AP Physics 2: Algebra-Based FRQ Room

Adjustable Pipe Flow Experiment

In an experiment, water flows through a pipe whose cross-sectional area can be mechanically adjusted

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

Analysis of Flow in a Curved Pipe

Water flows through a curved pipe, where the curvature induces additional centrifugal effects.

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 Data Analysis

An experiment is conducted where a fluid flows through a horizontal pipe. A graph showing the variat

Bernoulli’s Equation in a Constricted Pipe

A fluid flows through a horizontal pipe that gradually constricts. At the wide section (Point 1) the

Bernoulli's Equation in Constricted Flow

Water flows through a horizontal pipe that gradually narrows. At Point 1, the cross-sectional area i

Bernoulli’s Principle and Air Flow Over an Airfoil

An airfoil (wing cross-section) diagram shows streamlines of air with different velocities above and

Bernoulli's Principle in Lift Generation

Aircraft wings generate lift in part due to differences in airspeed above and below the wing. (a) Ex

Buoyancy Analysis: Floating and Sinking Objects

A laboratory study on buoyancy involves placing an object in a container of ethyl alcohol. The objec

Buoyancy and Submerged Volume

An object with a mass of $$150 \cdot kg$$ and a volume of $$0.75 \cdot m^3$$ is placed in a fluid wi

Buoyancy in a Variable-Density Atmosphere: Weather Balloon Analysis

A weather balloon is launched at ground level, where the atmospheric density is $$1.225\,kg/m^3$$. A

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

Buoyant Force Measurement Experiment

In an experiment designed to measure buoyant force, the weights of submerged objects were recorded.

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

Calculating Fluid Density and Pressure

Consider a cylindrical container filled with a fluid. The container has a volume V and holds a mass

Comparative Analysis of Fluids: Air vs. Water

Consider two vertical columns of equal height (10 m): one filled with water (density $$1000 \; kg/m^

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: Flow in a Pipe

A horizontal pipe carries water and has a section where its cross-sectional area changes. At Point 1

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 and Fluid Identification

This problem focuses on calculating density and using that result to discuss buoyancy. Answer the fo

Density Measurement Using a Hydrometer

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

Density Variation in Immiscible Fluids

An object is submerged partly in oil and partly in water. A table provides mass and volume data for

Designing a Buoyant Object for Submarine Rescue

An engineering team is designing a buoyant device to lift a submerged object with mass 2000 kg. Anal

Designing a Fluid Dynamics Experiment Using Bernoulli's Principle

A student is tasked with designing an experiment to investigate the relationship between fluid speed

Designing a Water Distribution System using the Continuity Equation

An engineering water distribution system uses a main pipe which eventually splits into several branc

Dynamic Pressure and Airspeed from Pitot Tube Measurements

A Pitot tube is used on an aircraft to measure dynamic pressure, which is then used to calculate the

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

Experimental Design: Measuring Fluid Density Using Displacement

A researcher aims to measure the density of an unknown liquid using a water displacement method in a

Flow Rate and Pipe Constriction

Water flows through a horizontal cylindrical pipe that narrows from a radius of 4.0 cm to a radius o

Flow Rate Consistency in a Pipe

An experiment measured the flow characteristics in two sections of a pipe with different radii. The

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 Using the Continuity Equation

Water flows through a horizontal pipe that changes diameter. At Section 1 the pipe has a radius of 3

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

Fluid Density and Hydrostatic Pressure Calculation

A liquid sample has a mass of $$0.8 \; kg$$ and occupies a volume of $$10^{-3} \; m^3$$. In a separa

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

Hydrostatic Pressure Analysis

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

Hydrostatic Pressure in a Fluid

Consider an open tank containing water. The water has a density of 1000 kg/m³. Atmospheric pressure

Hydrostatic Pressure in a Fluid Column

A cylindrical tank is filled with a liquid of density $$\rho = 1000\,kg/m^3$$ to a height of $$h = 3

