AP Physics 1: Algebra-Based FRQ Room

Acceleration and Deceleration in a Race

A sprinter accelerates from rest and then decelerates to a stop during a race. Analyze the different

Air Resistance Effects on Projectile Motion

In this investigation, a student launches projectiles of different shapes but identical masses and i

Analysis of Position vs. Time Graph for Kinematic Insights

A student obtained a Position vs. Time graph with a quadratic relationship. Answer the following que

Analyzing a Cyclist's Journey

A cyclist's route is divided into five segments with the following details: | Segment | Distance (k

Analyzing Non-Uniform Acceleration from a Velocity-Time Graph

This question challenges you to analyze a velocity-time graph with non-uniform acceleration. Refer t

Average Acceleration in Non-uniform Motion

An object’s velocity is recorded over time as shown in the table below.

Baseball Projectile Motion

A baseball is hit off a bench, following a projectile trajectory under ideal conditions with no air

Centripetal Acceleration in Circular Motion

A particle moves in a circle of radius 2.0 m at a constant speed of 4 m/s. Analyze the centripetal a

Centripetal Motion Error

A student designs an experiment to measure the centripetal acceleration of an object moving in a cir

Comparative Analysis: Scalar vs. Vector Quantities on a Circular Track

A runner completes several laps on a circular track at a constant speed. Answer the following.

Comparison of Scalar and Vector Quantities

Consider two objects: Object A moves 15 m east and Object B moves 15 m west over the same time perio

Comparison of Speed and Velocity in Different Trials

An experiment involves two trials where an object takes the same path length, but with different net

Determining Acceleration from Position Data

A cart's position as a function of time is given by $$s(t)= 2*t^2 - 4*t + 1$$, where s is measured i

Determining Average Velocity and Instantaneous Acceleration from a Graph

A position vs. time graph is provided. Analyze it to answer the following questions.

Distance and Displacement Analysis

An object follows a path with several segments as outlined in the table. The object moves from point

Distance and Displacement Analysis Experiment

In this experiment, a small robotic car is programmed to follow a predetermined, winding path on a f

Distance and Displacement Conceptual Analysis

A car travels along a curved route such that the total distance traveled is $$200\ m$$, while its ne

Distance and Displacement from Position Data

An object is moving along a straight line and its position is recorded at various times as shown in

Distance and Displacement in a Hiker's Journey

A hiker embarks on a journey with four segments as given in the table below. Using the information p

Distance vs. Displacement

This question examines your understanding of the fundamental differences between distance and displa

Distance vs. Displacement: Analyzing Motion Paths

A researcher records the motion of a toy car along a winding track. The car moves from point A to B

Force Vector Addition Experiment

In a laboratory setup, an object is subjected to multiple forces applied at different angles using s

Free Fall Analysis

An object is dropped from a height of 80 m under free-fall conditions.

Free Fall Experiment Analysis

In a free fall experiment, a small mass is dropped from a certain height and its fall time is record

Free Fall Motion Lab

In a free fall experiment, a ball is dropped from rest. Use the data provided to analyze the motion.

Free Fall: Motion Under Gravity

A researcher drops a ball from a 45 m tall building. Neglecting air resistance, answer the following

Friction in Inclined Plane Experiment Error

A student sets up an experiment on an inclined plane to determine the coefficient of kinetic frictio

Graphical Interpretation: Projectile Motion Trajectory

A graph of a projectile’s height vs. time is provided. Answer the following parts.

Identifying Vector vs. Scalar Quantities

A table lists several physical quantities recorded during an experiment. Classify each quantity as e

Interpreting a Runner’s Position vs. Time Graph

A runner’s position over time is tracked and represented by a piecewise graph that includes segments

Laboratory Measurement of Gravitational Acceleration

A student performs an experiment to determine the acceleration due to gravity (g). The following dat

Manual Timing Reaction Error

A student measures the time of flight of a projectile using a manual stopwatch. The procedure requir

Motion Analysis: Distance Versus Displacement using Lab Data

A robot is programmed to follow a specific path in the lab, visiting the following coordinates: A (0

Multi-Stage Motion Analysis

A vehicle undergoes three stages of motion: (1) accelerates uniformly from rest at 2 m/s² for 5 s, (

