AP Physics 2: Algebra-Based FRQ Room

Accelerated Fluid in an Elevator Experiment

A sealed container filled with water (density = $$1000 \; kg/m^3$$) is placed inside an elevator tha

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

Analyzing Experimental Data on Fluid Flow

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

Application of Bernoulli's Equation

In a horizontal pipe, a pump forces water (density $$1000\;kg/m^3$$) from point 1 into a constricted

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 Equation in a Constricted Pipe

A pump forces water through a horizontal pipe that gradually constricts. At point 1 (where the pipe

Bernoulli's Equation in a Venturi Meter Experiment

An engineer uses a Venturi meter to measure the flow speed of water in a horizontal pipe. The meter

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

Bernoulli's Principle in a Venturi Tube

A Venturi tube is installed in a horizontal pipe. At section 1 the cross-sectional area is $$A_1$$ a

Buoyancy Analysis of a Floating Object

An object with a mass of 150 kg and a volume of 0.75 m³ is placed in a fluid. Consider a fluid with

Buoyancy and Density Ratio Experiment

An experiment is conducted to study the buoyancy of various objects in different fluids. The followi

Buoyancy and Floating Object Experiment

An object with a mass of $$150 \; kg$$ and a volume of $$0.75 \; m^3$$ is placed in ethyl alcohol, w

Buoyancy and Submerged Fraction

An object with mass m = 150 kg and volume V = 0.75 m³ is floating in ethyl alcohol (density = 800 kg

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

Buoyant Force and Fraction Submerged

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

Comparative Analysis: Density and Fluid Compressibility

This problem probes the conceptual differences between liquids and gases with respect to compressibi

Comparative Study of Fluids Using a U-Tube Manometer

In a laboratory, students use a U-tube manometer to compare the densities of two unknown fluids. The

Comparing Fluid Pressures in Different Media

Two open-top tanks contain different fluids. Tank 1 is filled with water (density = $$1000 \cdot kg/

Composite Material Density and Pressure Analysis

A materials scientist tests a new composite material by first measuring a 0.001 m³ sample with a mas

Continuity Equation and Variable Pipe Flow

A horizontal pipe carrying a fluid branches into two tubes of different diameters. Analyze the situa

Density Determination via Fluid Displacement

Design an experiment to measure the density of an irregularly shaped object using the method of flui

Design Considerations for Submerged Structures

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

Determining Buoyant Force on a Partially Submerged Object

A physics student examines the buoyant force experienced by an object when it is partially submerged

Determining Fluid Density

A sample of an unknown liquid has a mass of $$1.2 \times 10^{0} \text{ kg}$$ and occupies a volume o

Discrepancies in Pipe Flow Measurements

In an experiment to measure water velocity in a pipe, the predicted velocity in a constricted (narro

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

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 Viscous Forces on Laminar and Turbulent Flow

In an experiment, a fluid flows through a smooth, straight pipe. At low speeds, the flow is observed

Energy Conservation in Fluid Flow: Laminar vs. Turbulent Regions

In a horizontal pipe, regions of laminar and turbulent flow are observed. Pressure and velocity meas

Energy Conservation in Fluid Flows

Using Bernoulli's equation, derive an expression that relates the change in kinetic energy per unit

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 Determination of Fluid Viscosity Using Flow Rate Measurements

A researcher seeks to determine the viscosity of a fluid using a capillary tube method. In the exper

Flow in a Constricted Pipe: Continuity Equation Application

Water flows through a horizontal pipe that narrows from a section with a radius $$r_1 = 2.0\,cm$$ an

Flow Rate Analysis in Variable Cross-Section Pipes

A water flow experiment is conducted using a pipe with two sections of different diameters. The meas

Flow Rate in a Non-uniform Pipe

A researcher examines fluid flow through a non-uniform circular pipe where the fluid is assumed to b

Fluid Depth Pressure Graph Analysis

A pressure sensor is used to measure the pressure at different depths in a water tank. The following

Fluid Exit Velocity: An Orifice Flow Experiment

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

Fluid Flow in Curved Pipes and Centrifugal Effects

In a chemical processing plant, fluid flows through a curved pipe. The curvature induces centrifugal

Hydrostatic Pressure and Density Experiment

A researcher conducts an experiment to investigate hydrostatic pressure in two fluids, water and oil

Hydrostatic Pressure in an Open Tank

A researcher investigates hydrostatic pressure within an open water tank. The study aims to measure