Hydrostatic Pressure in a Stratified Lake

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

Hydrostatics: Force on Submerged Surfaces

A rectangular plate measuring $$2\,m \times 1\,m$$ is submerged vertically in water (density = 1000

Inclined Pipe Flow with Incorrect Gravitational Component

A student analyzes fluid flow in an inclined pipe by measuring pressure at the upper and lower secti

Interpretation and Analysis of a Fluid Flow Schematic

A schematic diagram is provided that represents fluid flow in a horizontal pipe system. The diagram

Investigating Fluid Pressure with a Manometer

A researcher employs a U-tube manometer to measure the gauge pressure in a pressurized system using

Investigating Temperature Dependence of Fluid Density

The density of a liquid changes with temperature. A table below provides measurements of density at

Investigating Viscosity in Fluid Flow

A researcher explores the effect of fluid viscosity on flow rate through a narrow tube. Two liquids

Mapping Fluid Pressure Distribution Using Sensors

Design an experiment to map the pressure distribution within a fluid container by using multiple pre

Measurement Uncertainty in Fluid Density

In a laboratory experiment, the density of an unknown fluid is measured using a pycnometer. The mass

Mixed Fluid Continuity Experiment Error

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

Modeling Pressure as a Function of Depth in a Fluid

A graduate student models the pressure distribution in a tank filled with a liquid of constant densi

Non-Uniform Fluid Acceleration in a Varying Pipe

Consider a horizontal pipe whose cross-sectional area changes along its length. A segment of the pip

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 and Force Distribution on a Submerged Curved Dam

A dam has a curved, vertical face that is 15 m high and 30 m wide. The pressure on the dam increases

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 Distribution in a Fluid at Rest

Consider a tank filled with a liquid of density $$\rho$$. The pressure at a given depth is described

Pressure in a Fluid with Depth-Dependent Density

In a non-uniform fluid, the density varies with depth according to $$\rho(y) = \rho_0 + \alpha y$$,

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 Variations in a Natural Lake

This question connects fluid mechanics with environmental applications by calculating hydrostatic pr

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

Rotational Effects on Fluid Surface Shape

In a rotating cylindrical container, the surface of a liquid forms a parabolic shape due to the bala

Static vs Dynamic Pressure in Pipe

An experiment was conducted to measure the pressure components in a streamlined flow within a horizo

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.

Temperature Effects on Fluid Viscosity and Flow

In an experiment, the flow rate of a viscous fluid through a fixed nozzle is measured at various tem

Using a Pitot Tube to Measure Flow Velocity

A Pitot tube measures fluid velocity by converting the kinetic energy into a pressure difference bet

Viscosity Effects on Flow Rate in Capillary Tubes

Design an experiment to study how fluid viscosity affects the flow rate through capillary tubes. You

Visualization of Laminar Flow in Pipes

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

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

Adiabatic Process Analysis

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

Adiabatic Process Work Calculation

A researcher analyzes an expansion process of a gas that is performed adiabatically (i.e., no heat e

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 Real Gas Behavior

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

Analyzing Energy Conversion Efficiency in a Heat Engine

A novel power plant operates a heat engine that draws heat from a high-temperature source at $$850\;

Analyzing Temperature Effects on Molecular Speeds

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

Average Kinetic Energy and RMS Velocity in Gases

Using the kinetic theory of gases, consider a sample of an ideal gas at T = 300 K. (a) Calculate the

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

Convection Versus Conduction in Fluid Heating

In a laboratory experiment, two identical metal cylinders are heated on their sides. One cylinder co

Designing a Controlled Experiment for Ideal Gas Behavior

A scientist is planning an experiment to test the Ideal Gas Law $$PV = nRT$$ under controlled condit

Designing an Experiment to Measure Thermal Conductivity

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

Energy Conservation in a Closed System

A sealed container undergoes a process during which 500 J of heat is added and 200 J of work is perf

