AP Physics 1: Algebra-Based FRQ Room
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AP Physics 1: Algebra-Based Free Response Questions
The best way to get better at FRQs is practice. Browse through dozens of practice AP Physics 1: Algebra-Based FRQs to get ready for the big day.
Analysis of a Velocity-Time Graph
Examine a velocity vs time graph of an object to analyze its motion characteristics.
Analyzing Position vs Time Graph
A student tracks the motion of an object along a straight track and records its position over time.
Angular Sensor Misalignment Error
A student sets up a light sensor to measure the displacement of a robot moving along a hallway by de
Average Acceleration in Non-uniform Motion
An object’s velocity is recorded over time as shown in the table below.
Car Acceleration Analysis
A car starting from rest accelerates uniformly along a straight road. Sensors record the car’s motio
Car Acceleration and Deceleration Analysis
A car undergoes a three-phase journey. First, it accelerates uniformly from rest with an acceleratio
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
Collision Analysis: Elastic vs Inelastic Collisions
An experiment is designed using gliders on an air track to study collisions. Two types of collisions
Comparing Uniform and Non-Uniform Acceleration
Discuss the differences in the graphical representations of uniformly accelerated motion versus non-
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
Decomposing Projectile Motion into Components
A projectile is launched at an angle from the horizontal.
Designing a Motion Sensor Experiment
A team is tasked with designing an experiment to track the acceleration of a toy car along a straigh
Designing an Experiment to Measure Acceleration
You are tasked with designing a controlled experiment to measure the acceleration of an object. Cons
Determining Displacement from a Speed-Time Graph
A runner’s speed (magnitude only) was recorded over time, with the data below: | Time (s) | Speed (
Determining Instantaneous Velocity Using Video Analysis
Design an experiment that utilizes video analysis to determine the instantaneous velocity of an obje
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 in One-Dimensional Motion
A small cart travels along a straight track and its position is recorded at various times. Use the p
Distance vs. Displacement Analysis
A researcher records the motion of a runner who follows a multi-segment track. The runner starts at
Effects of Friction on Motion
A block is sliding on a horizontal surface with an initial speed of 12 m/s. Due to friction, the blo
Evaluating Air Resistance in Projectile Motion
An experiment measured projectile ranges at various launch angles. Compare the theoretical and measu
Experiment on Uniform Acceleration
A student conducts a laboratory experiment to study uniform acceleration of a cart on a track. The f
Force Vector Addition Experiment
In a laboratory setup, an object is subjected to multiple forces applied at different angles using s
Free Fall and Impact Speed
An object is dropped from a height of 80 m from rest.
Free-Fall Motion Analysis
An object is dropped from a height of 45 m. Neglect air resistance for this problem.
Friction in Inclined Plane Experiment Error
A student sets up an experiment on an inclined plane to determine the coefficient of kinetic frictio
Hiking Trail: Distance vs. Displacement
A hiker embarks on a trail that forms a loop. The hiker starts at the base camp, hikes to a lookout
Horizontal Launch from Elevated Platform
A researcher studies a projectile launched horizontally from an elevated platform. The platform is 2
Instantaneous vs. Average Speed
An object’s position as a function of time is given by $$x(t) = 2 * t^3 - 5 * t^2 + t + 10$$, with x
Interpreting a Graph with Error Bars
An experiment measures the position of a moving object over time with data points that include error
Interpreting a Visual Diagram: Position vs. Time Graph Analysis
Below is a diagram intended to represent a position vs. time graph for an object undergoing interval
Jogger's Path Analysis: Distance and Displacement
A local news article reports that a jogger's displacement during his run was equal to the total dist
Kinematics of a Decelerating Vehicle
A truck decelerates uniformly from an initial speed until it comes to a stop. Analyze the following.