Path Analysis: Distance vs. Displacement

An object moves along a path composed of three segments: first, it travels 4 m east, then 3 m north,

Pendulum Length and Period Experiment

In a pendulum experiment designed to investigate the relationship between length and period, student

Projectile Motion Analysis

A ball is launched from the ground with a given initial speed and launch angle. Use the equations of

Projectile Motion Analysis

An experiment investigates projectile motion by launching an object at different angles. The followi

Projectile Motion Angle Error

A student investigates the effect of launch angle on projectile range by using a projectile launcher

Projectile Motion Experiment

A projectile is launched from ground level with an initial speed of $$20 \; m/s$$ at an angle of $$3

Projectile Motion with Varying Launch Angle

A projectile is launched with an initial speed of \(v_0 = 25\,m/s\) at varying angles. Consider two

Projectile Motion: Basketball Shot Analysis

A researcher investigates the trajectory of a basketball shot. The ball is launched with an initial

Projectile Motion: Launched Ball

A ball is launched from ground level at an angle of $$30^\circ$$ with an initial speed of $$20\,m/s$

Radio Control Car Motion Analysis

In an experiment with a radio control (RC) car, its position is recorded at regular time intervals a

Ramp Acceleration and Slope Measurement Experiment

In an experiment involving a cart on an adjustable ramp, students measure the time taken for the car

Scalar vs. Vector: Lab Report Analysis

A student lab report claims that a measured value of 50 m represents both the distance traveled and

Scalars vs. Vectors: Identifying Quantities

A researcher compiles data for several physical quantities in an experiment, including temperature,

Speed versus Velocity

Examine and compare the concepts of average speed and average velocity.

Speed vs. Velocity Concepts

This question explores the conceptual differences between speed and velocity. Answer the following p

Speed vs. Velocity: An Object's Journey

An object moves in four segments as given in the table below. Analyze the object's motion by calcula

Uniform Acceleration Analysis using the BIG FIVE Equations

A car accelerates uniformly from rest for a period of 10 seconds. This experiment uses the BIG FIVE

Uniform Acceleration: Big Five Equations Validation

You are tasked with validating the Big Five Equations of Motion using experimental data from a unifo

Uniformly Accelerated Motion Calculations

A car undergoes two phases of motion on a straight road. First, it accelerates uniformly from rest,

Vector Addition and Net Displacement

A traveler moves according to three displacement vectors: $$\vec{d_1} = (3, 4)\, m$$, $$\vec{d_2} =

Vector Addition: Calculating Net Force

This question requires you to resolve force vectors into components and determine the net force acti

Vector and Scalar Quantities in Motion

In a motion experiment, a sensor recorded the velocity of an object as a function of time. Using the

Vector Components: Ballistic Launch Analysis

A researcher observes a ball being thrown from the ground with an initial speed $$v_0 = 20$$ m/s at

Velocity-Time Graph Analysis

A vehicle's motion is represented by a velocity versus time graph. The graph shows that for the firs

Action-Reaction in Everyday Life

Newton's Third Law states that every action has an equal and opposite reaction. Evaluate this law in

Analysis of a Rope-Pulley and Force System in a Rescue Operation

During a rescue operation, a team uses a rope and pulley system to lift a victim from debris. The vi

Analysis of an Acceleration vs. Time Graph

A graph of acceleration versus time for an object is provided. Use the graph to analyze the impulse

Analysis of System Equilibrium on a Rough Surface

A block is placed on a horizontal rough surface. A gradually increasing horizontal force is applied

Analyzing Frictional Forces on a Horizontal Surface

A student investigates how friction affects the acceleration of a cart on a horizontal surface by ap

Atwood Machine Dynamics Investigation

In an Atwood machine experiment, students set up a pulley system with two masses connected by a stri

Block on Horizontal Surface with Kinetic Friction

In this experiment, students apply a constant force to a block on a horizontal surface to study the

Center of Mass and Tipping Point Experiment

A composite object consisting of two connected masses is placed on an inclined plane to determine th

Circular Motion on a Banked Curve

A car of mass $$m$$ travels at speed $$v$$ along a banked circular road of radius $$r$$ and banking

Dynamic Analysis of a Multi-car Train

A train consists of three cars, each with a mass of 5000 kg, pulled by a locomotive that provides a