Energy Conservation in Thermodynamic Processes

For any process, the First Law of Thermodynamics states that $$\Delta U=Q+W$$. (a) Calculate the cha

Entropy and the Second Law

Consider a process where 200 J of heat is transferred from a reservoir at 500 K to a reservoir at 30

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

Evaluating Heat Transfer Mechanisms in a Fluid System

A fluid heating system employs both convection and radiation to transfer heat from a furnace to an a

Exploring Kinetic Molecular Theory via Maxwell-Boltzmann Distribution

An experiment is conducted to study the speed distribution of gas molecules. The data is represented

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

Graphical Interpretation of Thermodynamic Process Data

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

Heat Conduction Through Materials

Heat conduction in a material is governed by the equation $$\frac{Q}{\Delta t} = \frac{k * A * \Delt

Heat Engine Efficiency Analysis

A heat engine operates by drawing heat from a high-temperature source and rejecting part of it as ex

Heat Engine Efficiency and Cycle Analysis

A heat engine operates in a cyclic process. In one cycle, it draws 1000 J of heat from a high-temper

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

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 Pressure Analysis

A cylindrical container with a closed lid has a radius of $$0.15\;m$$ and a height of $$0.30\;m$$. I

Identifying Thermodynamic Processes

A series of experiments with a gas record measurements of pressure, volume, and temperature. The dat

Net Force on a Surface in Thermal Equilibrium

A lid covers a cylindrical container with an internal gas pressure of $$1.018 \times 10^5\,Pa$$, whi

Pressure Force on a Container Lid Using the Ideal Gas Law

Using the Ideal Gas Law, determine the force exerted by a gas on the lid of a cylindrical container

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

Real vs. Ideal Gas Behavior

While the Ideal Gas Law $$PV = nRT$$ describes the behavior of gases under many conditions, real gas

Reversibility and Work in Thermodynamic Cycles

A reversible thermodynamic cycle is performed, and a P–V diagram of the cycle is recorded. Use the d

Temperature and Kinetic Energy Relations

This experiment investigates the relationship between temperature and the average kinetic energy of

Thermodynamic Efficiency and Real Engines

Real heat engines are subject to various losses and cannot achieve the ideal efficiencies predicted

Understanding Temperature Scales in Thermodynamic Calculations

A student records a room temperature of 25°C for an experiment.

Verification of RMS Speed Dependence on Temperature

An experiment measured the RMS speed of gas molecules at different temperatures, with the following

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

Analysis of Equipotential Maps and Electric Field Lines

Consider a dipole formed by two equal but opposite point charges. Analyze the relationship between e

Balancing Forces in a Uniform Electric Field

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

Capacitor Design Challenge

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

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 Induction on Conductors vs. Insulators

A charged rod is brought near two spheres—one made of a conductor and one made of an insulator—that

Charge Quantization and Conservation

A small, isolated conducting sphere is observed to carry a net charge of $$+3.2 \times 10^{-19}\,C$$

Charge Redistribution in Conducting Spheres

Two identical conducting spheres, initially uncharged, are brought into contact and then separated.

Charged Oil Drop Experiment: Uniform Field and Drag Force Error

In a modified oil drop experiment intended to verify the quantization of electric charge, tiny oil d

Charged Particle Acceleration in a Uniform Electric Field

A charged particle is accelerated in a uniform electric field. The following table gives its measure

Charging an RC Circuit

Consider an RC circuit connected to a 12 V battery. The circuit consists of a resistor with resistan

Charging by Induction: Analysis and Prediction

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

Charging by Induction: Conductors vs. Insulators

A negatively charged rod is brought near two separate initially neutral spheres: one made of metal (

Charging Methods and Redistribution of Charge

Two identical, initially neutral conducting spheres are brought into contact. Then, a positively cha

Charging Methods Comparison

A researcher conducts two experiments to charge a neutral metal sphere. In Experiment 1, the sphere

