AP Physics 2: Algebra-Based FRQ Room

Airfoil Lift and Pressure Differential Measurements

An aerospace student designs an experiment in a wind tunnel to measure the lift generated by an airf

Analysis of Fluid Flow Measurements in a Laboratory Pipe

A researcher collects flow measurements along a pipe with varying cross-sections. The following data

Analyzing Fluid Flow in a River System

A river exhibits variations in cross-sectional area and flow speed along its course. Measurements at

Analyzing Pressure in a U-Tube Manometer

A U-tube manometer utilizes two different fluids (water and mercury) to measure pressure differences

Application of Bernoulli's Equation in a Constricting Pipe

A pump forces water through a pipe that gradually narrows. At Point 1 (the wider section), the cross

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 Principle and Pressure Measurements

Water is pumped through a horizontal pipe that constricts and expands in diameter. At Point 1 in the

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 Submerged Volume of a Submarine

A submarine with a total volume of 300 m³ is designed to be neutrally buoyant in seawater (density $

Buoyancy Experiment: Verifying Archimedes' Principle

Design an experiment to measure the buoyant force on objects immersed in different fluids and thereb

Buoyancy Force Miscalculation Experiment

A student aims to measure the buoyant force acting on an object immersed in ethyl alcohol using a sp

Buoyancy in Marine Vessel Design

A researcher studies how buoyancy principles are applied to ensure that marine vessels float.

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

Buoyant Force in Varied Fluids

A solid object with a mass of $$200 \; kg$$ and a volume of $$0.5 \; m^3$$ is immersed in three diff

Continuity and Bernoulli in a River Channel

A river flows from a wide channel into a narrow section. In the wide channel, the cross-sectional ar

Continuity Equation and Flow Rate Through a Pipe

Water flows through a horizontal pipe that changes diameter. At section 1, the pipe has a radius of

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 Constricted Pipe Experiment

A student sets up a horizontal pipe with two sections: one wide and one significantly constricted. T

Density and Hydrostatic Pressure Calculation

A container holds an oil sample with a measured mass of $$1.6$$ kg and a volume of $$2.00 \times 10^

Density Determination Experiment

A student performs an experiment to determine the density of three different liquids by measuring sm

Determining the Net Force on a Submerged Object

An object fully submerged in a fluid experiences gravitational, buoyant, and drag forces. Analyze th

Developing an Experiment for Continuity Equation Verification

Design a controlled experiment to verify the continuity equation using water (density $$1000\;kg/m^3

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

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

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 Rate in a Constricted Pipe

This question applies the continuity equation to determine flow rates and velocities in a pipe with

Flow Rate in a Constricted Pipe

Consider a circular pipe carrying water. The pipe has a radius of 2 cm and the water flows at a spee

Flow Through a Rectangular Duct

A duct has a rectangular cross-section with a width of 0.3 m and a height of 0.5 m.

Flow Through Irregular Channels

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

Fluid Force on a Submerged Surface

A civil engineering team is studying the pressure distribution on a dam wall due to the water it hol

Fluid Velocity and Pipe Cross-Section Experiment

According to the continuity equation, the product of cross-sectional area and velocity remains const

Graphical Analysis of Flow Continuity

This problem uses a provided graph to analyze the relationship between flow speed and pipe cross-sec

Hydraulic Press and Force Amplification

A hydraulic press consists of two pistons connected by an incompressible fluid. The larger piston ha

Hydrostatic Pressure Analysis

A researcher investigates hydrostatic pressure in a fluid system. In an experiment conducted with wa

Hydrostatic Pressure in a Liquid Column

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

Hydrostatic Pressure in a Tank

This problem analyzes hydrostatic pressure in a fluid and the effect of atmospheric pressure on tota

Hydrostatic Pressure in an Open Tank

A researcher is investigating the hydrostatic pressure in an open water tank. The tank holds water w

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

Industrial Fluid Density and Pressure Calculation

A researcher in an industrial laboratory is studying fluid properties for engineering applications.