Dynamics FRQ #1: Net Force and Acceleration Analysis

A block on a frictionless surface of mass 5.0 kg is acted upon by two horizontal forces. A force of

Dynamics FRQ #14: Rotational Equilibrium on a See-Saw

A uniform see-saw 4.0 m long and weighing 20 kg is pivoted at its center. Child A, weighing 30 kg, s

Dynamics in Non-Inertial Frames

An elevator accelerates upward with an acceleration $$a = 2 * m/s^2$$. A passenger of mass $$m = 70

Dynamics in Non-Inertial Reference Frames

In an accelerating elevator, a person experiences an altered sensation of weight. Analyze this pheno

Dynamics in Rotational Motion and Angular Acceleration

A rotating disk experiences a net torque that causes it to accelerate rotationally. A researcher exa

Dynamics of a Multi-Force System: Tension, Normal, and Friction

A 4 kg block sits on a 20° inclined plane and is attached via a rope to a 2 kg hanging mass over a f

Dynamics of a Pendulum’s Forces

A simple pendulum with a bob of mass 1.0 kg and a string length of 2.0 m swings with a maximum angul

Dynamics of a Rolling Object on an Incline

A solid sphere of mass $$m = 0.5 * (kg)$$ and radius $$r = 0.1 * (m)$$ rolls without slipping down a

Dynamics of a Suspended Mass: Tension Analysis

A mass \(m\) is suspended by a rope. Analyze the forces acting on the mass when it is at rest and wh

Dynamics of a Two-Block System on a Frictionless Surface

Two blocks with masses $$m_1 = 3.0\; kg$$ and $$m_2 = 5.0\; kg$$ are connected by a light, inextensi

Dynamics of Coupled Oscillators: Mass-Spring Systems

A researcher examines a system of two coupled oscillators connected by a spring to study the interpl

Dynamics Problem 5: Tension and Friction in a Two-Block Pulley System

Two blocks are connected by a light, inextensible string over a frictionless pulley. Block A (mass =

Dynamics Problem 11: Effects of Friction on a Cart

A small cart of mass $$m = 3\ kg$$ moves along a horizontal track. Initially, the cart moves on a fr

Dynamics Problem 13: Experimental Acceleration Analysis

A student conducted an experiment to study the relation between applied force and acceleration on a

Dynamics Problem 14: Impulse and Momentum in a Collision

Two objects collide on a frictionless surface. Object 1 (mass = $$3\ kg$$) moving at $$4\ m/s$$ coll

Dynamics Problem 18: Effects of Air Resistance on Free-Fall

An object in free-fall is subject not only to gravity but also to a constant air resistance force $$

Effect of Friction on Circular Motion

In an experiment on circular motion, the maximum speed of an object moving in a circle is determined

Effect of Inclined Plane Angle on Acceleration: Experimental Analysis

In an experiment, a student measures the acceleration of an object sliding down ramps of varying ang

Exploring Centripetal Force in Circular Motion

Design an experiment to measure the centripetal force acting on a mass rotating in a horizontal circ

Free-Body Diagram Analysis on an Inclined Plane

Analyze the forces acting on an object on an inclined plane by constructing a free-body diagram and

Free-Body Diagram and Dynamics Analysis

An object of mass $$m$$ is placed on a frictionless inclined plane at an angle $$\theta$$. Analyze t

FRQ2: Projectile Motion Analysis Using a Velocity-Time Graph

A projectile is launched vertically upward. A velocity vs. time graph is provided. Analyze the graph

FRQ11: Multi-Force System Dynamics

A block is subjected to multiple forces simultaneously: an applied force, friction, and a tension fo

FRQ13: Tension Effects in a Two-Mass Pulley System

In a two-mass pulley experiment, different mass combinations yield different accelerations. Analyze

Inelastic Collision Experiment on a Track

Students conduct an experiment on a low-friction track to investigate momentum conservation during i

Investigating Acceleration in Circular Motion

An object moves in a circle of radius $$r$$ with a constant speed $$v$$.