Measuring Displacement in Complex Paths Using Smartphone GPS Data
Design an experiment that utilizes smartphone GPS data to measure both the total distance traveled a
Methods for Calculating Displacement
Design a controlled experiment to compare two different methods for calculating displacement: one us
Motion on an Incline: Kinematics and Friction
A ball rolls down an inclined plane and its position is recorded over time. Answer the following par
Motion on an Inclined Plane
An object slides down a frictionless inclined plane that is 5 m long and inclined at an angle of 30°
Motion with a Stopping Force and Reaction Delay
A skateboarder is moving at 6 m/s. Due to a reaction time delay of 0.5 s, no deceleration occurs dur
Multi-Phase Motion: Train Journey Analysis
A train journey consists of three distinct phases: acceleration from rest, travel at constant speed,
Navigational Vector Addition
A boat is attempting to cross a river. The boat’s engine provides a velocity of 8 m/s due north rela
Oscillatory Motion of a Mass on a Spring
A mass on a spring oscillates horizontally on a frictionless surface with a position function given
Projectile Motion Experiment Design
Design a controlled experiment to investigate the effects of launch angle on the range of a projecti
Projectile Motion in Wind
A soccer player kicks a ball with an initial speed of $$20\ m/s$$ at an angle of $$40^\circ$$ above
Projectile's Time of Flight and Range Experiment
Design an experiment to measure and analyze the relationship between a projectile's time of flight a
Race Track Analysis: Distance vs Displacement
A runner completes a race track composed of several straight segments in different directions. The r
Relative Motion Analysis of Two Objects
Two objects, A and B, are moving along the same straight line. Use the information below to analyze
River Crossing Challenge
A boat aims to cross a river that is 100 m wide by pointing directly across. However, the river has
Scalar vs. Vector Quantities
Discuss the difference between scalar and vector quantities and classify some common physical quanti
Simulated Impact Test: Speed and Velocity
In a crash simulation lab, a test vehicle decelerates from a high speed and various sensors record i
Solving Kinematic Equations with Given Data
This question involves using kinematic equations to analyze motion given experimental data. Refer to
Surface Friction Experiment: Effects on Motion
Students design an experiment to study how surface friction affects the motion of a sliding block al
Uniform Acceleration Data Analysis using Tables
A student records the following data for a toy car undergoing uniform acceleration: | Time (s) | Ve
Uniformly Accelerated Free Fall Analysis
A rock is dropped from a building and its motion is analyzed using both kinematics and a provided ve
Uniformly Accelerated Motion and BIG FIVE Equations Lab
A lab experiment involves releasing a cart from rest down a ramp to study uniformly accelerated moti
Verification of the Equation $$v = u + a*t$$
Design an experiment using a motion sensor on an inclined plane to verify the linear relationship de
Vibrational Motion and Simple Harmonic Motion (SHM) Experiment
A mass-spring system is used to investigate simple harmonic motion. The period of oscillation is rec
Video Analysis of Accelerated Motion
In this experiment, students record a toy car moving along a track using a video camera to determine
Air Track and Glider System Experiment
In an effort to study nearly frictionless motion, students use an air track with a glider and record
Analysis of a Two-Force Pulley System
In a pulley system, a 4 kg block rests on a 40° inclined plane with a kinetic friction coefficient o
Analyzing Equilibrium on an Inclined Plane
An object remains at rest on an inclined plane due to a balance of forces. A researcher explores the
Application of Newton’s Laws in Sports Dynamics: The Soccer Ball Kick
A sports science article claims that the acceleration of a soccer ball immediately after being kicke
Block on an Inclined Plane with Friction Analysis
A block of mass $$m$$ slides down an inclined plane with an angle $$\theta$$. The coefficient of kin
Chain of Collisions: Newton's Third Law and Momentum Transfer
A series of carts on a frictionless track undergo sequential elastic collisions. Cart A (mass $$m_A
Characterizing Friction on a Sloped Surface
An experiment measured the acceleration of blocks sliding down inclined planes with different coeffi
Circular Motion on a Banked Curve
A car of mass $$m$$ travels at speed $$v$$ along a banked circular road of radius $$r$$ and banking
Collision Dynamics: Elastic vs Inelastic
Examine collisions to understand the differences between elastic and inelastic interactions.