Interpreting a Diagram of Fluid Density Distribution

A container holds multiple immiscible fluids layered according to density. The provided diagram show

Mixed Fluid Continuity Experiment Error

A student sets up an experiment to test the continuity equation by measuring the flow rate through a

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 Analysis with Fluid Dynamics Principles

A student designs an experiment to study fluid flow in a pipe with sections of varying cross-section

Pipe Flow Continuity

An experiment examines fluid flow through a pipe with a constricted section. The following table sho

Pressure and Buoyancy in Submerged Particles

Consider two small particles submerged in the same fluid. Particle A has a density slightly greater

Pressure at an Interface of Two Fluids

A container holds two immiscible fluids. A layer of oil (density $$800\;kg/m^3$$, depth $$0.5\;m$$)

Pressure Calculations in Submerged Structures

A structural engineering team is testing a scale model of a submerged tunnel to study the effects of

Pressure Sensor Calibration in Fluid Storage Tanks

An engineer uses a pressure sensor at the bottom of a water storage tank to measure the fluid level.

Pressure Variation in a Fluid Column

A tall building has a water tank located on its roof, 50 m above ground level. (a) Calculate the hyd

Quantitative Analysis of Pressure Distribution in an Accelerating Fluid

A rectangular container with a length of $$2 \cdot m$$ is filled with water (density = $$1000 \cdot

Siphon Action Analysis

A siphon is used to transfer water from a container. The highest point of the siphon tube is 2 m abo

Torricelli’s Law and Fluid Ejection

An open tank at atmospheric pressure contains water (density $$1000\;kg/m^3$$) with a free surface l

Turbulent vs. Laminar Flow: Reynolds Number Misinterpretation

A student conducts an experiment to study the transition from laminar to turbulent flow in a pipe by

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

Visualizing Fluid Flow Using Dye Injection

Design an experiment to visualize streamlines and measure flow velocities in a fluid by injecting dy

Adiabatic Process Analysis

In an adiabatic process, no heat is exchanged with the surroundings. (a) Define an adiabatic process

Adiabatic Process Calculations

An ideal gas undergoes an adiabatic expansion, meaning that no heat is exchanged with the surroundin

Adiabatic Process Compression Experiment Error

A student conducts an experiment to study adiabatic compression in a gas contained within a piston-c

Adiabatic vs. Isothermal Transition Timing Experiment Error

A student designs an experiment to compare adiabatic and isothermal expansions of a gas by rapidly m

Analysis of Real Gas Behavior

The Ideal Gas Law assumes ideal behavior, but real gases deviate from this under certain conditions.

Analyzing Deviations from the Ideal Gas Law

A researcher measures the pressure of a gas at various volumes and observes deviations from the Idea

Analyzing Work Done in Different Thermodynamic Paths

A gas undergoes changes between states along two alternate paths on a P–V diagram. Path 1 is a const

Chemical Reaction Heat and Gas Pressure Changes: Integrating Thermodynamics and Kinetic Theory

Exothermic chemical reactions can cause changes in gas pressure due to heat release. Design an exper

Designing a Thermos: Minimizing Heat Transfer

A thermos is designed to keep liquids hot by minimizing heat transfer. Discuss the design features c

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 Convective Heat Transfer

A researcher aims to measure the convective heat transfer coefficient in a fluid flowing over a heat

Effect of Molecular Mass on RMS Velocity

The root-mean-square velocity of gas molecules is given by $$v_{rms} = \sqrt{\frac{3k_BT}{m}}$$. (a)

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 Changes in an Irreversible Process with Friction

Consider an ideal gas in a piston that is being compressed irreversibly. Due to friction in the pist

Error Analysis in Pressure and Temperature Measurements

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

Gas Pressure Calculation and Net Force Analysis

A 0.8 mole sample of an ideal gas is confined in a cubic container with a side length of 0.5 m at a

Graphical Interpretation of Thermodynamic Process Data

A researcher plots the pressure versus volume for a gas undergoing multiple thermodynamic processes.

