AP Physics 2: Algebra-Based FRQ Room

Airflow and Aerodynamic Lift

A researcher investigates the role of airflow in generating lift over an airplane wing using Bernoul

Airflow and Lift on an Airfoil

An airplane wing is designed so that the air above the wing travels at a different speed than the ai

Airflow and Lift over an Airfoil

An experimental report claims that the difference in airspeed over the top and bottom surfaces of an

Airflow Over an Airfoil and Lift Generation

In a wind tunnel experiment, an airfoil is subjected to an airflow of $$20\,m/s$$. Pressure sensors

Airflow over an Airfoil Experiment

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

Analyzing Flow Rate Data from a Pipe

An experiment measures water flow through a pipe of varying diameters. The following data table show

Analyzing Submerged Structures in Fluids

A marine structure is designed to float partially submerged in a lake. The structure has a total mas

Application of Bernoulli’s Equation in Fluid Flow

A researcher studies water flow through a pipe system that gradually narrows. Bernoulli’s equation,

Bernoulli's Equation in Pipe Flow

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

Bernoulli's Principle and Aircraft Lift

Air flows over the upper and lower surfaces of an airplane wing. In a certain section along the wing

Bernoulli's Principle in a Constricted Flow System

Water flows through a horizontal pipe that gradually constricts. At point 1, the fluid has a cross-s

Buoyancy and Archimedes' Principle Investigation

In a laboratory experiment, a researcher investigates the buoyancy of objects using ethyl alcohol (d

Buoyancy and Volume Fraction Analysis

A researcher studies buoyancy by examining how much of an object is submerged when floating. The exp

Buoyant Stability and Metacentric Height in Floating Bodies

A floating vessel is designed with specific dimensions to ensure stability. A diagram of the vessel’

Calculating Buoyant Force

An irregular object is completely submerged in water (density $$1000\;kg/m^3$$) and displaces a volu

Capillary Rise Error due to Contact Angle Misunderstanding

A student investigates the capillary rise effect by immersing a thin glass tube in water and measuri

Complex Pipe Network Analysis

This challenging problem involves analyzing a complex pipe network where a main pipe splits into two

Density Measurement Using a Hydrometer

A hydrometer is an instrument that measures liquid density by floating at a level where the buoyant

Density Measurement via Displacement Experiment

In this experiment, a student uses the displacement method to measure the density of an unknown liqu

Density Variation with Temperature in Liquids

A researcher measures the density of water at different temperatures and obtains the following data:

Design of a Venturi Meter for Flow Rate Measurement

A venturi meter is used to measure fluid flow by inducing a pressure difference through a constricte

Designing a Fluid Flow Experiment in a Lab Environment

You are tasked with designing an experiment to measure the volume flow rate of water through a horiz

Designing a Pipeline: Balancing Pressure and Flow Rate

An engineering project requires designing a pipeline to transport water over long distances. Changes

Designing an Experiment to Validate the Continuity Equation

An engineering team aims to validate the continuity equation for an incompressible fluid flowing thr

Determining Object Volume through Fluid Displacement

A student in a laboratory measures the volume of an irregularly shaped stone by submerging it in wat

Dynamics of a Floating Body in Fluid

A student investigates the dynamics of a floating object in water. The hypothesis is that when an ob

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

Effect of Temperature on Fluid Density and Hydrostatic Pressure

Design an experiment to measure how the density of a fluid changes with temperature and how these ch

Effect of Temperature on Fluid Density and Pressure

A container holds a fluid that is heated from 20°C to 80°C, causing its density to decrease from 100

Effect of Temperature on Fluid Properties

This problem investigates how temperature changes affect fluid properties such as density and viscos

Evaluation of Laminar vs. Turbulent Flow in Viscous Fluids

A research paper claims that water flowing in a pipe with a diameter of 5 cm at a velocity of 2 m/s

Experimental Analysis of Flow Speed Using Continuity Equation

In an experiment, water flows through a horizontal pipeline with varying cross-sectional areas. The

Experimental Design in Hydrostatics

You are tasked with designing an experiment to measure hydrostatic pressure at different depths in a