Comparing Gravitational and Inertial Mass
This question addresses the relationship and differences between gravitational mass and inertial mas
Comparing Gravitational and Inertial Mass using a Pendulum Experiment
A researcher is using a pendulum to explore the concepts of gravitational mass and inertial mass. Th
Critical Analysis of an Experiment on Air Resistance in Free Fall
A study reports that when air resistance is taken into account, the acceleration of objects in free
Designing a Multi-Factor Experiment for Vehicle Safety Dynamics
Design a comprehensive experiment to investigate how various forces (such as friction, tension, and
Designing a Pulley System to Study Accelerated Motion
Develop an experimental design using an Atwood machine (a pulley system with two masses) to measure
Determining Net Force on an Object on a Rough Incline
An object of mass $$5\,\text{kg}$$ rests on a rough incline. A researcher analyzes the forces acting
Dynamic Equilibrium on a Rotating Platform
A person stands on a rotating platform and remains stationary relative to it. The person is located
Dynamics Experiment 7: Frictional Force Analysis on a Horizontal Surface
A student conducts an experiment to determine the kinetic friction acting on a cart sliding across a
Dynamics Experiment 19: Skater Motion on a Tilted Surface
A student analyzes the dynamics of a skater gliding on a tilted surface using motion sensors to meas
Dynamics FRQ #1: Net Force and Acceleration Analysis
A block on a frictionless surface of mass 5.0 kg is acted upon by two horizontal forces. A force of
Dynamics FRQ #6: Circular Motion on a Banked Curve
A car of mass 1500 kg is rounding a frictionless banked curve of radius 50 m. The curve is banked at
Dynamics FRQ #8: Friction on a Rough Surface
A 10.0 kg block slides on a horizontal surface. A constant 30 N force is applied, while the coeffici
Dynamics FRQ #9: Newton's Third Law in Action
Two ice skaters are initially at rest on frictionless ice and push off against each other. Skater A
Dynamics FRQ #14: Rotational Equilibrium on a See-Saw
A uniform see-saw 4.0 m long and weighing 20 kg is pivoted at its center. Child A, weighing 30 kg, s
Dynamics FRQ #16: Terminal Velocity with Air Resistance
A skydiver of mass 70 kg experiences an air resistance force proportional to velocity given by $$F_{
Dynamics of a Block on an Incline with Applied Force
An experiment investigates the motion of a block on an inclined plane while an additional force is a
Dynamics of a Ladder Against a Wall
A ladder of length $$L = 4 * m$$ leans against a frictionless wall and rests on a rough ground with
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 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 Connected Masses on an Incline and Pulley
A 4 kg mass is placed on a frictionless inclined plane with an angle of 25°. It is connected by a li
Dynamics of Linked Blocks on a Frictional Surface
Two blocks, A and B, with masses 3 kg and 5 kg respectively, are connected by a light rope and pulle
Dynamics Problem 6: Circular Motion and Friction
A car is negotiating a flat circular curve of radius $$r = 20\ m$$. The coefficient of static fricti
Effect of Changing Mass on a Rotating Platform Dynamics
A person stands on a frictionless rotating platform holding weights. Initially, with the weights hel
Effects of Air Resistance in Projectile Motion
Examine how air resistance affects projectile motion by modifying the standard equations of motion.
Evaluating Frictional Force Variations in a Lab Experiment
An experimental report investigates frictional forces for different materials sliding over a surface
Forces in a Two-Box Pulley System
Investigate the forces acting in a two-box pulley system and derive the acceleration of the system.