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 Mechanism Identification

A long metal rod is heated at one end, and after some time, the entire rod becomes warm. Answer the

Investigation of Pressure in Confined Gases

A researcher conducts an experiment using a sealed, rigid container fitted with a pressure sensor to

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

Phase Diagrams and Critical Points

Phase diagrams provide insight into the states of a pure substance under various conditions. (a) Des

Radiative Heat Transfer Analysis

A researcher examines the radiative heat transfer between two parallel surfaces acting as black bodi

Refrigeration Cycle Energy Analysis

A researcher studies a refrigeration cycle that operates through a closed loop consisting of compres

RMS Velocity and Temperature

The RMS (root-mean-square) velocity of molecules in an ideal gas is given by $$v_{rms} = \sqrt{\frac

Temperature Change and Molecular Speed Distribution

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

Thermal Conductivity through Conduction

An experiment measures the rate of heat transfer through a material using the conduction formula $$\

Thermal Equilibrium and the Zeroth Law

Thermal equilibrium is a key concept in thermodynamics. (a) Define thermal equilibrium and its relat

Thermodynamic Stability and Phase Transitions

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

Work and Internal Energy in an Isochoric Process

A gas is contained in a rigid, fixed-volume container. During a heating process, the pressure of the

Work Calculation in an Isobaric Process

A gas undergoes expansion inside a cylinder at constant pressure. The process is represented on a P–

Work Calculation in Gas Expansion Experiment Error

A student investigates the work done by a gas during expansion by measuring the displacement of a pi

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

Analysis of Electric Dipole Field Measurements

An experimental setup measures the electric field magnitude at various distances along the perpendic

Balancing Forces in a Uniform Electric Field

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

Balancing Gravitational and Electric Forces in a Uniform Field

This problem involves determining the amount of charge required on a small object such that the upwa

Capacitor Network Analysis in Series and Parallel

In a circuit, three capacitors are connected as follows: capacitor C1 (4 μF) is connected in series

Charge Redistribution in Connected Conductors

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

Charging Methods Experiment: Conduction vs. Induction

This experiment compares two methods of charging an object: conduction and induction. Two identical

Comparison of Dipole and Monopole Field Mapping

A simulation experiment compares equipotential maps for a single point charge (monopole) and for a d

Derivation of Potential Difference Between Concentric Equipotential Surfaces

The electric potential due to a point charge is given by $$V = \frac{k \times Q}{r}$$. Using this re

Electric Charge Distribution on Conductors: Capacitance Influence Error

In an experiment aimed at studying charge distribution, two metallic spheres of different radii are

Electric Dipole Field Analysis

A dipole is composed of two point charges, $$+Q$$ and $$-Q$$, each of magnitude $$4.0\;nC$$, separat

Electric Dipole Moment Experiment with External Field Perturbation

In an experiment designed to measure the dipole moment of aligned molecules, a sample is placed in a

Electric Field Due to a Uniformly Charged Rod

A thin rod of length 0.5 m carries a uniform linear charge density of $$\lambda = 2.0*10^{-6}$$ C/m.

Electric Field Lines and Equipotential Mapping Misinterpretation

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

Electric Field Lines at Media Boundaries

This problem examines how electric field lines behave at the boundary between two different media an

Electric Field Superposition in a Triangular Configuration

Three point charges are fixed at the vertices of an equilateral triangle. A fourth charge is placed

Electric Potential Due to a Point Charge

A point charge of $$+2.0*10^{-9}$$ C creates an electric potential in the surrounding space. (a) Ca

Electric Potential Gradient from a Point Charge

A student measures the electric potential \(V\) as a function of distance \(r\) from a fixed point c

Electrostatic Shielding

A researcher investigates the phenomenon of electrostatic shielding by placing a charged rod near a

Energy Conversion in Point Charge Interaction

A fixed positive charge $$Q = +2.0 \times 10^{-6} \; C$$ creates an electric field in vacuum. A nega

Energy Stored in a Capacitor

A capacitor with a capacitance of 10 nF is charged to a potential difference of 500 V.