Investigating Action-Reaction Forces

In an experiment, two carts in contact on a track, equipped with force sensors, record the forces ex

Investigating Gravitational vs Inertial Mass

In an experiment, a cart is placed on a low-friction track. A known net force is applied to the cart

Investigating Variable Mass in Rocket Propulsion

A research article claims that the traditional form of $$F = m * a$$ does not adequately describe ro

Mass Distribution and Acceleration

A cart with an adjustable mass distribution is used to study how the location of added mass affects

Mass Distribution and Center of Mass

Explore the concept of center of mass and its influence on the dynamics of a system.

Measuring Air Resistance Effects in Free-Fall Motion

Design an experiment to study how air resistance affects the free-fall motion of objects with identi

Measuring Inertial Mass Experimentally

Design an experiment to measure the inertial mass of an object.

Measuring Spring Constant via Dynamics

A spring is loaded with various masses, and the corresponding displacements are measured along with

Moment of Inertia Measurement

A disk is rotated by applying a constant tangential force at its edge, and its angular acceleration

Multiple Forces Acting on a Single Object

Consider an object on a rough horizontal surface that is subject to multiple forces including fricti

Projectile Motion and Air Resistance in a Thrown Ball Experiment

A sports news report claims that for a ball thrown at speeds below $$20$$ m/s, air resistance has a

Projectile Motion and Force Analysis Experiment

Students launch a projectile using a catapult and attach a force sensor to record the initial force

Rate of Change of Momentum

Examine the relationship between net force, impulse, and the rate of change of momentum.

Rocket Propulsion and Reaction Forces

A rocket of mass \(m\) in deep space suddenly expels gas to produce a thrust force. Analyze the forc

Rotational-Translational Dynamics in a Rolling Cylinder

A student investigates a cylinder rolling down an inclined plane without slipping. The experiment in

Tension Analysis in a Two-Mass Pulley System

In a two-mass pulley system, experimental data shows that the measured acceleration of the masses do

Tension and Acceleration in a Pulley System

A frictionless pulley system connects two masses, $$m_1$$ and $$m_2$$, with $$m_1 < m_2$$. The syste

Analysis of Centripetal Force Data

A researcher studies the centripetal force required for an object in uniform circular motion by meas

Analyzing Circular Motion in a Race Car Turn

A race car with a mass of 800 kg is negotiating a circular turn of radius 50 m at a constant speed o

Analyzing Data: Impact of Variable Speed on Centripetal Force

In a lab experiment, a 0.5 kg mass is whirled in a circle, and the tension in the string (which prov

Car Dynamics on a Circular Track

A car is rounding a circular curve with a constant speed. The car’s speed is 20 m/s and the radius o

Centripetal Force in a Circular Motion Experiment

A 0.2 kg ball is attached to a 0.50 m long string and swung in a horizontal circle at a constant spe

Centripetal Forces in a Vehicle's Turn

A 1500 kg car is navigating a curve with a radius of 30 m at a speed of 18 m/s.

Charged Particle in Circular Orbit

A stationary charged sphere with charge $$Q = 5.0 \times 10^{-6} \;C$$ is fixed at the center of a f

Comparative Analysis of Gravitational Acceleration on Different Planets

This problem examines how planetary mass and radius affect surface gravitational acceleration.

Comparative Analysis of Gravitational and Electric Forces

In an experiment, both gravitational and electric forces are measured between two pairs of objects.

Comparative Analysis: Gravitational Force vs Electric Force

This problem focuses on comparing gravitational and electric forces, including the similarities in t

Comparing Methodologies: Damped Pendulum versus Free Fall for g Measurement

Design two experimental procedures—one using a damped pendulum and one using free fall—to measure th

Conservation of Angular Momentum in Variable Radius Circular Motion

A 1.0 kg mass moving in a horizontal circle on a frictionless table has an initial speed of 4 m/s at

Designing a Centripetal Force Experiment

You are tasked with designing an experiment to measure how centripetal force depends on both the spe

Designing an Experiment to Measure Centripetal Acceleration

Design an experiment to measure the centripetal acceleration of an object in uniform circular motion

Effect of Changing Charge on Electric Force

In a lab experiment, the magnitude of the charge on two spheres was varied and the resulting force b

Effect of Magnetic Forces on Uniform Circular Motion

Design an experiment to investigate how an applied magnetic field influences the circular motion of

Electric vs. Gravitational Forces

Two small spheres each have a mass of $$m_1 = m_2 = 0.01\,kg$$ and carry an equal charge of $$q_1 =