Exploration of Hydrostatic Pressure in a Dam Wall

A dam holds back a reservoir of water with a density of $$1000~kg/m^3$$. Consider the dam's vertical

Exploring Buoyancy in Variable Fluid Densities

A block with a volume of $$0.5\,m^3$$ and a mass of $$400\,kg$$ is placed in two different fluids. I

Floating Object in Stratified Fluids

An object with a volume of 0.5 m³ and a density of 850 kg/m³ is placed in a container holding two im

Flow Rate Variation in a Branching Pipe

A horizontal pipe carrying a total flow rate of $$0.012\,m^3/s$$ splits into two branches. One branc

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 Dynamics in Natural Systems: River Flow Analysis

A river exhibits variations in cross-sectional area along its course due to natural and man-made con

Fluid Flow in a River: Application of the Continuity Equation

A field study of a river involves measuring water flow through sections of differing cross-sectional

Fluid Flow in Circular and Rectangular Channels

Two channels are used to transport water: Channel 1 is circular with a diameter $$d$$, and Channel 2

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

Hydrostatic Pressure and Exit Velocity from a Reservoir

A large dam reservoir holds water with a density of 1000 kg/m³. Atmospheric pressure is $$101325\;Pa

Hydrostatic Pressure in a Stratified Lake

In a lake experiencing a temperature gradient, water density increases with depth. Suppose the top 0

Hydrostatic Pressure in Fluid Tanks

A tank is filled with water (density = $$1000 \cdot kg/m^3$$). The gauge pressure in the tank is mea

Hydrostatic Pressure Profile in a Tank

An open tank is filled with a liquid of density $$\rho$$. The pressure at a depth h is given by $$P

Hydrostatic Pressure Variation

Consider a large open tank filled with water (density = 1000 kg/m³). The atmospheric pressure is giv

Measurement and Correction of Fluid Pressure

A pressure sensor installed in a water tank provides the following readings at different depths: |

Measuring Hydrostatic Pressure in an Underwater Environment

An oceanographer sets up an experiment to measure the hydrostatic pressure as a function of depth in

Modeling Fluid Flow in a Conical Pipe

Consider a conical pipe whose radius decreases linearly with distance x according to $$r(x) = r_0 -

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

Open Tank Pressure and Total Pressure Calculation

A tank is open to the atmosphere and is filled with water. The total (absolute) pressure at any dept

Pipe Flow and the Continuity Equation Experiment

A student is investigating fluid flow through a pipe whose diameter varies along its length. The hyp

Pipe Flow Dynamics in Constriction

An experiment measures the flow speed of water in different segments of a pipe with varying radii. T

Pressure Exerted by a Fluid Column

A concrete column has a height of 3 m, a base area of 1 m², and a density of 2400 kg/m³. Answer the

Pressure Measurements in a Deep Lake

A diver uses a pressure sensor to measure the absolute pressure at various depths in a deep lake. Th

Reynolds Number and Flow Regime Analysis

In an experiment, water flows through a pipe with a diameter of $$0.05\,m$$ at a velocity of $$2.0\,

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

Tank Discharge Flow Experiment

An experiment investigates the discharge of water from a tank through a small orifice at the bottom.

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 Impact of Temperature on Fluid Viscosity and Flow

During an experiment, it was observed that the viscosity of a fluid decreases as temperature increas

Turbulent vs. Laminar Flow in a Conduit

A fluid flows through a horizontal pipe, and its flow regime (laminar or turbulent) depends on the R

Venturi Tube Misapplication of Bernoulli's Equation

A student constructs a Venturi tube apparatus to measure changes in fluid velocity by recording pres

Viscosity Neglect in Pipeline Flow Rate Experiment

A student conducts an experiment to measure the volume flow rate of oil through a pipeline with sect

Water Distribution in a City Pipeline

A city water supply pipeline has an initial section with a circular cross section of radius $$5.0\,c

Analysis of Thermodynamic Processes on a P–V Diagram

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

Application of the First Law of Thermodynamics

A gas within a piston undergoes a quasi-static process in which 500 J of heat is added to the system

Calorimetry Experiment: Measuring Specific Heat Capacity Using Temperature Changes