Friction and Motion Experiment
A car of mass $$m$$ decelerates on a roadway due to kinetic friction. The experiment measures the ca
FRQ1: Dynamics on a Frictionless Track
In an experiment, a cart is pushed along a frictionless track with varying net forces. Analyze the d
FRQ17: Suspended Mass Dynamics under Horizontal Forces
In an experiment, a suspended mass is subjected to varying horizontal forces. The resulting horizont
Gravitational and Inertial Mass Comparison Experiment
A researcher aims to compare gravitational mass and inertial mass using two different experimental s
Impact of Varying Mass on Acceleration
Two carts move along a frictionless track. One cart has mass $$m$$, and the other has a slightly inc
Impulse and Momentum in Collisions
During collisions, the impulse delivered to an object is closely related to its change in momentum.
Investigating Inertia on an Air Track
An experiment is set up on an air track to minimize friction and test Newton's first law (inertia).
Investigating Motion on an Inclined Plane
A student studies a frictionless object's acceleration on an inclined plane by measuring acceleratio
Mass Distribution and Acceleration
A cart with an adjustable mass distribution is used to study how the location of added mass affects
Measuring Frictional Forces on a Horizontal Surface
A block of mass $$8 ~kg$$ is pulled across a horizontal surface by a force sensor. The applied force
Motion on an Inclined Plane
A block of mass $$m$$ is placed on a frictional inclined plane with an angle $$\theta$$. Analyze the
Motion on an Inclined Plane
A block is placed on a frictionless inclined plane that makes an angle $$\theta$$ with the horizonta
Multiple Forces on an Inclined Plane
A 10 kg block slides down a 30° inclined plane with a coefficient of kinetic friction of 0.2. Analyz
Newton's Third Law: Analysis of Action-Reaction Forces
A collision experiment is conducted where two objects interact over a short interval of time. A grap
Newton's Third Law: Collision Analysis
Two objects, A and B, collide on a frictionless surface. Analyze the forces during the collision to
Pendulum Dynamics in a Non-Inertial Frame: A Moving Train Study
A researcher claims that observations of a pendulum inside a moving train (a non-inertial reference
Pendulum Experiment for Gravitational Acceleration
A student sets up a pendulum with a long string and heavy bob to measure the gravitational accelerat
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 with Air Resistance Idealization
A projectile is launched with an initial speed $$v_0 = 20 * m/s$$ at an angle $$\theta = 30°$$ above
Rotational-Translational Dynamics in a Rolling Cylinder
A student investigates a cylinder rolling down an inclined plane without slipping. The experiment in
Static Friction and Threshold of Motion
A 5 kg block on a horizontal surface is gradually pushed until it starts to move. The minimum force
Static vs. Kinetic Friction Experiment
Investigate the differences between static and kinetic friction through definitions, experimental da
Tension and Pulley Systems
A 5 kg block on a frictionless horizontal surface is attached to a string that goes over a pulley an
Translational and Rotational Dynamics in Rolling Motion
Examine the dynamics of rolling motion by differentiating between translational and rotational compo
Analysis of a Rotating Space Station for Artificial Gravity
A proposed rotating space station creates artificial gravity on its inner surface by rotating as a c
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
Banked Curve Dynamics
A car negotiates a banked curve with a 30° incline and a radius of 100 m. Answer the following:
Calculation of Gravitational Acceleration on a Different Planet
A probe lands on a small planet and records the following parameters: mass of the planet is $$5.0 \t
Centripetal Force in a Banked Curve
A car rounds a banked curve where the road is inclined at a certain angle, and friction is negligibl
Charged Particle in Circular Orbit
A stationary charged sphere with charge $$Q = 5.0 \times 10^{-6} \;C$$ is fixed at the center of a f
Comparative Analysis of Gravitational Acceleration on Different Planets
A table provides the mass and radius for two different planets. Use these data to analyze the gravit
Comparative Analysis of Gravitational Acceleration on Different Planets
This problem examines how planetary mass and radius affect surface gravitational acceleration.