Energy Considerations in Circular Motion: Kinetic and Potential Energy Analysis

Design an experiment to measure the kinetic and potential energy of an object undergoing uniform cir

Evaluating the Effects of Air Resistance on Circular Motion

A small ball attached to a string is swung in a circular path in air, where air resistance is not ne

Experiment on Mass Dependence in Centripetal Force

A student conducts an experiment by rotating objects of different masses attached to a constant-leng

Experimental Analysis of Centripetal Acceleration

An experiment is conducted by swinging a cart attached to a string in a circle at a constant speed o

Gravitational Acceleration and Free Fall

This problem investigates gravitational acceleration and its effects on objects in free-fall motion.

Impact of Radius Variation on Uniform Circular Motion

In an experiment designed to study uniform circular motion, a student varies the radius of the circu

Investigating the Role of Mass in Circular Motion

A 1.0 kg mass is moving in uniform circular motion in a horizontal circle of radius 2.0 m with a con

Lab Investigation: Effect of Radius on Centripetal Acceleration

A lab experiment investigates how the radius of circular motion affects the observed centripetal acc

Misinterpretation in Force Multiplication Experiment

In an experiment to investigate force interactions, a student sets up a system where multiple forces

Multi-Part Analysis of a Rotational Dynamics Experiment

In an experiment studying rotational dynamics, measurements of tangential speed, centripetal acceler

Satellite Orbital Motion: Gravitational and Centripetal Force

A satellite orbits the Earth in a circular path. In such an orbit, the gravitational force provides

Synthesis of Circular Motion and Energy Principles in a Pendulum

A simple pendulum with small oscillations undergoes circular motion near the bottom of its swing. (

Uniform Circular Motion of a Car on a Circular Track

A car of mass m drives along a circular track at constant speed. Analyze the forces involved in this

Block Sliding on a Rough Surface: Friction Work

A 5 kg block slides on a rough horizontal surface. It is given an initial speed of 8 m/s and comes t

Comparing Power Ratings of Motors

An electric motor with a power rating of $$500 W$$ performs $$200 J$$ of work during a task. Answer

Comparing Work Done at Varying Force Angles

An object is pulled by a constant force of $$50\;N$$. The force is applied at angles of $$0^{\circ}$

Compound Motion on an Incline with Friction

A 2 kg block is released from rest on a frictionless 30° incline. Midway during its descent, frictio

Conservation of Energy in a Bouncing Ball

A 0.3 kg ball is dropped from a height of 2.5 m and rebounds to a height of 1.8 m. The experiment in

Conservation of Mechanical Energy with Nonconservative Forces

Consider the experimental data showing initial and final kinetic and potential energies, alongside a

Crane Lifting with Force Angle

A crane lifts a 2000 kg load vertically by 10 m using a cable that makes a 15° angle with the vertic

Determining Frictional Work on a Block on an Incline

Develop an experiment to quantify the work done by friction on a block sliding down an inclined plan

Determining the Influence of Mass on Work Done

A researcher investigates the work required to push objects of various masses over a fixed distance

Effective Force Measurement in a Pulley Experiment

A student tests a pulley system by lifting a load and measuring the force using a calibrated weight

Efficiency in a Lifting Machine

A lifting machine is used to raise a 200 kg mass to a height of 2.5 m. The machine’s input energy fo

Energy Loss in a Frictional Slide

A sled of mass $$50 kg$$ slides down a snow-covered hill with a slope length of $$15 m$$. The sled s

Evaluating the Impact of Nonconservative Forces in a Pendulum

A simple pendulum is released from rest at a height of $$1.00\,m$$ above its lowest point. Due to ai

Exploring Mechanical Advantage and Energy Transfer in a Compound Pulley System

An experiment uses a compound pulley system to lift a load. The input force and the distance over wh

Frictional Work Calculation in a Box-Pulling Experiment

In this experiment, a student investigates the work done by friction on a box sliding across a horiz

Inclined Plane with Pulley

A 10 kg block is moved up a 30° incline via a combined system of an inclined plane and a pulley over

Investigation of Work Done on a Lifted Dumbbell

In this experiment, students aim to measure the work done on a dumbbell as it is lifted by a rope. T