Calorimetry is used to measure the specific heat capacity of substances. Design an experiment using

Comparative Analysis of Heat Engine Cycles

Two heat engines, Engine A and Engine B, operate under different conditions. Their heat inputs and o

Comparing Real and Ideal Gas Behavior

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

Conduction Heat Transfer: Experimental Design for Material Thermal Conductivity Measurements

Heat conduction through materials depends on their thermal conductivity. Design an experiment to mea

Conversion between Energy and Work in Cyclic Processes

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

Data Analysis of an Adiabatic Process

An ideal gas undergoes an adiabatic process during which experimental data for pressure and volume a

Derivation and Calculation of RMS Speed

The root-mean-square (RMS) speed of gas molecules is given by the formula $$v_{rms} = \sqrt{\frac{3\

Design Considerations for a High-Efficiency Heat Engine

A company aims to design a heat engine that approaches the maximum theoretical (Carnot) efficiency.

Designing a Convection Experiment

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

Determining Force Exerted by Gas on a Container Lid

A cylindrical container with the following measured parameters is used in an experiment: the radius

Determining Heat Engine Efficiency

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

Determining Molecular Mass of a Gas via Ideal Gas Law Measurements: Experimental Design

The molecular mass of a gas can be determined by measuring its pressure, volume, temperature, and th

Effect of Molar Mass on Gas Velocity

The relation $$v_{rms} = \sqrt{\frac{3 * k_{B} * T}{m}}$$ indicates that the molar mass of gas molec

Entropy Change in Gas Mixing Experiment

Two chambers, each containing 0.5 moles of an identical ideal gas at 300 K and with a volume of 0.01

Entropy vs. Temperature Measurement Experiment Error

A student aims to study the change in entropy of a material as it is gradually heated. A thermocoupl

Experimental Verification of the Zeroth Law of Thermodynamics

An experiment is devised to verify the Zeroth Law of Thermodynamics using three objects. Object C is

Force on Container Lid from Confined Gas

A cylindrical container has a radius of 15 cm and a height of 30 cm. It contains 0.6 moles of an ide

Gas Pressure in Constant Volume Experiment

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

Heat Capacity and Calorimetry

In calorimetry, the specific heat capacity of a substance is determined by measuring temperature cha

Heat Engine Efficiency Experiment Error

In an experiment designed to measure the efficiency of a heat engine, a student records the amount o

Heat Engines and Maximum Efficiency

No heat engine can achieve 100% efficiency due to inherent energy losses. (a) Explain why complete c

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 by Convection

Heat transfer by convection occurs due to the movement of fluids. (a) Explain the mechanism by which

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 Law Calibration Experiment Error

A student conducts an experiment to verify the Ideal Gas Law using a cylindrical container with a mo

Isothermal and Adiabatic Processes in Ideal Gases

An ideal gas undergoes an isothermal expansion from an initial volume $$V_1$$ to a final volume $$V_

Isothermal vs. Adiabatic Processes

In a laboratory experiment, a gas is compressed in a piston under two different conditions: one proc

Maxwell-Boltzmann Distribution Analysis

A researcher claims that increasing the temperature of a gas not only increases the average speed of

Net Work in a Cyclic Thermodynamic Process

A cyclic thermodynamic process is depicted in a provided P–V diagram. Summarize the key characterist

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

Temperature Change and Molecular Speed Distribution

The root mean square speed of gas molecules is given by $$v_{rms} = \sqrt{\frac{3 * k_{B} * T}{m}}$$

Thermodynamic Stability and Phase Transitions

Phase transitions in materials can be understood in terms of thermodynamic stability. (a) Define th

Work Done in Thermodynamic Processes

A gas undergoes two different expansion processes between the same initial and final states as descr

Analyzing the Inverse Square Nature of Electric Fields

A point charge Q produces an electric field that is expected to vary with distance r according to an

Assessing the Impact of Fringing Fields on Capacitance

A parallel-plate capacitor with plate area A and separation d is ideally described by $$C = \frac{\v

Balancing Forces in a Uniform Electric Field

In an experiment to study the balance between gravitational and electric forces, a charged object of