Charging Methods Experiment: Conduction vs. Induction

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

Comparative Analysis of Electrostatic and Gravitational Forces

Design an experiment to compare the magnitudes of electrostatic forces and gravitational forces betw

Comparing Electric and Gravitational Forces in a Hydrogen Atom

Consider theoretical estimates for the forces acting between a proton and an electron in a hydrogen

Dipole Electric Field Calculation and Explanation

A dipole is formed by two point charges: a positive charge of $$+4.0*10^{-9}$$ C and a negative char

Effect of a Non-uniform Electric Field on a Moving Charge

A charged particle with charge $$q$$ is accelerated through a non-uniform electric field generated b

Effect of Temperature on Dielectric Constant in Capacitors

Propose an experimental setup to study how temperature affects the dielectric constant of a capacito

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 from an Infinite Charged Sheet

Consider a large sheet with a uniform surface charge density σ = 1.5 × 10⁻⁶ C/m².

Electric Field Lines at Media Boundaries

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

Electric Field Mapping and Equipotential Surfaces

In an experiment, equipotential maps are generated for a charge configuration. These maps illustrate

Electric Field Mapping in a Non-Uniform Field

A point charge is fixed on an insulating board. A voltage probe is used to measure the electric pote

Electric Field Variation with Distance

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

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

Enhancement of Capacitance with a Dielectric

A capacitor with an initial capacitance of C₀ is filled with a dielectric material having a dielectr

Equipotential Curves for an Electric Dipole

An electric dipole consists of two equal and opposite charges separated by a small distance. (a) S

Equipotential Mapping Experiment

Students conduct an experiment to map the equipotential lines created by a single fixed point charge

Equipotential Maps and Field Line Analysis

An equipotential map of a two-charge system is provided in the stimulus. Answer the following: (a)

Evidence of Charge Quantization in Oil-Drop Experiment

An experiment modeled after Millikan's oil-drop experiment produced the following measurements for t

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

Influence of Medium Permittivity on Electrostatic Force

Design an experiment to measure the changes in the force between two fixed point charges when differ

Investigating the Role of Dielectric Materials in Capacitors

Design an experiment to measure how the capacitance of a parallel-plate capacitor changes with the i

RC Circuit Capacitor Charging Analysis

An RC circuit containing a capacitor is studied as the capacitor charges from 0 V to its maximum vol

Square Charge Configuration

A researcher sets up a square configuration in vacuum with four point charges placed at the corners

Superposition of Electric Fields: Square Charge Configuration

Four identical positive point charges are fixed at the vertices of a square with side length 0.20 m.

Superposition of Electric Potentials and Work Done on a Test Charge

Two fixed point charges, $$q_1 = +4.0 \times 10^{-6}\,C$$ and $$q_2 = +4.0 \times 10^{-6}\,C$$, are

Work Done in a Uniform Electric Field

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

Analysis of Ammeter and Voltmeter Placement

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

Analysis of Current Flow in a Circuit with Mixed Components

An experiment involves a circuit that includes a combination of resistors and a capacitor branch. Th

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

Analyzing Series-Parallel Combinations of Capacitors

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

Analyzing the Effect of Wire Geometry on Resistance Measurements

A student investigates how the resistance of a wire depends on its length and cross-sectional area b

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

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

Capacitor Charging Experiment in an RC Circuit

A student assembles an RC circuit that includes a 12 V battery, a 3 Ω resistor, and an initially unc

Capacitor Combinations and Equivalent Capacitance

A circuit contains three capacitors with the following capacitances: 4 μF, 6 μF, and 12 μF. In the c

Circuit Simulation Verification

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

Data Analysis of Electric Circuit Measurements

In a laboratory experiment, students measured the voltage drop across a resistor at various currents

Designing an Experiment to Measure Current in a Complex Circuit

Propose an experimental procedure to measure the current distribution in a complex circuit containin

Effect of Varying Resistivity

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

Effects of Capacitor Arrangements in a Circuit

Two identical capacitors, each with a capacitance of 10 μF, are connected across a 12 V battery in t

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 for Series and Parallel Configurations

Two capacitors, one of $$4 \text{ F}$$ and the other of $$6 \text{ F}$$, are arranged in different c

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\

Evaluation of Energy Storage in a Capacitor

A capacitor with a capacitance of 10 μF is charged to a potential difference of 12 V.