Measurement of Flow Rate in a Venturi Meter

A venturi meter is installed in a pipeline to measure flow rate by producing a pressure drop at the

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 Dynamics in Constriction

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

Pressure Variation with Depth in a Liquid

Consider a deep freshwater lake with a density of $$1000~kg/m^3$$. a) Derive an expression for the

Structural Column Pressure

This question examines the calculation of pressure exerted by a vertical structure and how variation

Submerged Object Buoyant Force Evaluation

A hollow cylindrical object is partially submerged in water. Its cross-sectional area is 0.1 m² and

Temperature Effects on Fluid Density and Pressure

A particular fluid has a density of 950 kg/m³ at 20°C and its density decreases by 0.2% for every 1°

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}$

Time-Varying Fluid Flow Analysis

In an experiment, the volume flow rate of water through a horizontal pipe is found to vary with time

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 in a Conduit

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

Variable Buoyancy: Measuring Submerged Fraction of an Object

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

Venturi Tube Misapplication of Bernoulli's Equation

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

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 a Carnot Cycle

A Carnot engine operates between two thermal reservoirs with temperatures $$T_H$$ and $$T_C$$. A cyc

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

Comparing Heat Transfer Mechanisms: Conduction vs Convection in Fluids

Heat can be transferred via conduction and convection in fluids. Design an experiment to isolate and

Comparing Isothermal and Adiabatic Processes in a P-V Diagram Experiment

An experiment uses a P-V diagram to compare isothermal and adiabatic processes. Two distinct paths a

Comparison of Isothermal and Adiabatic Processes

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

Conduction, Specific Heat, and Temperature Change

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

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\

Deviations of Real Gases from Ideal Behavior

The ideal gas law, $$PV = nRT$$, describes gases under ideal conditions. However, at high pressures

Effect of Temperature on rms Velocity

An experiment is conducted to investigate how changes in temperature affect the root mean square (rm

Effects of Mole Number on Gas Pressure

In a series of experiments with a fixed-volume container at constant temperature, the number of mole

Energy Conservation in Thermodynamic Processes

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

Entropy Change in a Heating Process

An ideal gas (1 mole) undergoes a reversible isobaric process in which its temperature increases fro

Entropy Change in a Thermodynamic Cycle

During a cyclic process, an experiment measures the change in entropy during various stages. Analyze

Entropy Change Measurement in a Spontaneous Process: Experimental Design

Entropy is a measure of disorder and increases in spontaneous processes. Design an experiment to mea

Error Analysis in Thermodynamics Measurements

A laboratory experiment measuring the temperature and pressure of a gas in a sealed container shows

Experimental Analysis of Gas Kinetic Energy

In a set of experiments, Maxwell-Boltzmann speed distribution graphs were obtained at different temp

Experimental Test of the First Law of Thermodynamics in an Isobaric Expansion Process

The First Law of Thermodynamics states that $$\Delta U = Q + W$$. Design an experiment to test this

Experimental Verification of the Maxwell–Boltzmann Distribution in Gas Molecules

The Maxwell–Boltzmann distribution predicts the speed distribution of molecules in a gas. Design an

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

First Law Application: Heat Input and Work Output

During an experiment, a system undergoes a process in which 600 J of heat is supplied and it perform

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

Heat Conduction in a Metal Rod

A researcher studies heat transfer through a long, homogeneous metal rod that is heated at one end w

Heat Engine Efficiency

A heat engine operates in a cyclic process where heat is taken in from a high-temperature source, pa

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 Cycle Analysis

Examine a heat engine that draws heat from a high-temperature source and rejects waste heat. Analyze

Impact of Temperature Variations on Gas Density

An experiment investigates how the density of a gas in a container changes as the temperature is inc

Investigating the Second Law of Thermodynamics in Cyclic Processes

Consider a closed system undergoing a cyclic process. Analyze the net entropy change for both revers

Investigating Thermodynamic Processes: Isobaric vs Isochoric

In a controlled experiment, a gas undergoes two distinct processes: an isobaric expansion followed b

Irreversible Processes and Entropy Analysis

A claim is made that during an irreversible process in an isolated system, the total entropy always

Kinetic Energy and Temperature Relationship

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

Molecular Speed and Temperature

Consider an ideal gas composed of molecules each having mass m. The root‐mean‐square speed is given

Refrigerator Cycle and Coefficient of Performance

A refrigerator operates on a reversed Carnot cycle. (a) Draw a schematic diagram (P–V or T–S) of th

