday’s Law and Rotating Loop

A circular loop rotates in a uniform magnetic field, inducing an emf according to Faraday’s Law. Ana

Force Comparison: Permanent vs. Electromagnets

In a laboratory experiment, the attractive force between a fixed magnet and a piece of iron is measu

Impact of Magnetic Field Reversal on Induced EMF

Consider a single-turn loop in which the magnetic flux initially is $$\Phi_i = B*A$$. If the externa

Investigating the Impact of Magnetic Field Strength on Induced Current

This FRQ examines how changes in magnetic field strength affect the induced current in a circuit wit

Investigating the Magnetic Field of a Solenoid

A solenoid with length $$L$$, number of turns $$N$$, and carrying current $$I$$ produces a uniform m

Magnetic Braking in a Rotating Metal Disk

A metal disk is set into rotation and brought near a set of fixed magnets arranged so that eddy curr

Magnetic Field around a Current-Carrying Wire

A long, straight wire carries a current of $$I = 10 A$$. a) Using the formula $$B = \frac{\mu_0}{2

Magnetic Field Diagram Analysis

Examine the provided diagram of a bar magnet's magnetic field. The diagram shows a bar magnet labele

Magnetic Field Visualization

This FRQ explores the nature of magnetic fields and how magnetic field lines are used to represent t

Magnetic Flux Through a Rotating Loop

A circular loop of radius $$r = 0.03 \; m$$ is placed in a uniform magnetic field of strength $$B =

Magnetic Force on a Moving Charge

A researcher examines the force on a charged particle moving in a uniform magnetic field. The partic

Magnetic Force on a Moving Charge

A charged particle moves through a uniform magnetic field. Use the relationship that the magnetic fo

Magnetic Permeability and Field Mapping

A researcher investigates the effect of material magnetic permeability on the distribution of magnet

Mapping Magnetic Field Using Iron Filings

Students perform an experiment to visualize the magnetic field around a bar magnet by sprinkling iro

Power and Energy Conversion in Motional EMF

A conducting rod of length $$L = 0.5 m$$ moves at a constant speed of $$v = 3 m/s$$ through a unifor

Qualitative Analysis of Magnetic Field Lines Using Iron Dust Technique

A scientist uses finely milled iron dust to visualize the magnetic field lines around a permanent ba

Radius of Circular Motion vs. Velocity

In a controlled experiment, charged particles are injected into a uniform magnetic field and follow

Trajectory Analysis of a Charged Particle in a Non-Uniform Magnetic Field

A charged particle with charge $$q$$ and mass $$m$$ enters a region where the magnetic field varies

U-Shaped Wire Current Balance

A researcher studies a U-shaped wire with three segments (two vertical legs and one horizontal segme

Using a Hall Probe to Measure Magnetic Fields

In a laboratory setup, students use a Hall probe to measure the magnetic field around a long, straig

Zero Net Force in U-Shaped Wire Experiment

In a controlled experiment, a U-shaped wire with three segments is partially immersed in a magnetic

Analyzing the Polarization of Electromagnetic Waves

Polarization describes the orientation of light waves. In this problem, you will explain polarizatio

Calculating Lens Power from Image Magnification

An object is placed $$10 \text{ cm}$$ in front of a converging lens and produces a real image that i

Concave Mirror Image Analysis

An object of height $$4 \text{ cm}$$ is placed $$30 \text{ cm}$$ in front of a concave mirror with a

Concave Mirror Image Formation

An object of height 5 cm is placed 20 cm from a concave mirror with a focal length of 10 cm. Answer

Converging Lens Magnification Experiment

A student performs an experiment with a converging (bi-convex) lens. In this setup, an object is pla

Convex Mirror Image Formation

An object of height $$h_o = 5 \ cm$$ is placed at a distance of $$d_o = 25 \ cm$$ in front of a conv

Critical Angle Determination for Various Media

A researcher is studying critical angles when light passes from glass (with $$n=1.5$$) into differen

Determining Lens Power: Experimental Measurement via Object-Image Distance

Design an experiment to determine the power of a converging lens by measuring object and image dista

Diffraction Grating Analysis

A diffraction grating with 5000 lines per centimeter is used to analyze white light. Consider the fi