Charge Conservation and Quantization

In an isolated system, charge is conserved and the charge on any object is an integer multiple of a

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 Quantization: Detector Calibration and Noise Issues

An experiment is performed to verify the quantization of electric charge by isolating individual cha

Charge Redistribution in Connected Conductors

In a series of experiments, two conducting spheres initially carrying different charges were connect

Charged Projectile Motion: Vector Decomposition Error

An experiment is set up to study the trajectory of a charged projectile launched horizontally in the

Charging and Discharging of a Capacitor – Time Response Analysis

This problem examines the time-dependent behavior of a capacitor in an RC circuit and requires you t

Charging by Induction: Analysis and Prediction

Two identical conducting spheres, initially uncharged, are placed on an insulating stand. A negative

Coulomb’s Pendulum Experiment Error Analysis

In an experiment designed to measure the electrostatic force between two identically charged spheres

Design of a Charging by Induction Experiment

Two initially neutral conducting spheres are to be charged by induction. Design an experiment to dem

Electric Dipole Analysis

A researcher studies an electric dipole consisting of a positive charge of $$+4.0 \; nC$$ and a nega

Electric Field Due to a Dipole

A dipole consists of two point charges: $$+4.0 \times 10^{-9} \; C$$ and $$-4.0 \times 10^{-9} \; C$

Electric Field Lines and Equipotential Mapping Misinterpretation

In a laboratory experiment, a student is tasked with mapping electric field lines and equipotential

Electric Field Mapping Experiment

A researcher employs a scanning probe to measure the local electric field near a large, charged plat

Electric Field Variation with Distance

An experiment measures the magnitude of the electric field produced by a point charge as a function

Electric Force Sensor Alignment Experiment

A student uses an electric force sensor mounted on a pivot to measure the net force on a test charge

Electric Potential Energy Conversion in a Point Charge Field

A positive charge is released from rest at a distance of 10 cm from a fixed positive charge and is l

Electrostatic Shielding and Induced Charges on a Conducting Shell

A hollow, spherical, conducting shell is placed in a uniform external electric field of magnitude $$

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 Storage: Impact of Plate Separation in a Capacitor Connected to a Battery

A parallel-plate capacitor connected to a battery maintains a constant potential difference V. Initi

Force on Test Charge in a Uniform Electric Field

A test charge of $$+3.0*10^{-9}$$ C is placed in a uniform electric field of magnitude 400 N/C that

Fringing Effects in Capacitor Design Experiment

An experiment is designed to measure the variations in the electric field at the edges of a parallel

Influence of Plate Area on Capacitor Capacitance

Design an experiment to determine how changing the area of the plates of a parallel-plate capacitor

Measurement and Analysis of Charge Distribution on a Sphere

A non-conducting sphere of radius 5 cm carries a total charge of 2×10⁻⁸ C uniformly distributed thro

Methods of Charging: Friction, Conduction, and Induction

There are three primary methods for charging objects: by friction, conduction, and induction. (a) D

Motion of a Charged Particle in a Non-Uniform Electric Field

A particle with charge \(q\) and mass \(m\) moves into a region where the electric field varies with

Motion of a Charged Particle in a Uniform Electric Field

A small charged particle with charge q = 2.0×10^-6 C and mass m = 2.0×10^-3 kg is released from rest

Parallel-Plate Capacitor: Potential Difference and Plate Area

A parallel-plate capacitor stores a charge of 50 μC on each plate and has a capacitance of 10 nF. (

Series and Parallel Capacitor Network Analysis

A capacitor network is constructed by connecting capacitors in both series and parallel arrangements

Setup of a Uniform Electric Field Using Parallel Plates

Design a laboratory experiment to create a uniform electric field using two parallel plates and to m

Superposition in Electric Field Calculations

Three point charges are arranged along a straight line: q₁ = +2 μC is located at x = 0, q₂ = -3 μC a

Superposition in Electric Field Measurement – Data Analysis

In an experiment, a pair of point charges (one positive and one negative, each of magnitude 1.0 × 10