Experimental Design: Measuring the Electric Force on a Charged Particle

A research team aims to design an experiment to measure the electric force on a small charged partic

Experimental Mapping of Electric Field Lines in a Uniform Field

Design an experiment to map the electric field lines and equipotential regions between two large par

Force and Potential Energy in the Hydrogen Atom

For a hydrogen atom, consider the proton and electron separated by a distance of 0.5×10^-10 m. Using

Force Comparison in Hydrogen Atom

A researcher compares the electric and gravitational forces between the proton and electron in a hyd

Graphical Analysis of Electric Field Variation with Distance

Experimental measurements were made of the electric field strength at varying distances from a charg

Impact of Dielectrics on Capacitance

A recent report claims that inserting a dielectric with a dielectric constant of 3 into a parallel-p

Induction Charging Experiment: Charge Redistribution Oversight

An experiment is conducted to study charging by induction using two initially uncharged metal sphere

Influence of Plate Area on Capacitor Capacitance

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

Invariance of Electric Charge

Electric charge is considered invariant under transformation between inertial frames. This question

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

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

Net Force on a Central Charge in a Square Configuration

Four equal positive point charges are placed at the vertices of a square with side length 10 cm, and

Parallel Plate Capacitor Experiment: Dielectric Misconception

An experiment is designed to measure the capacitance of a parallel-plate capacitor by arranging two

Parallel-Plate Capacitor Design

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

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

RC Discharge of a Capacitor

A capacitor charged to an initial potential of 100 V is connected in series with a resistor, forming

Surface Charge Density and Electric Field Experiment

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

Three-Dimensional Vector Addition of Electric Forces

Accurately calculating the net electric force on a test charge in a three-dimensional configuration

Verification of Coulomb’s Law through Force Measurements

An experiment was conducted to verify Coulomb’s Law by measuring the electric force between two char

Analysis of Ammeter and Voltmeter Placement

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

Analyzing Power Dissipation in a Resistor Network

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

Analyzing Power Efficiency in Batteries with Internal Resistance

A battery with an EMF of 15 V and internal resistance $$r = 0.5\,Ω$$ is connected to a load resistor

Analyzing Transients in RC Circuits with Switching

Consider a circuit where a capacitor, initially uncharged, is connected in series with a resistor an

Assessing Charging Curves of Capacitors in Series and Parallel

An experiment claims that the charging curves of capacitors differ based on whether they are arrange

Basic Circuit Analysis: Applying Ohm's Law

A battery providing $$9~V$$ is connected to a single resistor with a resistance of $$10~\Omega$$. An

Battery Internal Resistance Analysis

A battery with an electromotive force $$\varepsilon = 12\,V$$ and internal resistance $$r = 1\,\Omeg

Battery Internal Resistance and Terminal Voltage

A study claims that the terminal voltage of a battery decreases noticeably when a load is connected

Capacitor Charging in an RC Circuit

In an RC circuit, a capacitor is charged by connecting it to a battery through a resistor. Consider

Circuit Design for Energy Efficiency

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

Circuit Simulation Verification

An experiment is conducted to compare the theoretical predictions of a circuit simulation with actua

Comparative Analysis of Capacitor Charging Profiles

Two RC circuits are set up using identical resistor and capacitor values: $$R = 3 \Omega$$ and $$C =

Designing a Circuit for Controlled Power Dissipation

Design a circuit that will safely dissipate 50 W of power when connected to a 12V battery. This desi

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 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 and Power Dissipation in Capacitors

A capacitor with a capacitance of 50 μF is charged to a voltage of 10 V. Answer the following:

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

Evaluation of Circuit Performance with a Faulty Capacitor (Capacitor Failure Analysis)