Measuring Energy Transfers in a Martian Environment

A researcher simulates the work done by nonconservative forces in a Martian environment. On Mars, th

Modeling Energy Loss in Oscillatory Motion

A pendulum with a length of 2 m and a mass of 1 kg is released from an angle of 30° relative to the

Power Consumption in a Conveyor Belt System

A researcher analyzes an assembly line where a conveyor belt moves packages horizontally. In one tri

Work at an Angle Experiment Analysis

This question presents experimental data on work done by applying a force at different angles. Analy

Work Done Against Friction on a Sliding Block

A block slides on a rough horizontal surface and comes to a stop due to friction. The work done by f

Work Done by Friction on an Inclined Plane

A researcher studies the motion of a 4 kg block sliding down a 30° inclined plane with a length of $

Work Done Lifting a Weight

A person lifts a 50 kg weight vertically upward by 2 m. Use $$g = 9.8\,m/s^2$$. Answer the following

Work Measurement Under Non-Uniform Acceleration

In this experiment, a student measures the work done on a cart that accelerates along a track. A for

Work-Energy Analysis in a Variable-Mass System

In an advanced experiment, a student investigates the work-energy theorem using a cart that loses ma

Work-Energy Calculations in a Laboratory Experiment

In a lab experiment, a cart is subjected to a constant force during three separate trials as it move

Work-Energy Theorem and Friction

Analyze the provided experimental data related to a block sliding on a rough surface. Use the data t

Work-Energy Theorem on an Inclined Plane

A 3 kg block is released from rest on a 15° inclined plane that is 5 m long. Upon reaching the botto

Air Track Momentum Experiment

In an air track experiment, two gliders undergo a collision. Glider 1 (mass $$0.50\,kg$$) has an ini

Basic Momentum Calculation and Vector Analysis

Consider an object with mass $$m = 5\,kg$$ moving with a constant velocity of $$v = 2\,m/s$$. Using

Billiard Ball Elastic Collision

Two billiard balls undergo an elastic collision on a frictionless table. Before the collision, Ball

Collisions with External Forces

A 2.0 kg cart moving at 5 m/s on a frictionless track collides with a stationary 3.0 kg cart. Howeve

Crash Test Analysis: Impulse and Momentum

An automobile crash test provides the following force vs. time data: | Time (s) | Force (N) | |----

Designing a Collision Experiment with Air Tracks

You are tasked with designing a lab experiment using air tracks to investigate the conservation of m

Elastic Collision Analysis

A 2 kg object (A) moving at 4 m/s collides elastically with a 3 kg object (B) moving at –1 m/s. Use

Elastic Collision with Known Kinetic Energy

Two identical masses, where one is moving at 8 m/s and the other is at rest, undergo a head-on elast

Experimental Design: Effect of Mass on Momentum

Design an experiment to investigate the hypothesis that, for a constant velocity, increasing the mas

Experimental Uncertainty in Momentum Measurements

During an experiment to measure the momentum of a moving cart, various uncertainties arise in measur

Explosive Separation: Momentum Analysis

A stationary object with a mass of 50 kg explodes into two pieces. Experimental data shows that Piec

Impulse Calculation from a Time-Varying Force Function

A force is applied to an object according to the function $$F(t) = 5 * t$$ (in newtons) for $$0 \le

Impulse in Sports: Baseball Analysis

A baseball of mass $$0.145$$ kg is hit by a bat. The ball accelerates from rest to $$40$$ m/s in $$0

Inelastic Collision Investigation

A researcher observes an inelastic collision in which two vehicles collide and stick together. The e

Investigating Momentum Conservation in a Pendulum Collision

Two pendulum bobs, each of mass $$1.5 \ kg$$, are suspended. Bob A is set in motion and collides wit

Investigation of the Relationship between Force, Time, and Momentum Change

Design an experiment using a cart on a track and a variable force launcher to investigate the relati

Misinterpretation of Force-Time Graph in Impulse Determination

In this experiment, students used a force sensor to record data during an object’s collision and plo

Momentum Analysis in a Variable Mass System: The Leaky Cart

A cart on a track loses mass steadily (for example, leaking sand) as it moves. Answer the following:

Momentum Change in a Two-Collision Experiment

In a laboratory collision experiment on a low-friction track, two carts undergo sequential collision

Momentum Conservation in a Two-Car Collision

A scenario involving two cars colliding at a right angle is provided. Use conservation of momentum t

Momentum in Rotational Collisions

A uniform rod of length $$L = 2$$ m and mass $$M = 4$$ kg is pivoted at one end and is initially at

Momentum Transfer in a Baseball Collision

A 0.145 kg baseball is traveling at 40 m/s towards a bat. After being hit, it rebounds in the opposi

Momentum Transfer in a Soccer Collision

In a soccer game situation, a 0.43 kg soccer ball is kicked and travels at 25 m/s toward a 70 kg goa

Momentum Transfer in Rocket Propulsion

A simplified model of rocket propulsion involves ejecting mass to generate forward momentum in a fri

Multi-Stage Cart Collision

Three carts are placed on a frictionless track. Cart A (1.0 kg) is moving at 4.0 m/s toward Cart B (

Neglecting Air Resistance in a Falling Object Impact Experiment

In this experiment, an object is dropped from a height and its impact velocity is measured to calcul

Over-Simplified Analysis of Two-Dimensional Collisions

In this experiment conducted on an air table, two pucks undergo a two-dimensional glancing collision

Perfectly Inelastic Collision: Stuck Together Objects

Two objects collide and stick together. The data provided show that Object A has a mass of $$3\,kg$$

Rocket Propulsion and Momentum Conservation

A small rocket engine expels fuel to generate thrust, demonstrating momentum conservation in rocket

Time-Interval Effects on Impulse

Two collisions result in the same impulse magnitude of $$1.5\,Ns$$ but have different contact times.

Two-Dimensional Collision with Angular Components

Two objects on a frictionless surface collide. Object A (mass $$1.5$$ kg) is moving at $$4$$ m/s hor

Amplitude Independence of Period in SHM

In ideal simple harmonic motion, the period is independent of the amplitude. Answer the following pa

Analyzing Force vs. Displacement Graph in a Spring System

A force vs. displacement graph was generated for a spring system. Analyze the graph to determine if

Characteristic Analysis of Spring-Block Oscillator

A spring-block system oscillates with displacement described by $$x = A*\cos(\omega*t + \phi)$$. Exp

Conservation of Energy Over a SHM Cycle

A block attached to a spring oscillates with constant total mechanical energy. (a) Write expression

Damped Harmonic Oscillation Experiment

An experiment involving a mass-spring system is modified by attaching a damping mechanism (such as a

Derivation of Acceleration in SHM from Newton's Second Law

Derive the acceleration expression for a system undergoing simple harmonic motion using Newton's Sec

Effect of Spring Constant Variation on Oscillation

In an experiment, a mass-spring system is used where different springs with varying spring constants

Energy Conservation in SHM: Experimental Data Analysis

An experiment records the displacement of a mass-spring system over time. Use the data to analyze en

Energy Loss Mechanisms in SHM

Discuss the mechanisms of energy loss in a system undergoing simple harmonic motion and propose a me

Evidence of Damping in Oscillatory Motion

An experiment studying a damped oscillator records the amplitude of oscillation at successive time i

Experimental Determination of Angular Frequency

An experiment recorded the displacement of a mass-spring oscillator at various times (see table belo

Experimental Verification of the Mass-Spring Period

An experiment is performed with a mass of $$0.3\,kg$$ attached to two different springs, one with sp

Exploring SHM in Pendulums

Examine the validity of the small-angle approximation used in simple pendulum motion.

Graphical Analysis of SHM: Displacement vs. Time

A graph of displacement over time for a mass-spring system is shown. (a) From the graph, identify t

Impact of Phase Shift in SHM

A mass-spring system is described by the displacement function $$x = A*cos(ω*t+φ)$$. Answer the foll

Misinterpretation of SHM Sinusoidal Graph Data

A student uses an oscilloscope to record the displacement versus time for a mass-spring system under

Oscillating Mass on a Spring

A block of mass $$m$$ is attached to a spring with spring constant $$k$$ and oscillates on a frictio

Oscillatory Motion with Variable Amplitude

Explore the behavior and safety implications of a driven harmonic oscillator with variable amplitude