RMS Velocity and Temperature Relationship

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

Thermal Insulation Effectiveness Experiment Error

A student conducts an experiment to test the effectiveness of different insulation materials by meas

Transient Heat Conduction Analysis

The transient heat conduction in a solid can be described by the heat equation: $$\frac{\partial T}{

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 Sequential Thermodynamic Processes

A gas undergoes a two-step process: an isobaric expansion followed by an isochoric heating. Using th

Work Done in a Non-Constant Pressure Process

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

Work Done in Thermodynamic Processes

The following P–V diagram represents two different paths between the same initial state (point a, $$

Analysis of an Electric Dipole Field

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

Balancing Gravitational and Electric Forces

A 5 g object is placed 2 cm above a large, uniformly charged horizontal plate producing a uniform el

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

Charge Redistribution by Induction

Two initially neutral metallic spheres are suspended by insulating strings. A positively charged rod

Charge Redistribution in Connected Conductors

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

Charge Redistribution via Induction

Two identical, initially neutral conducting spheres are placed in contact on an insulating stand. A

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

Comparative Analysis of Charging Methods

In a laboratory setting, two objects made from different materials—one metal (a good conductor) and

Complex Charge Arrangement: Net Electric Field Calculation

Consider a system of four point charges arranged at the vertices of a rectangle: q₁ = +3 μC at (0, 0

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

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

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

Dielectric Effects on Capacitance Experiment

In a parallel-plate capacitor experiment, the capacitance is measured with and without the insertion

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 Mapping and Equipotential Surfaces

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

Electric Field Mapping Experiment

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

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

Electric Potential Variation in a Conical Capacitor

A non-standard capacitor is constructed with one plate conically shaped, leading to non-uniform sepa

Electric vs. Gravitational Forces in a Hydrogen Atom

Consider a hydrogen atom where the proton (charge $$+e$$) and electron (charge $$-e$$) are separated

Energy Storage in a Parallel-Plate Capacitor

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

Equipotential Surfaces and Field Lines

A researcher maps the equipotential surfaces around an isolated charged sphere.

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

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 Capacitor Energy Storage Versus Separation Distance

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

Kinetic Energy Gain of a Test Charge in a Non-Uniform Electric Field

A test charge of $$q = +5.0 \times 10^{-9}\,C$$ is released from rest at a distance of $$0.20\,m$$ f

Mapping Electric Field Around a Point Charge

Design an experiment to map the electric field in the vicinity of a point charge using a test charge

Measuring Electric Field Intensity from a Conductive Plate

Design an experiment to measure the electric field intensity at various distances along the axis per

Non-Uniform Charge Distribution Effects

A researcher examines the electric field created by a hemispherical charge distribution with total c

Parallel-Plate Capacitor Characteristics and Energy Storage

A parallel-plate capacitor has a capacitance of $$10\,nF$$ and stores a charge of $$50\,\mu C$$ on e

Parallel-Plate Capacitor Design

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

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. (

RC Circuit Charging

A researcher investigates the charging behavior of a capacitor in an RC circuit. The circuit contain

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

Superposition of Forces in a Square Configuration

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

Surface Charge Distribution on Irregular Conductors

The distribution of surface charge on conductors is influenced by the geometry of the surface. This

Advanced Transient Analysis in Electric Circuits

A complex circuit contains multiple RC branches with different resistances and capacitances. The tra

Analysis of Variable Resistance in a Circuit

A circuit is set up with a rheostat (variable resistor) controlling the current through a motor powe

Analyzing Ammeter and Voltmeter Measurements

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

Analyzing Equivalent Resistance in a Mixed Resistor Network

A student conducts an experiment to find the equivalent resistance of a circuit that includes a 4 Ω

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

Application of Kirchhoff’s Laws in Complex Circuits

Consider a circuit that has two branches: one branch contains a single resistor and the other branch

Battery Internal Resistance Analysis

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

Battery Performance and Power Output

A 12 V battery is connected to a resistor, and its terminal voltage, current, and power output are r

Capacitor Charging in an RC Circuit

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

Capacitors in Series and Parallel: Equivalent Capacitance Analysis

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

Circuit Design and Optimization: An Integrated Approach

Design a circuit that delivers a steady current of $$2~A$$ to a load while minimizing power loss and