A capacitor in an RC circuit, which is expected to be 47 μF, is suspected of being faulty due to lea

Experiment to Determine Battery Internal Resistance

Batteries can be modeled as an ideal electromotive force (EMF) in series with an internal resistance

Exploring the Concepts of Internal Resistance and Circuit Efficiency

A study claims that batteries with lower internal resistance operate more efficiently, resulting in

Impact of Temperature on Capacitance in a Dielectric-Filled Capacitor

The capacitance of a parallel-plate capacitor is given by $$C = k * ε_0 * \frac{A}{d}$$, where k is

Investigating the Effect of Capacitor Dielectric Constant on Capacitance

In a laboratory experiment, capacitors are built using different dielectric materials. The capacitan

Investigating the Effect of Series and Parallel Resistor Arrangements on Circuit Efficiency

A circuit is configured in two ways using three resistors with values 100 Ω, 150 Ω, and 250 Ω. In Co

Investigation of Capacitor-Battery Interaction under Variable Conditions

In an experiment, a capacitor is charged under two conditions: with the battery connected and with t

Investigative Lab on Short-Circuiting Capacitors and Resistors

A misconfigured circuit experiment resulted in a capacitor being inadvertently short-circuited by co

Kirchhoff's Laws in Multi-Loop Circuits

In a multi-loop circuit, measurements of current at various junctions are taken. Use Kirchhoff’s law

Multi-loop Circuit Analysis with a Capacitor

A circuit consists of two loops. In the first loop, a resistor of $$4\,\Omega$$ is connected in seri

Power Dissipation in Resistors

In circuits, resistors convert electrical energy into heat. This problem explores the concept of pow

RC Circuit Transients and Time Constants

An RC circuit is comprised of a resistor $$R = 5\times10^3\,\Omega$$ and a capacitor $$C = 2\,\mu F$

Series and Parallel Resistor Analysis

This question examines the behavior of resistors arranged in series and parallel in simple circuits.

Temperature Effects on Material Resistivity

The resistivity of a material is given by the formula $$\rho = \rho_0 [1 + \alpha (T - T_0)]$$. A wi

Transient Analysis with Switch Operation in RC Circuits

An RC circuit consists of a $$10~V$$ battery, a resistor of $$500~\Omega$$, and a capacitor of $$200

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

Analysis and Improvement of a Textbook Magnetic Field Diagram

A textbook diagram intended to illustrate the magnetic field around a bar magnet is provided. The di

Analysis of a Two-Component Magnetic Circuit

Consider a magnetic circuit composed of two adjacent materials (A and B) with different permeabiliti

Analysis of Electromagnetic Induction in a Rotating Coil

A circular coil rotates in a magnetic field and experiences an induced emf. Analyze the instantaneou

Analysis of Magnetic Field vs. Distance for a Current-Carrying Wire

An experiment measures the magnetic field at various distances from a long, straight current-carryin

Analyzing a U-Shaped Wire in a Magnetic Field

A U-shaped wire is immersed in a uniform magnetic field of magnitude 0.5 T. The wire consists of two

Analyzing Circular Motion of a Charged Particle in a Magnetic Field

Design an experiment to analyze the circular motion of a charged particle in a uniform magnetic fiel

Application of the Right-Hand Rule in 3D

The direction of the magnetic force on a moving charge is determined using the right-hand rule. Answ

Bar Magnet and Induced EMF Experiment

In this experiment, a student swings a bar magnet through a solenoid coil and measures the induced e

Calculating Magnetic Flux in a Non-Uniform Magnetic Field

A rectangular loop with width $$w = 0.2$$ m and height $$h = 0.3$$ m is placed in a magnetic field t

Charged Particle in a Uniform Magnetic Field

A positively charged particle with charge $$q = 2.0 * 10^{-6}$$ C enters a region with a uniform mag

Comparative Analysis of Induced Currents

A physics laboratory is set up to compare three different methods of inducing a current in a wire lo