Comparing Gravitational and Electric Force Effects
A series of experiments compare the magnitudes of gravitational and electric forces between pairs of
Comparing Observed and Predicted Acceleration in Circular Motion
In an experiment, the observed centripetal acceleration was compared with the theoretical prediction
Comparing Orbital Motion with Circular Motion on Earth
A comparative study has compiled data from satellites in orbit and vehicles navigating circular test
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
Determining Angular Speed from Tangential Speed
A rotating disc has a marked point on its edge, and its tangential speed is measured directly. Use t
Electric Force Measurement in Circular Motion Setup
A student designs an experiment in which a charged particle is directed into a circular path by elec
Electric Force: Experimental Measurement Analysis
This problem requires analysis of experimental data to verify Coulomb's Law through measured electri
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
Escape Velocity Derivation
A satellite must achieve escape velocity to break free from a planet’s gravitational field. Using en
Free-Body Diagram and Force Analysis for Circular Motion
A 1 kg mass is whirled on a horizontal table in a circular path by a string attached to a fixed pivo
Graphical Analysis of Angular Motion
A graph showing angular displacement $$\theta$$ (in radians) versus time $$t$$ (in seconds) for an o
Investigating Free Fall using Sensor Data
An object is dropped in a vacuum chamber and its displacement is recorded over time using a high-spe
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
Measuring Gravitational Acceleration Variation on Earth's Surface
An experiment was conducted in a mountainous region to measure gravitational acceleration at various
Orbital Mechanical Energy Analysis
An object in a circular orbit around a planet has both kinetic energy and gravitational potential en
Satellite Orbital Motion: Gravitational and Centripetal Force
A satellite orbits the Earth in a circular path. In such an orbit, the gravitational force provides
Spring-Connected Particle in Circular Motion
A particle of mass m is attached to a spring (with spring constant k and natural length \(L_0\)) tha
Tension in a Rotating System: Analysis of Centripetal Force
A student investigates the role of tension in a string as the provider of centripetal force in a rot
Transition from Circular to Projectile Motion
This problem investigates the transition of motion from uniform circular to projectile motion when t
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
Analyzing Work Against Friction with an Angled Force
A 4 kg block on a horizontal surface with a kinetic friction coefficient $$\mu_k = 0.25$$ is pushed
Calculating Kinetic Energy Change from Work
A 3 kg cart initially moves at 2 m/s and experiences a net work of 50 J. Answer the following:
Determination of Engine Power in a Towing Experiment
A student sets up an experiment to calculate the power output of an engine towing a sled. The appara
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 Work of Friction in a Sled on Snow
A 15 kg sled is sliding on snow with a coefficient of kinetic friction of 0.1. The sled slows from 4
Efficiency Analysis of a Mechanical System
A machine requires an input energy of $$5000\;J$$ and produces a work output of $$3200\;J$$. Calcula
Efficiency Analysis of an Electric Motor
An electric motor is tested for its efficiency in converting electrical energy into mechanical work.