Surface Charge Density and Electric Field Experiment

In an experiment, several large plates are charged to different surface charge densities, $$\sigma$$

Work Done in a Uniform Electric Field

A positive charge $$q$$ is moved from one equipotential surface to another within a region that has

Work Done in a Uniform Electric Field

A positive charge $$q$$ is moved through a distance $$d$$ in a uniform electric field $$E$$. Analyze

Work Done on a Charge in a Radial Electric Field

A positive charge $$q = 2.0*10^{-6}$$ C is moved radially away from a fixed point charge $$Q = 1.0*1

Work Required to Assemble a Triangular System of Point Charges

Three point charges are fixed in place forming a triangle. The charges and separations are: Q₁ = +2.

Analysis of Ammeter and Voltmeter Placement

This question addresses the proper usage of ammeters and voltmeters in a circuit for accurate measur

Analyzing Series-Parallel Combinations of Capacitors

Capacitors can be combined in series or parallel to yield different equivalent capacitances. Answer

Battery Internal Resistance and Terminal Voltage

A battery can be modeled as an ideal EMF in series with an internal resistance. Consider a battery w

Circuit Design for Energy Efficiency

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

Comparing Conductor Materials: Effect on Efficiency

Different materials have different resistivities, which affect their performance in circuits. Consid

Designing an RC Circuit for a Target Time Constant

Design an RC circuit that achieves a time constant of $$0.5\,s$$. You are provided with capacitors r

Determining Equivalent Resistance in Mixed Resistor Networks

A circuit is constructed using three resistors: one resistor of 100 \(\Omega\), one of 200 \(\Omega\

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 Adding a Parallel Resistor in a Series Circuit

Consider a circuit consisting of a 9 V battery connected in series with a 12 Ω resistor. A 24 Ω resi

Effect of Dielectric on Capacitance in a Parallel-Plate Capacitor

A parallel-plate capacitor with plate area A and separation d is initially filled with air (dielectr

Effect of Varying Resistivity

A wire of constant length and cross-sectional area is fabricated from different materials. This prob

Effects of Series and Parallel Combinations on Circuit Functionality

An experimental setup features several combinations of resistors and capacitors arranged in both ser

Evaluating Circuit Design with Kirchhoff’s Laws

A complex circuit is constructed on a breadboard that includes a 20 V battery, three resistors, and

Evaluating the Combination of Multiple Battery Cells on Circuit Performance

A student builds a circuit by connecting three battery cells in series to increase the output voltag

Evaluation of Charging Rates in Varied Capacitor Designs

Two different capacitor designs are tested in an RC circuit. Capacitor A has a plate area of $$0.01\

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

Impact of Temperature on Resistor Performance

A researcher investigates how the resistance of a metallic resistor changes as the temperature is in

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 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

Kirchhoff's Laws in a Multi-branch Circuit

An experimental circuit with multiple junctions is analyzed using Kirchhoff's laws. The table below

Modeling the Behavior of a Heated Resistor in an Electrical Circuit

A resistor with an initial resistance of 100 Ω at 20°C has a temperature coefficient of 0.004/°C. If

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 in Resistive Circuits

A resistor with a resistance of $$10\,\Omega$$ is connected to a $$9\,V$$ battery. Answer the follow

Power Dissipation in Resistor Circuits

A resistor circuit is tested under various load conditions. The table below provides the measured vo

Resistor Network Analysis

Consider a circuit with multiple resistors arranged in series and parallel. The table below provides

Role of Resistivity in Material Conduction

The resistance of a wire is given by the equation $$R = \rho \frac{l}{A}$$. A table below provides p

Series and Parallel Resistor Networks

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

Series Circuit Analysis and Ohm's Law Application

A battery of 9 V is connected in series with two resistors: one having a resistance of 100 Ω and the

Analysis of Magnetic Torque on a Current Loop

A rectangular loop carrying a current $$I = 2.0$$ A is placed in a uniform magnetic field of strengt

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

Assessing Magnetic Field Strength Using Iron Filings

An experiment uses iron filings spread over a sheet of paper placed atop a bar magnet to visualize t