Comparing Conductor Materials: Effect on Efficiency

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

Complex Circuit Analysis Using Kirchhoff's Laws

A 12 V battery is connected to a circuit where a resistor of 4 Ω is in series with a parallel combin

Current Flow Analysis in a Simple Battery Circuit

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

Design of an Experiment: Measuring Capacitance

Design an experiment to accurately measure the capacitance of a parallel-plate capacitor. Your desig

Designing a Circuit for Energy Efficiency Testing

A recent study claims that by reconfiguring a circuit, the overall power loss in resistors can be mi

Designing a Circuit for Specific Power Dissipation

You are tasked with designing a simple circuit that will dissipate 4.5 W of power across a resistor

Designing a Voltage Divider Circuit

Design a voltage divider that converts a 24 V supply to a 5 V output using two resistors in series.

Determination of Material Resistivity

A student is conducting an experiment to determine the resistivity of wires made from different mate

Determining Resistivity of Various Materials

Resistance (R) and resistivity (\(\rho\)) are related by the expression $$R = \rho*\frac{l}{A}$$. Yo

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

Direct Current Flow and Potential Drop in a Simple Circuit

A simple circuit is constructed using a 12 V battery and a single resistor of 6 Ω connected by wires

Effect of Varying Resistivity

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

Effects of a Variable Resistor on Circuit Behavior

A variable resistor is used in a series circuit powered by a 15V battery.

Effects of Altering Capacitance on a Charged Capacitor

A capacitor with an initial capacitance of $$10\,\mu F$$ is charged to $$12\,V$$ by a battery, and t

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

Experimental Design: Effect of Resistor Arrangements on Circuit Behavior

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

Experimental Errors in Electric Circuit Measurements

In a laboratory setting, students measure various parameters such as voltage, current, and resistanc

Graphical Analysis of Battery Discharge

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

Impact of Wire Dimensions on Resistance

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

Investigating Non-Ohmic Behavior in an AC Circuit

A student conducts an experiment on an incandescent light bulb powered by a 120 V AC source and atte

Investigating the Effect of Capacitor Dielectric Constant on Capacitance

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

Kirchhoff's Laws in a Multi-Loop Circuit

A circuit consists of two loops sharing a common resistor. In Loop 1, a 12 V battery is connected in

Kirchhoff’s Laws: Loop and Junction Analysis

An experiment was conducted on a multi-loop circuit to test Kirchhoff's loop and junction rules. The

Maximum Power Transfer in a Circuit with Internal Resistance

A battery with an EMF of 9 V and an internal resistance of $$1\;\Omega$$ is connected to an external

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

Multi-loop Circuit Analysis: Equivalent Resistance Calculation

Consider a circuit with two interconnected loops sharing a common resistor. Loop 1 contains a batter

Power Dissipation Analysis

A laboratory experiment is conducted to measure the electrical characteristics of resistors. The fol

Power Dissipation Analysis in Resistive Networks

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

Power Dissipation in Circuit Components

A simple circuit consists of a resistor connected to a battery. Consider a scenario where a 9 V batt

RC Circuit Analysis with Switch Operations

In an RC circuit with a switch, experimental measurements indicate that immediately after closing th

Resistivity and Material Properties

In a study of different conductive materials, wires of identical dimensions (length = 2 m, cross-sec

Resistor Combination Analysis: Series and Parallel

A report claims that complex resistor networks can be simplified into a single equivalent resistance

Resistor Network Analysis

Consider a circuit where a 4 Ω resistor is connected in series with a parallel combination of a 3 Ω

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

Studying the Transient Response in an RC Circuit with a Variable Resistor

A student investigates the charging process of a capacitor in an RC circuit by connecting a 12 V bat

Terminal Voltage Variation Under Different Load Conditions

In an experiment, a battery's terminal voltage is measured under varying load resistances. The table

Analysis of Experimental Data in a Motional EMF Investigation

In an experiment, a sliding conductor is moved through a uniform magnetic field at various speeds, a

Analysis of Solenoids: Field Uniformity and Enhancements

The performance of a solenoid as an electromagnet depends on its design. Investigate the factors inf

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

Changing Magnetic Flux Through a Circuit

Magnetic flux through a loop can be altered by changes in the loop’s area, the strength of the magne

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 Forces on Charges and Wires

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

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

Designing a Magnetic Levitation Experiment

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

Determination of Solenoid Current through Field Measurements

Students aim to determine the current flowing through a solenoid by measuring the magnetic field ins