Energy Transfers in a Bungee Jump
A bungee jumper with a mass of $$70\,kg$$ jumps from a bridge $$50\,m$$ above the river and reaches
Energy Transformation in a Multi-stage Process
A 5 kg block is dropped from a height of 8 m onto a spring with a force constant $$k = 200\,N/m$$. T
Evaluating Mechanical Advantage in a Pulley System
A pulley system is used to lift a 100 kg load. The system requires an applied force of $$150 N$$ ove
Exploring Conservation of Mechanical Energy in Bouncing Ball Dynamics
A ball is dropped from a set height and allowed to bounce multiple times on a hard surface. The peak
Exploring the Relation Between Power Output and Time in Lifting Tasks
Design an experiment to explore how power output varies during the lifting of weights. Power is defi
Exploring the Relationship Between Force, Work, and Time in Athletic Performance
An athlete pushes a sled with a time-varying force given by $$F(t)= 100 - 5 * t$$ (in N) for t from
Frictional Work Analysis on a Moving Block
A researcher pushes a 2 kg block on a rough horizontal surface. The block has an initial speed of $$
Interpreting a Work-Energy Graph
Examine the following graph which plots the kinetic energy (KE) of an object versus its displacement
Investigating Kinetic Energy Change in Collisions
Two carts on a frictionless track collide inelastically. Cart 1 (2 kg) is moving at 4 m/s, and Cart
Lifting a Dumbbell at an Angle
A person lifts a 10 kg dumbbell from the floor by applying a force at an angle of 30° above the hori
Measurement of Work Done by Frictional Forces
A block traveling on a rough horizontal track comes to a stop due to friction. The initial kinetic e
Mechanical Energy Conservation on an Inclined Plane
A skateboarder starts from rest at the top of a frictionless ramp of height $$3.0\,m$$. Using the gr
Mechanical Energy in a Bouncing Ball
A ball with a mass of $$0.2\;kg$$ is dropped from a height of $$2\;m$$. On the first bounce, it reac
Timing Error in Motor Power Experiment
In this experiment, a student measures the power output of a motor by timing how long it takes to mo
Variable Force from a Graph
A force acting on an object varies with displacement as shown in the graph below. Using the graph, d
Work and Efficiency in a Pulley System
A researcher experiments with a pulley system used to lift a mass. A 10 kg mass is lifted vertically
Work and Power in a Lifting Scenario
A person lifts a 50 kg weight vertically by 2 m in 5 seconds. Answer the following:
Work Done Along Different Paths
A cart is moved from point A to point B by applying a constant force of 50 N. Two paths are availabl
Work Done by Variable Forces
A variable force is applied to an object as it moves along a straight line. The force as a function
Work Done on an Inclined Plane
A 10 kg sled is pulled up a frictionless hill along its surface for 20 m. The hill is inclined at 25
Work Done with an Angled Force
A worker applies a force to move a crate along a horizontal surface in two different scenarios. Refe
Work Measurement Under Non-Uniform Acceleration
In this experiment, a student measures the work done on a cart that accelerates along a track. A for
2D Collision Analysis in a Skate Park
Two skateboarders collide at an intersection in a skate park. Skateboarder A (mass $$50\,kg$$) is mo
Analysis of Elastic Collision Using Graph Data
A high-speed camera records the velocities of two objects involved in an elastic collision. The grap
Automotive Crumple Zone Analysis
Engineers are analyzing the performance of crumple zones in automobiles during collisions. A car of
Basic Momentum and Impulse Calculation
A 1500 kg car is moving to the right with a velocity of $$20\,\text{m/s}$$. Answer the following:
Basic Momentum Calculation
A 5 kg object is moving to the right with a velocity of 3 m/s. Part (a): Calculate the object's mome
Basic Momentum Calculation
This problem introduces the concept of momentum. Answer the following: (a) In your own words, define
Collision Analysis: Conservation of Momentum
In a collision experiment, two carts on a frictionless track are recorded. The following table provi
Comparative Analysis of Elastic and Inelastic Collisions
An experiment is set up to compare elastic and inelastic collisions using two carts. Answer the foll
Comparative Impulse Analysis
Two collision scenarios are conducted in a laboratory: Scenario A: A constant average force of 2000
Data Analysis of Collision from Velocity Graph
The velocity vs. time graph for Glider A during a collision on an air track is provided. Assume Glid
Data Analysis of Elastic versus Inelastic Collisions
A series of collision experiments were performed and the momentum values before and after collisions
Elastic Collision Analysis
A researcher investigates an elastic collision between two gliders on an air track. The experiment t
Experimental Design: Effect of Mass on Momentum
Design an experiment to investigate the hypothesis that, for a constant velocity, increasing the mas
Explosive Separation in a Projectile
A projectile of total mass 5.0 kg explodes mid-air into two fragments. One fragment has a mass of 3.