Experimental Determination of Resistivity

You are tasked with determining the resistivity $$\rho$$ of an unknown metallic wire. Given: length

Heat Generation and Power Dissipation in Resistors

A circuit experiment provides measurements of voltage and current for different resistors. Use the d

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

Microcontroller-Based Circuit Measurement Setup

Design a circuit that integrates a microcontroller to continuously measure the current and voltage i

Modeling a Circuit with Mixed Resistors and Capacitors

An experimental study claims that in an RC circuit, a capacitor acts like a short circuit immediatel

Multi-Loop Circuit Analysis Using Kirchhoff’s Laws

A circuit consists of two loops sharing a common resistor. Loop 1 contains a battery of $$10 \text{

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

Series and Parallel Resistor Analysis

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

Series and Parallel Resistor Networks

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

Time Constant Determination from RC Circuit Current Decay

A series of measurements in an RC circuit provides the decay of current over time after the switch i

Transient Response Analysis in an RC Circuit

An RC circuit is connected to a $$10 \text{ V}$$ battery with a resistor of $$5 \Omega$$ and a capac

Validating Ohm's Law with a Non-Ohmic Conductor

A student attempts to validate Ohm's law by plotting the voltage-current (V–I) relationship for a fi

Angular Dependence of Magnetic Force

A series of experiments measures the magnetic force on a charged particle moving in a constant magne

Assessing Iron Dust Experiments for Bar Magnets

A study uses iron dust to demonstrate that the magnetic field inside a bar magnet is continuous and

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

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 =

Comparing Magnetic Field Mapping Techniques

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

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

Effect of Loop Orientation on Induced EMF

An experiment examines how the orientation angle of a loop in a uniform magnetic field affects the i

Electromagnetic Induction and Energy Conversion

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

Electromagnetic Induction in Generators

This FRQ integrates the principles of Faraday's law to model the operation of an electromagnetic gen

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 Determination of the Right-Hand Rule

This FRQ involves analyzing experimental data to verify the right-hand rule in a current-induced mag

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

Experimental Verification of Lenz's Law

Design an experiment to verify Lenz's Law by demonstrating that the direction of the induced current

Faraday's Law in Rotating Loop Experiment

An experiment is conducted in which a circular loop rotates at a constant angular speed in a uniform

Force on a Moving Charge in a Magnetic Field

A charged particle moves through a uniform magnetic field. Determine the magnetic force acting under

Induced EMF and Conductor Length

An experiment is conducted in which a conducting rod moves through a magnetic field, and the induced

Magnetic Dipoles: Bar Magnet and Current Loop

A researcher compares the magnetic field produced by a permanent bar magnet with that produced by a

Magnetic Field from a Current-Carrying Wire

Consider a long, straight wire carrying an electric current. Answer the following regarding the magn

Magnetic Force vs. Current in a Wire

An experiment examines the magnetic force acting on a straight current-carrying wire placed in a uni

Magnetic Torque on a Current Loop

A rectangular loop of wire with length $$L = 0.1 \; m$$ and width $$w = 0.05 \; m$$ carries a curren

Mapping Magnetic Field Lines using Iron Dust

In an experiment, a bar magnet is placed on a sheet and iron dust is sprinkled over it to visualize

Mapping Magnetic Field Lines with Iron Dust

A recent experimental report claims that by sprinkling iron dust on a piece of paper placed over a b

Mapping Magnetic Field Strength vs. Distance

Design an experiment to map how the magnetic field strength decreases with distance from a magnet. Y