Effect of Changing Magnetic Field Strength on Induced Current

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

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

Effect of Magnetic Permeability on Solenoid Magnetic Field

A long solenoid with $$n = 500\; turns/m$$ carries a current of $$I = 2 \; A$$. With an air core, th

Evaluating Magnetic Forces on a Current-Carrying Wire

An experiment investigates the net magnetic force on a U-shaped current-carrying wire immersed in a

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°

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

Induced EMF in a Rectangular Loop with Changing Area

A rectangular loop of wire has one side that can slide, causing the area of the loop to increase ove

Induced EMF in a Sliding Rod Circuit

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

Investigating Induced EMF and Electrode Separation

An experiment investigates how the induced emf in a rod moving through a magnetic field changes with

Investigating the Effect of Coil Turns on Induced EMF

An experiment is conducted using solenoids with different numbers of turns to study their effect on

Lenz’s Law and Induced Current Direction

In an experiment, a coil is subjected to a changing magnetic flux by moving a magnet toward and then

Magnetic Field from a Current-Carrying Wire

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

Magnetic Field Mapping with Iron Filings

Permanent magnets produce complex magnetic fields that can be visualized using iron filings. In this

Magnetic Force on a Current-Carrying Conductor

A U-shaped wire is partially immersed in a uniform magnetic field. Parts of the wire experience diff

Mapping Magnetic Field Lines using Computer Simulation

Students use a computer simulation to model the magnetic field lines around a bar magnet and analyze

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 Using Iron Filings

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

Measuring Magnetic Permeability Experiment

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

Motional EMF and Velocity

In an experiment, a conducting rod moves perpendicular to a uniform magnetic field at various speeds

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

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 and Faraday’s Law Experiment

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

Solenoid Magnetic Field

This FRQ explores the magnetic field inside a solenoid through derivations, calculations, and concep

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

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

Advanced Thin Lens Systems in Compound Microscopes

A compound microscope uses two converging lenses: an objective lens with a focal length of $$f_o = 0

Analysis of Polarization and Malus' Law

This question explores the concept of polarization, quantitative analysis using Malus' law, and requ

Chromatic Aberration in Lenses

Chromatic aberration occurs when a lens fails to focus all wavelengths to the same point. Answer the

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 Characteristics

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

Concave Mirror Ray Diagram: Reflection Error Analysis

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

Convex Mirror Image Formation

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

Determining Indices and Critical Angles

Light travels from a glass medium into air. In one experiment, a beam in glass strikes the interface

Diffraction Grating Experiment: Determining Wavelength of Light

Design an experiment using a diffraction grating to determine the wavelength of a light source. Your

Diffraction Grating Spacing Effects on Diffraction Pattern

Design an experiment to investigate how the spacing of a diffraction grating affects the resulting d

Electromagnetic Spectrum Frequency Calculation

A researcher is exploring the electromagnetic spectrum. The researcher is working with green light,

Electromagnetic Wave Generation and Analysis

An oscillating charge in an antenna generates electromagnetic waves. Consider a radio transmitter op

Electromagnetic Wave Interference and Phase Difference

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

Experimental Verification of the Law of Reflection

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

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

Image Formation with a Concave Mirror

A concave mirror has a focal length of 10 cm. An object 5 cm tall is placed 20 cm in front of it. Us

Impact of Wavelength on Single Slit Diffraction Patterns

In an experiment, a student investigates how changing the light's wavelength affects the diffraction

Lens Power Calculation from Image Magnification

A student uses a converging lens to investigate magnification. In the experiment, an object is place

Lens-Mirror Combination Instrument

A researcher designs an optical instrument that integrates a converging lens with a focal length of

Magnification in Diverging Lens: Formula Misapplication Error Analysis

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

Optical Instruments - Microscope Lens System

A compound microscope uses two converging lenses. The objective lens has a focal length of 0.8 cm, a

Oscillating Charges and the Generation of EM Waves

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

Plane Mirror Image Formation and Analysis

Plane mirrors reflect light according to the law of reflection and produce images that are virtual a

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, Refraction, and Snell's Law in Optical Media

Light interaction with media boundaries is governed by the laws of reflection and refraction. This q

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

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

Thin Converging Lens Image Formation

An object of height 10 cm is placed 40 cm from a converging lens with a focal length of 15 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

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

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

Bohr Model and Atomic Spectra

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

Photodisintegration of a Deuteron

A study is conducted on the photodisintegration of deuterium. Given that the binding energy of a deu

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