Comparing Magnetic Field Mapping Techniques

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

Deflection of Charged Particles in Crossed Fields

In an experiment, charged particles are passed through a region where perpendicular electric and mag

Designing a Magnetic Levitation Experiment

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

Energy Storage in an Inductor

In an electrical circuit, an inductor with inductance $$L = 0.5 H$$ carries a current of $$I = 3 A$$

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

Force Cancellation in a U-Shaped Conductor

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

Graphical Analysis of Magnetic Force Data

A proton is accelerated to different speeds and moves through a uniform magnetic field, where its ve

Induced EMF in a Loop with Time-Varying Magnetic Field

A circular loop with a constant area of $$A = 0.02 m^2$$ is placed in a magnetic field that increase

Induced EMF in a Sliding Rod Circuit

Consider a circuit formed by a sliding rod of length $$\ell$$ that moves on conducting rails, comple

Induced EMF in a Time-Varying Solenoid Field

A solenoid with 300 turns and a cross-sectional area of 0.05 m² produces an axial magnetic field tha

Investigating the Uniform Magnetic Field Within a Solenoid

A researcher sets up a solenoid experiment to measure the uniform magnetic field inside the coil. Th

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 Lines Visualization

In this FRQ, you will explore the physical basis and representation of magnetic fields around a bar

Magnetic Flux Change in a Rotating Loop

A circular loop of wire is rotating in a uniform magnetic field, causing a time-dependent change in

Magnetic Force on a Current-Carrying Wire

A current-carrying wire placed in a uniform magnetic field experiences a force. Analyze both the mag

Magnetic Force on a Moving Charge

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

Mapping the Magnetic Field Around a Straight Current-Carrying Wire

In this experiment, students use a Hall sensor to measure the magnetic field (B) at various distance

Measuring Magnetic Permeability Experiment

An experiment is designed to determine the magnetic permeability of a new material. A coil is wound

Measuring Magnetic Permeability via Compass Deflection

An experiment attempts to determine the magnetic permeability of a material by measuring the deflect

Motion of a Charge in Perpendicular Electric and Magnetic Fields

A charged particle with charge $$q$$ and mass $$m$$ enters a region where there is a uniform magneti

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

Right-Hand Rule Application in a Multi-Charge System

Three particles are moving in a uniform magnetic field of $$0.4$$ T with the following properties: •

Rotating Coil Induced Current

A coil consisting of N turns and area A rotates in a uniform magnetic field of strength B with a con

Testing the Right-Hand Rule for Magnetic Force Directions

An experiment is performed where charged particles are propelled in known directions through a unifo

Time-Dependent Magnetic Flux in a Square Loop

A square loop of wire with side length 0.4 m is placed in a magnetic field that increases uniformly

Time-Varying Magnetic Flux in a Rotating Loop

This FRQ explores the time dependency of magnetic flux in a rotating loop and the resulting induced

U-Shaped Wire Current Balance

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

Uniform Magnetic Field in a Solenoid Experiment

An experiment is conducted using a solenoid as an electromagnet, and it is claimed that the magnetic

Vector Analysis of Magnetic Force

A charged particle moves in a three-dimensional space under the influence of a magnetic field. The v

Comprehensive Verification of Lens and Mirror Equations

In a comprehensive optics experiment, a student designs a setup to simultaneously verify the lens eq

Concave Mirror Image Characteristics

Concave mirrors can produce images that are real or virtual depending on the object position. Analyz

Converging Lens Experiment: Measuring Focal Length Using Object-Image Distances

Design an experiment to measure the focal length of a converging lens using object and image distanc

Converging Lens Image Formation

A converging lens has a focal length of $$15 \text{ cm}$$, and an object is placed $$25 \text{ cm}$$

Converging Lens Power Determination

A converging lens forms a real image that is twice the height of the object. When an object is place