Diverging Lens Experiment: Investigating Virtual Image Formation

Design a controlled experiment to study the image characteristics produced by a diverging lens. Your

Electromagnetic Wave Characteristics and Frequency Calculation

Using the table provided, analyze the relationship between wavelength and frequency of electromagnet

Electromagnetic Wave Oscillation Diagram Analysis

Using the provided diagram showing oscillating electric (E) and magnetic (B) fields of an electromag

Electromagnetic Wave Propagation in a Vacuum

Maxwell's equations imply that electromagnetic waves propagate in a vacuum at a constant speed $$c$$

Fiber Optics and Total Internal Reflection

An optical fiber operates on the principle of total internal reflection. The core of the fiber has a

Frequency Calculation for Green Light

Using the provided table of wavelengths for visible light, calculate the frequency of green light an

Interference and Diffraction Patterns

A coherent light source with a wavelength of $$500 * 10^{-9}$$ m illuminates a double-slit apparatus

Interference Patterns and Young's Double Slit Experiment

An experiment using Young's double-slit setup produced the table below showing fringe positions. Ass

Lens Power Calculation

When an object is placed 10 cm from a converging lens, a real image is formed that is twice the heig

Magnification in Diverging Lens: Formula Misapplication Error Analysis

A student performs an experiment with a diverging lens by measuring object height, image height, obj

Multi-Wavelength Interference Experiment

In an experiment using a diffraction grating, two monochromatic light sources are employed: red ligh

Plane Mirror Image Characteristics

An object is placed in front of a plane mirror at a distance of $$d = 2.0 \ m$$.

Plane Mirror Image Formation

A person stands 2.0 m from a flat plane mirror. Answer the following:

Polarization and Brewster's Angle

When unpolarized light strikes a glass surface, the reflected light becomes partially polarized. Con

Polarization and Light Intensity Experiment

A student in an optics lab investigates the effect of polarization on light transmission. The experi

Prism Dispersion and Light Deviation

A student uses a triangular prism to study the dispersion of white light into its constituent colors

Radio Waves in Communication

Radio communications often use electromagnetic waves with wavelengths on the order of meters. (a) C

Real vs. Virtual Images in Combined Optical Systems

An optical system is constructed by combining a concave mirror with a converging lens. Answer the fo

Reflection and Refraction at a Glass Surface

A beam of light traveling in air is incident on a flat glass surface at an angle of $$30^\circ$$ rel

Reflection and Refraction at an Interface

A beam of light traveling in air (index of refraction $$n_1 = 1.0$$) strikes the surface of a glass

Reflection and Refraction: Index Determination Error Analysis

A student sets up an experiment to measure the index of refraction of a piece of glass by directing

Reflection and Refraction: Measuring Indices of Refraction

An experiment is conducted where a light ray passes from air into an unknown medium, and the followi

Reflection and Refraction: Snell's Law

A beam of light traveling in air (with an index of refraction, n = 1.0) strikes a glass surface (n =

Single Slit Diffraction Experiment: Determining Slit Width

Design an experiment to measure the width of a single slit by analyzing its diffraction pattern. You

Single-Slit Diffraction: Experimental Error Analysis

In an experiment aimed at studying single-slit diffraction, a student sets up a coherent light sourc

Thin Diverging Lens Imaging

A diverging lens with a focal length of -15 cm is used to form an image of an object 9 cm tall place

Thin Lenses: Converging Lens Analysis

In an experiment involving a converging lens, measurements were taken for various object distances.

Total Internal Reflection

When light travels from water ($$n = 1.33$$) to air ($$n = 1.0$$), total internal reflection can occ

Total Internal Reflection at Air-Water Interface

Light traveling within water (with an index of refraction $$n_{water} \approx 1.33$$) approaches the

Total Internal Reflection in Prisms

A triangular prism made of glass with an index of 1.6 is used to redirect a light beam. A light ray

Young's Double Slit Experiment Analysis

In a Young's double slit experiment, monochromatic light of wavelength $$589 \times 10^{-9}\,m$$ pas

Young's Double Slit Experiment Analysis

In Young's double slit experiment, coherent light passing through two closely spaced slits produces