Mapping Magnetic Field Using Compasses

You are provided with a long, straight current-carrying wire and several small compass needles. Your

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

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 Conducting Rod

A conducting rod of length $$l = 0.2$$ m moves at a constant speed $$v = 3.0$$ m/s through a uniform

Motional EMF in a Moving Conductor

A conducting rod moving through a magnetic field develops an induced emf due to magnetic forces on f

Motional EMF in a Sliding Bar Circuit

A U-shaped rail of length 1 m is connected by a sliding conductive bar, forming a rectangular circui

Optimizing Solenoid Configuration for Maximum Magnetic Field

An engineer is tasked with designing a solenoid to produce the strongest possible uniform magnetic f

Rotating Coil and Faraday’s Law Experiment

Design an experiment to test Faraday’s Law of electromagnetic induction by using a coil rotating in

Testing the Right-Hand Rule for Magnetic Force Directions

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

Trajectory of a Proton Near a Current-Carrying Wire

A proton moving at a speed of $$2 \times 10^5 \;m/s$$ passes at a distance of 4 cm from a long, stra

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

Combined Mirror-Lens System Analysis

An optical system is constructed using a converging lens and a concave mirror arranged along a commo

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 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

Concave Mirror Ray Diagram: Reflection Error Analysis

A student is asked to draw ray diagrams for a concave mirror experiment. The student accurately reco

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 Analysis

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

Diverging Thin Lens Analysis

A researcher examines a diverging lens with a focal length of $$-20$$ cm. An object of height 8 cm i

Double-Slit Experiment Data Analysis with Table Stimulus

A researcher performs a double-slit experiment and records the intensity (in arbitrary units) at var

Electromagnetic Wave Properties and Polarization

An electromagnetic wave is produced by an oscillating charge in free space. Consider a green light w

Experimental Verification of Snell's Law via Measured Data

This question involves analyzing experimental data of incident and refracted angles to verify Snell'

Image Formation in Plane Mirrors

Consider a scenario where a person stands in front of a plane mirror at a distance $$d$$ from the mi

Interference and Phase Difference in Wave Superposition

Consider two coherent light waves with a constant phase difference.

Interference in Thin Films

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

Optical Fibers and Total Internal Reflection

Optical fibers use total internal reflection to transmit light signals with minimal loss. Consider a

Polarization and Light Intensity Experiment

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

Polarization Effects in Electromagnetic Waves: Experiment Design

Design an experiment to investigate the effect of polarizing filters on the intensity of light. Your

Ray Tracing Verification for Spherical Mirrors

Design an experiment to verify the mirror equation using ray tracing with a concave spherical mirror

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 using Snell's Law

A beam of light in air (with $$n_{air} = 1.0$$) is incident upon a glass surface (with $$n_{glass} =

Reflection and Refraction with Wavelength Effects

A beam of light travels from air ($$n_1 = 1.0$$) into a glass medium ($$n_2 = 1.5$$) at an incident

Single Slit Diffraction Analysis

A single slit of width $$a = 0.1\,mm$$ is illuminated by monochromatic light with a wavelength of $$

Single Slit Diffraction Pattern Analysis

A single slit of width $$0.2*10^{-3}$$ m is illuminated with light of wavelength $$600*10^{-9}$$ m.

Spectral Analysis Using Diffraction Gratings

A researcher uses a diffraction grating with a groove density of 3000 lines per centimeter to analyz

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 -15 cm.

Spherical Mirrors: Concave Mirror Analysis

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

The Doppler Effect for Electromagnetic Waves

In a laboratory experiment, the frequency of light from a moving source was measured under different

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

Thin Lenses: Converging Lens Analysis

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

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: Critical Angle Determination

A student sets up an experiment to observe total internal reflection using a container filled with w

Young's Double Slit Experiment Analysis

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

Young's Double Slit Experiment Analysis

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

Bohr Model and Atomic Spectra

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

Nuclear Composition and Isotope Identification

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