Critical Angle Determination for Various Media

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

Diffraction Grating Analysis

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

Diffraction Grating Analysis

A researcher uses a diffraction grating with 5000 lines per centimeter to analyze the spectrum of a

Diffraction Grating for Wavelength Determination

A diffraction grating with 5000 lines per cm is used to measure the wavelength of a light source. Th

Diffraction Gratings and Spectral Analysis

A diffraction grating is used to analyze the spectral composition of a light source. A graph showing

Double Slit Interference Analysis: Fringe Positions

In a Young's double slit experiment, light of wavelength $$589*10^{-9}$$ m passes through two slits

Double Slit Interference Experiment

In a Young's double-slit experiment, two slits separated by $$d = 1.5 \text{ mm}$$ are illuminated b

Effects of Wavelength Change in Interference Patterns

This question examines the effect of changing the wavelength of light on the interference patterns p

Electromagnetic Wave Interference and Phase Difference

A diagram is provided showing two coherent electromagnetic waves with a phase difference interfering

Electromagnetic Wave Propagation in a Vacuum

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

Electromagnetic Wave Propagation in Different Media

An experiment measured the speed of light in various media. The table below presents the recorded sp

Experimental Verification of the Law of Reflection

The law of reflection states that the angle of incidence equals the angle of reflection. This questi

Exploring the Relationship Between Frequency and Wavelength

A student conducts an experiment to examine the relationship between frequency and wavelength in dif

Image Formation by Convex Mirrors

A convex mirror has a focal length of $$20\,cm$$. An object is placed $$30\,cm$$ in front of the mir

Interference in Thin Films

A researcher studies the colorful interference patterns observed in a thin soap film, where film thi

Investigating Snell's Law: Relationship between Incident and Refraction Angles

Design an experiment to study the relationship between the angle of incidence and the angle of refra

Oscillating Charges and the Generation of EM Waves

An oscillating charge is a fundamental source of electromagnetic radiation. This problem involves ex

Polarization of Electromagnetic Waves

A schematic diagram is provided illustrating polarized light passing through a series of polarizers.

Polarization of Electromagnetic Waves

Consider a polarizing filter that transmits only the component of light aligned with its transmissio

Polarization of EM Waves: Experimental Error Analysis

A student sets up an experiment to measure the variation in light intensity as a polarizing filter i

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: Application of Snell’s Law

This question examines the application of Snell's law to a light beam incident on a glass surface an

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

A laser with a wavelength of $$632.8*10^{-9}\,m$$ is incident on a single slit of width $$a = 0.2*10

Spherical Mirrors - Concave Mirror Calculation

An object of height 4 cm is placed 30 cm in front of a concave mirror with a focal length of 10 cm.

Spherical Mirrors: Convex Mirror Analysis

A convex mirror is used in an experiment, and the following data on object distance, image distance,

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 Diverging Lens Image Formation

An object of height 12 cm is placed 30 cm from a diverging lens with a focal length of -20 cm. Answe

Thin Film Interference and Optical Coatings

A thin film coating on a glass surface is designed to produce constructive interference for light of

Thin Lens and Magnification Analysis

An object of height $$h_o = 6 \ cm$$ is placed at a distance of $$d_o = 20 \ cm$$ in front of a conv

Total Internal Reflection and Critical Angle Calculation

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

Young's Double Slit Experiment Analysis

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

Young’s Double Slit Experiment Analysis

Consider a Young’s double slit experiment where monochromatic light of wavelength 589 nm passes thro

Alpha Decay Analysis

A sample of a radioactive nuclide Y undergoes alpha decay according to the reaction: $$^{A}_{Z}Y \ri

Nuclear Composition and Isotope Identification

A researcher is examining a nuclide represented by $$^{63}_{29}X$$. Using this information, address

Photoelectric Effect on Aluminum

A researcher studies the photoelectric effect on an aluminum surface by illuminating it with light o

Wave-Particle Duality Experiment with Electrons

An experiment is conducted in which electrons are accelerated through a potential difference and the