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

Circular Motion of a Charged Particle in a Magnetic Field

A particle with charge $$q = 0.1 C$$ and mass $$m = 0.02 kg$$ enters a uniform magnetic field $$B =

Comparative Analysis of Magnetic Forces on Oppositely Charged Particles

Two particles, one with a positive charge of $$q_1 = +2 \times 10^{-6} \; C$$ and the other with a n

Compass Mapping of Bar Magnet Field

In an experiment, a bar magnet is used to map its magnetic field by measuring the deflection angle o

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 Speed Sensor Using Motional EMF

In a laboratory experiment, a metal rod moves through a uniform magnetic field of strength $$B = 0.5

Designing an Electromagnetic Induction Experiment

This FRQ requires designing an experiment to investigate how the speed of a sliding rod affects the

Determining Magnetic Force on a Moving Charge

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

Determining Magnetic Force on a Moving Charge

An experimental report describes the measurement of the magnetic force on a proton moving at $$2*10^

Effect of Magnetic Field Strength on Induced Current

Design an experiment to explore how varying the magnetic field strength affects the induced current

Electromagnetic Induction and Energy Conversion

This FRQ focuses on the conversion of mechanical energy into electrical energy via electromagnetic i

Energy Dissipation in Resistive Magnetic Systems

An experiment investigates energy dissipation in a circuit where an induced current flows through a

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

Evaluating the Magnetic Field of a Current-Carrying Wire

An experiment is conducted to measure the magnetic field strength around a long, straight current-ca

Exploration of Magnetic Flux Through a Rotating Loop

A circular loop of radius 0.03 m is placed in a uniform magnetic field of 0.2 T and rotated from 0°

Force Cancellation in a U-Shaped Conductor

Design an experiment to investigate the conditions under which the net magnetic force on a U-shaped

Force on a Charged Particle in a Non-Uniform Magnetic Field

A charged particle with charge $$q$$ moves with constant speed $$v$$ in a region where the magnetic

Force on a Current-Carrying Wire

Consider a U-shaped wire placed in a uniform magnetic field that is directed out of the page. A curr

Force on a Moving Charge

This FRQ focuses on calculating the magnetic force on a moving charge and interpreting its direction

Force on a Proton Near a Current-Carrying Wire

A proton moves near a long, straight wire that carries a constant current. Analyze the magnetic fiel

Induced EMF in a Rectangular Loop Under Rotation

A rectangular loop of wire measuring 0.1 m by 0.2 m is placed in a uniform magnetic field of 0.5 T.

Induced EMF in a Rotating Rod

A conducting rod of length $$L = 0.4 m$$ rotates about one end in a uniform magnetic field $$B = 0.3

Induced EMF in a Rotating Square Loop Experiment

A laboratory experiment involves a square loop of wire that rotates at a constant angular speed in a

Investigating Motional EMF in a Moving Conductor

In an experiment, a conducting rod of length $$\ell = 0.5\;m$$ is moved at a constant velocity throu

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

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 Levitation and Force Equilibrium

Investigate the conditions required for magnetic levitation using magnetic repulsion, and analyze po

Mapping Complex Magnetic Fields Using an Iron Dust Experiment

Iron dust can reveal the intricate structure of magnetic fields for different sources. Compare how t

Mapping Magnetic Field Using Iron Filings

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

Motional EMF in a Moving Conductor

A conducting rod of length $$l = 0.5 \; m$$ moves with a constant velocity $$v = 3 \; m/s$$ through

Motional EMF in Non-Uniform Magnetic Fields

Moving conductors in non-uniform magnetic fields can develop complex distributions of induced emf. A

Net Force on a Current-Carrying U-shaped Wire

Consider a U-shaped wire immersed in a uniform magnetic field of magnitude $$B = 0.2 \; T$$ directed

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

Radius of Circular Motion vs. Velocity

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

Time-Dependent Induced EMF in a Rotating Loop

Design an experiment to investigate how the induced emf in a rotating loop varies over time, particu

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

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

Aperture Diffraction Analysis

A rectangular aperture with a width of $$0.5*10^{-3}$$ m and a height of $$1*10^{-3}$$ m is illumina

Brewster's Angle and Reflective Polarization

At the interface of air and glass, light can become polarized upon reflection.