Pendulum Motion Comparison

Pendulums are a common example of systems exhibiting periodic motion. Answer the following:

Pendulum Period Analysis

A simple pendulum with a length of $$L = 1.0 m$$ is undergoing small-angle oscillations under gravit

Pendulum Period Calculation

A simple pendulum of length $$L$$ swings under the influence of gravity $$g$$. The period of a pendu

Phase Difference and Interference in Coupled Oscillatory Systems

Two identical mass-spring oscillators, each given by $$x(t) = A \cos(\omega*t + \phi)$$, oscillate w

Simple Harmonic Motion in Vertical Orientation

In a vertically oscillating mass-spring system, gravity shifts the equilibrium position. Analyze its

Small Angle Approximation in Pendulum Motion

For a simple pendulum, the small-angle approximation allows its motion to be approximated as simple

Accelerometer-Based Measurement in Rotational Motion

Propose an experiment that utilizes accelerometers attached to a rotating object to measure its angu

Amusement Park Ride Safety Check

An amusement park ride features a long rotating arm 10 m in length with a seat at the end. The ride

Angular Displacement from Arc Length Measurements

A small robot moves along a curved path that is part of a circle with a radius of $$r = 0.5\,m$$. It

Angular Momentum Conservation in a Rotational System

A figure skater is spinning with a given moment of inertia and angular velocity. By drawing in her a

Center of Mass in Rotating Systems

Design an experiment to study how the distribution of mass affects the location of the center of mas

Comparative Analysis of Moment of Inertia

Two wheels, each with a mass of $$10 kg$$ and a radius of $$0.5 m$$, have different mass distributio

Composite Moment of Inertia of a Composite Wheel

A composite wheel is constructed from a solid disk (mass $$2 \;kg$$, radius $$0.3 \;m$$) and a thin

Composite Rotational Systems with Coupled Cylinders

A researcher examines a system of two coupled solid cylinders rotating about the same axis. Cylinder

Connecting Linear and Angular Motion on a Rotating Disc

A point on the edge of a rotating disc is observed, and its motion is characterized by both linear a

Designing a Rotational Motion Experiment using a Torsional Pendulum

A student wishes to determine the moment of inertia of an irregular-shaped object using a torsional

Determining Angular Velocity from Linear Speed

A point on the rim of a rotating wheel with a radius of $$r = 0.2\,m$$ is observed to have a linear

Energy Considerations in Rotational Motion

An experiment measures both the rotational and translational kinetic energies of a rolling object. T

Energy in Rotational Motion

A flywheel rotates at 1200 revolutions per minute (rev/min) and has a moment of inertia of $$10 \tex

Graph Interpretation of Angular Velocity Data

Analyze a graph of angular velocity as a function of time to extract quantitative information about

Gyroscopic Precession Experiment Error

A student conducts an experiment on gyroscopic precession using a spinning top. The top is subjected

Hybrid Rotational Dynamics with a Sliding Mass

A hybrid system consists of a rotating disc and a sliding mass. The disc has a mass of $$8 kg$$ and

Impact of Body Position on Rotational Speed in Diving

A diver alters her body position during a dive, reducing her moment of inertia. Analyze how this cha

Linking Angular and Linear Accelerations

Design an experiment to explore how angular acceleration relates to linear acceleration at the rim o

Mass Distribution and Angular Acceleration

Design an experiment to examine how the distribution of mass affects the angular acceleration of a r

Oscillations of a Physical Pendulum

A uniform wooden rod of length 1 m oscillates as a physical pendulum about a pivot near one end. The

Rotational Deceleration of a Turntable due to Friction

A researcher studies the effect of friction on a rotating turntable that decelerates uniformly from

Rotational Kinetic Energy Experiment Error

A student attempts to measure the rotational kinetic energy of a spinning disk by recording its angu

Rotational Motion in Automotive Braking

A researcher studies the effect of a braking torque on a car wheel. The wheel has a radius of $$R =

Torque and Rotational Equilibrium in a Seesaw

Two children are sitting on a seesaw. Child A (30 kg) is 1.2 m from the pivot, and Child B (40 kg) i

Using Torque to Analyze Rotational Equilibrium

A uniform beam 4 m long is balanced on a pivot located 1 m from its left end. (a) A 30 N weight is h