Force-Time Graph Analysis for Impulse
A force–time graph for a hammer striking a nail is provided. The contact time is $$0.05\,s$$ and the
Hockey Puck Collision with a Wall
A 0.16 kg hockey puck is sliding on ice at 15 m/s, approaching a frictionless wall at an angle of 30
Impulse from a Time-Dependent Force
An object experiences a force that varies with time according to the equation $$F(t) = 4000 - 500 \t
Impulse in Non-collisional Interactions
An experiment uses a fluid jet that impinges on a paddle wheel, generating an impulse that rotates t
Inelastic Collision Investigation
A researcher observes an inelastic collision in which two vehicles collide and stick together. The e
Mid-air Collision Analysis
Two gymnasts collide mid-air and stick together. Gymnast A has a mass of $$55$$ kg and is moving at
Momentum and Safety Design in Car Crashes
Modern cars use design features like airbags and crumple zones to manage the impulse experienced dur
Momentum in Collisions Experiment
In a lab, two carts on an air track collide. The experiment aims to verify the conservation of momen
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
Oblique Collision in Billiards
In a game of billiards, a cue ball of mass $$0.17\,\text{kg}$$ traveling at $$2\,\text{m/s}$$ strike
Rebounding Ball Momentum Change
A ball of mass $$0.5\,kg$$ moving at $$3.0\,m/s$$ strikes a wall perpendicularly and rebounds with t
Rocket Propulsion and Momentum Conservation
A small rocket engine expels fuel to generate thrust, demonstrating momentum conservation in rocket
Soccer Kick: Impulse and Momentum
A soccer player kicks a ball, applying a variable force over the period of contact. A force-versus-t
Two-Body Collision Analysis
Two vehicles collide at an intersection. Vehicle A (mass 1200 kg) is traveling east at 15.0 m/s and
Understanding Momentum in Car Crash Reconstruction
In accident reconstruction, conservation of momentum is a key principle. Consider two vehicles: Car
Analyzing Energy Exchange in a Pendulum
A simple pendulum swinging with small amplitude exhibits SHM-like behavior. Answer the following:
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
Analyzing SHM Data to Determine Angular Frequency
A researcher collects data on the oscillation period for a mass-spring system with different masses
Calculation Error in Determining Angular Frequency
A student sets up an experiment to measure the angular frequency (ω) of a mass-spring oscillator by
Comparing Amplitude Effects
Two identical mass-spring systems oscillate with different amplitudes: System 1 has $$A_1 = 0.10 m$$
Effect of Amplitude on Force in SHM
Examine the relationship between amplitude and the restoring force in a mass-spring oscillator.
Effect of Mass on Angular Frequency in SHM
In a series of experiments on a mass-spring oscillator, the angular frequency was measured for diffe
Effect of Mass Variation on Oscillation Parameters
An investigation is conducted in which the mass attached to a spring in an SHM system is varied, whi
Energy Conservation Verification in a Spring-Mass System
A researcher tests the conservation of mechanical energy in a spring-mass system undergoing SHM. (a
Energy Distribution in SHM
A researcher investigates how kinetic and potential energy vary during SHM in a mass-spring system.
Energy Loss Mechanisms in SHM
Discuss the mechanisms of energy loss in a system undergoing simple harmonic motion and propose a me
Energy Partition in SHM
In a mass-spring system undergoing SHM, the kinetic energy $$K$$ and potential energy $$U$$ change a
Energy Transformation in SHM
In a mass-spring system undergoing SHM, the total mechanical energy is conserved and is partitioned
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
Graphical Estimation of SHM Parameters
A researcher obtains a graph of angular displacement versus time for a pendulum. The following graph
Mass-Spring Oscillator Analysis
A researcher studies a mass attached to a spring on a frictionless surface exhibiting simple harmoni
Mathematical Derivation in SHM
Derive the second-order differential equation governing the motion of a mass-spring system in SHM. A
Measurement of the Spring Constant via SHM Data
An experiment is designed to determine the spring constant, k, of a spring using a mass-spring syste
Non-Ideal Oscillations: Driven Harmonic Motion
A mass-spring oscillator is subjected to an external periodic force, resulting in driven harmonic mo
Pendulum Period and Length Determination
A simple pendulum consists of a small bob attached to a string of length $$L$$. (a) Write the expre
Pendulum Period Calculation
A simple pendulum in a clock tower has a length L = 2.5 m. Answer the following: (a) Derive the expr
Pendulum Small Angle Analysis
For a simple pendulum, answer the following: (a) Derive the expression for the period $$T=2π*\sqrt{L
Spring Constant Variation and Oscillation Frequency
Examine how variations in the spring constant affect the oscillation frequency of a mass-spring syst
Synchronization of Coupled Oscillators
Consider two masses connected by springs that are coupled, leading to synchronized oscillations. Ana
Analysis of Rotational Equilibrium on a Seesaw
A seesaw is in rotational equilibrium. A weight of 20 N is placed 1.0 m from the pivot on one side.