Calculating Lens Power from Image Magnification

The power of a lens is defined as the reciprocal of its focal length (in meters). Analyze an example

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 $$h_o = 4 \ cm$$ is placed at a distance of $$d_o = 30 \ cm$$ in front of a conc

Concave Mirror Image Analysis

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

Convex Mirror Image Analysis

Convex mirrors produce images that are always virtual, diminished, and upright. This question requir

Convex Mirror Image Formation

An object of height $$5 \text{ cm}$$ is placed $$20 \text{ cm}$$ in front of a convex mirror with a

Designing a Periscope: Light Path Analysis

A researcher is tasked with designing a periscope using plane mirrors to redirect light so that an o

Determining Slit Separation from Fringe Spacing

In a Young's double slit experiment, the measured fringe spacing on the screen is $$\Delta y = 2.5 \

Diffraction Grating Analysis

A diffraction grating with 5000 slits per centimeter is illuminated by monochromatic light of wavele

Diverging Lens Image Formation

A student investigates the behavior of a diverging (concave) lens. In the experiment, an object with

Effect of Medium on EM Wave Propagation: Frequency Invariance Error Analysis

A student investigates the propagation of electromagnetic waves through air with varying humidity le

Electromagnetic Spectrum Frequency Analysis

Electromagnetic radiation spans a wide range of wavelengths and frequencies. This question explores

Electromagnetic Wave Propagation: Error Analysis

A student designs an experiment to measure the speed of electromagnetic waves in a vacuum. The appar

Electromagnetic Waves: Frequency and Polarization

An electromagnetic wave in a vacuum travels at a constant speed of $$c = 3.0 * 10^8$$ m/s. Consider

EM Wave Generation and Field Relationships

An oscillating charge produces electromagnetic waves, characterized by oscillating electric and magn

Experimental Design: Evaluating Light Behavior in Combined Mirror-Lens Systems

An optical system combines a concave mirror and a converging lens to form an image. The following ta

Frequency Determination of Green Light: Speed of Light Misassumption

A student attempts to calculate the frequency of green light by measuring its wavelength with a spec

Image Formation in Plane Mirrors

A set of measurements has been taken using a plane mirror to form images. The data below compares ob

Investigation of Diffraction Gratings in Spectroscopy

Diffraction gratings are key components in spectroscopy, providing high resolution in wavelength sep

Medium Effects on Light Wavelength

When light enters a medium from a vacuum, its speed decreases while its frequency remains constant.

Multi-Wavelength Interference Experiment

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

Optical Sensors in Environmental Monitoring

Environmental scientists are developing optical sensors to monitor particulate matter in water. The

Plane Mirror Image Formation

An object is placed 25 cm in front of a plane mirror. (a) Determine the distance of the image from

Plane Mirror Ray Diagram Analysis

Examine the attached diagram of a plane mirror ray tracing setup. Answer the following:

Polarization and Brewster's Angle

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

Prism Dispersion and Light Deviation

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

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: 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: Experimental Error Analysis

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

Spherical Mirrors: Convex Mirror Analysis

An object of height 5 cm is placed 20 cm in front of a convex mirror with a focal length of $$-10$$

Thin Film Interference

A thin film of oil (index $$n = 1.25$$) rests on water (index $$n = 1.33$$). White light is incident

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 and Critical Angle Calculation

Total internal reflection occurs when light travels from a medium with a higher index of refraction

Wave Interference in a Medium: Misapplication of Light Formulas

A student uses a ripple tank to simulate interference patterns similar to those observed with light

Young's Double Slit Experiment Analysis

A coherent monochromatic light source with wavelength $$λ = 589*10^{-9} \ m$$ illuminates a barrier

Bohr Model and Atomic Spectra

A researcher is investigating the emission spectrum of a hydrogen-like ion. The energy levels in thi

Conservation Laws in Particle Collisions

In a high-energy collision experiment, two particles collide and produce two different particles. Co

Nuclear Fusion Reaction Analysis

A researcher studies the fusion reaction between deuterium nuclei represented by: $$^2H + ^2H \right