Angular Displacement from Arc Length Measurements
A small robot moves along a curved path that is part of a circle with a radius of $$r = 0.5\,m$$. It
Angular Kinematics Analysis
A rotating wheel starts from rest and undergoes constant angular acceleration. Use the data provided
Angular Kinematics Analysis: Table Data
A researcher collected data for a rotating turntable's angular displacement over 10 s. The data are
Center of Mass Calculation of a Two-Object System
A researcher is analyzing a system composed of two masses on a lightweight rod. Mass $$m_1 = 3.0\;kg
Coupled Rotational Systems and Energy Dissipation
Two discs are coupled via friction. Disc A has a moment of inertia of 3 kg*m² and is spinning at 12
Cylindrical Rod Angular Acceleration Experiment Error
A student conducts an experiment to measure the angular acceleration of a cylindrical rod pivoted at
Designing a Rotational Motion Experiment
Design an experiment to measure the moment of inertia of a solid cylinder. Outline the experimental
Effect of Mass Distribution on Moment of Inertia
Two discs with the same mass and radius but different mass distributions (a solid disc versus a ring
Energy Analysis of a Spinning Disc
A flat, circular disc in an industrial machine accelerates from rest to 100 rad/s in 10 seconds. Its
Energy Conversion in a Flywheel System
A flywheel with a moment of inertia $$I = 0.3 \;kg\cdot m^2$$ rotates at an angular velocity of $$\o
Evaluating Angular Displacement with Variable Acceleration
In an experiment using a rotating platform, the angular acceleration is not constant. Researchers cl
Experimental Investigation of Frictional Torque
A rotating wheel is observed to slow down over time due to frictional torque. This experiment aims t
Gyroscopic Precession Experiment Error
A student conducts an experiment on gyroscopic precession using a spinning top. The top is subjected
Impact of Body Position on Rotational Speed in Diving
A diver alters her body position during a dive, reducing her moment of inertia. Analyze how this cha
Influence of External Friction on Angular Acceleration
A student claims that increasing friction at the pivot of a rotating system significantly reduces it
Merry-Go-Round Rotation Measurement Error
A student analyzes the rotational motion of a merry-go-round by measuring its angular displacement a
Rolling Cylinder Angular Acceleration Measurement Error
A student investigates the acceleration of a rolling cylinder down an inclined plane. The experiment
Rotational Motion in Automotive Dynamics
A car is traveling at a constant speed, and its wheels are in rotational motion. Using the given par
Rotational Motion with Variable Angular Acceleration
A rotating object has an angular acceleration given by $$\alpha(t) = 0.2 * t \text{ rad/s}^2$$, with
Static Equilibrium in a Rotational System
A seesaw is used to study static rotational equilibrium. Two children of different masses sit on opp
Torque and Lever Arm in Rigid Body Rotation
A rigid bar rotates about a fixed pivot. Two forces act on it: a 50 N force applied 2 m from the piv
Using Video Analysis for Rotational Measurements
Design an experiment that utilizes video analysis to measure the rotational motion of an object. You
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