AP Physics 1: Algebra-Based FRQ Room

Acceleration Analysis in Uniform and Non-uniform Motion

A group of students records the motion of a toy car that initially starts from rest, accelerates uni

Analysis of a Velocity vs. Time Graph (Non-Uniform Acceleration)

Examine the velocity vs. time graph provided and answer the following questions about the object's m

Analyzing Position Data: Average Speed and Acceleration

A particle’s position is recorded over time as given in the table below. Use the data to determine t

Analyzing the Relationship Between Angle of Projection and Range in Projectile Motion

Design an experiment to determine how the angle of projection affects the range of a projectile. You

Analyzing Variable Acceleration

An object's velocity is measured at different times as shown below. Use the data to analyze the acce

Angled Motion and Range Calculation

A projectile is launched from a horizontal platform with an initial speed of $$25\ m/s$$ at an angle

Assessing Measurement Errors in Kinematic Graphs

During an experiment, a student recorded the position of a moving object over time. However, due to

Average Speed vs. Average Velocity from a Position-Time Table

Below is a table of an object’s position over time. Use the data to analyze the object's motion.

Average Speed vs. Average Velocity on a Circular Track

This question investigates the difference between average speed and average velocity. Consider a car

Baseball Projectile Motion

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

Car Acceleration and Deceleration

A car starts from rest, accelerates uniformly, travels at a constant speed, and then decelerates uni

Car Acceleration and Deceleration Analysis

A car undergoes a three-phase journey. First, it accelerates uniformly from rest with an acceleratio

Comparative Analysis of Distance vs. Displacement on a Winding Path

An object is set to traverse a course that includes various curves and turns. Design an experiment w

Comparing Scalar and Vector Descriptions in Motion

A delivery drone follows a route consisting of four segments: 2 km east, 3 km north, 2 km west, and

Comparing Scalar and Vector Quantities

An experiment records both the scalar speed and the vector velocity of an object during several tria

Comparing Speed and Velocity in a Track Experiment

In this field experiment, runners’ motions on a curved track are recorded using GPS sensors. The pro

Critical Analysis: Acceleration Measurements under Free Fall

In a free fall experiment, objects are dropped from a known height and their fall times are recorded

Data Sampling Error in Velocity Determination

A student uses a digital motion sensor to collect data on an object’s velocity while it accelerates

Deriving the Relationships Among the BIG FIVE Equations

Derive one of the kinematic equations used in uniformly accelerated motion. Answer the following ste

Designing a Motion Sensor Experiment

A team is tasked with designing an experiment to track the acceleration of a toy car along a straigh

Determining Acceleration in a Free Fall Drop Experiment

In a school laboratory drop experiment, the following data was recorded: | Height (m) | Time (s) |

Determining Instantaneous Velocity Using Video Analysis

Design an experiment that utilizes video analysis to determine the instantaneous velocity of an obje

Determining Kinematic Quantities from Graph Data

A motion sensor experiment simultaneously records position, velocity, and acceleration graphs for an

Determining the Acceleration Due to Gravity Using a Free-Fall Apparatus

In this experiment, students drop a ball from a known height and measure the fall time to calculate

Distance and Displacement Analysis Experiment

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

Effect of Launch Angle on Maximum Height

Develop an experiment to determine how varying the launch angle of a projectile affects its maximum

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 Vector Component Effects in Projectile Motion

A ball is launched with an initial velocity of $$15 \; m/s$$ at an angle of $$40^\circ$$ above the h

Experimental Data: Analyzing Speed and Velocity Graphs

A graph representing speed versus time for an object is given by the equation $$s(t) = 5*t+2$$. Anal

Free-Fall Motion Analysis

An object is dropped from a height of 45 m. Neglect air resistance for this problem.

Free-Fall vs. Projectile Motion: Impact of Launch Angle

Two objects are launched from the same height with identical initial speeds of 20 m/s but at differe

Graphical Analysis: Position, Velocity, and Acceleration

A researcher collects data on an object's motion and produces three graphs: a Position vs. Time grap

Horizontal Launch from Elevated Platform

A researcher studies a projectile launched horizontally from an elevated platform. The platform is 2

Inclined Plane Friction Analysis Error

A student sets out to determine the coefficient of kinetic friction by measuring the acceleration of

Interpreting Velocity-Time Graph with Non-Uniform Acceleration

Examine the following velocity vs time graph which represents non-uniform acceleration (the graph is

Investigating Circular Motion: Displacement vs. Distance

An object moves along a circular track. The experiment is designed to measure both the total distanc

Momentum and Impulse Error

A student conducts a collision experiment with two carts on a frictionless track to study momentum c

Motion Analysis: Cart on an Inclined Track

A researcher studies a cart moving on an inclined track. The experimental data is summarized in the

Motion on an Inclined Plane

A ball starts from rest and rolls down a smooth inclined plane of length $$10 \text{ m}$$ with a uni

Motion on an Inclined Plane: Calculating Acceleration and Displacement

A ball is released from rest at the top of an inclined plane. A researcher measures the time taken a

Motion with Reaction Time Delay

A sprinter has a reaction delay of 0.2 s. After the delay, he accelerates uniformly from rest at $$a

Multi-Phase Journey: Car Navigation

A researcher tracks a car that moves in two segments: first, 120 m east; then, 160 m north. Answer t

Non-uniform Acceleration Analysis

An experiment records the motion of an object experiencing non-uniform acceleration. The velocity vs

Pendulum Experiment to Measure Gravity

A researcher uses a simple pendulum to determine the acceleration due to gravity. Small swing angles

Pendulum Period Measurement Error

In an experiment to determine gravitational acceleration using a simple pendulum, a student records

Position vs Time Graph: Velocity Analysis

Examine the provided Position vs. Time graph to evaluate various aspects of the object's motion.

Projectile Motion Analysis

A ball is launched at an angle of $$30^\circ$$ above the horizontal with an initial speed of $$20\ m

Projectile Motion: Angle Dependence

A projectile is launched with an initial speed of $$25 \text{ m/s}$$ at an angle $$\theta$$ above th

Radio Control Car Motion Analysis

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

Relative Motion in Parallel Tracks

A researcher analyzes the relative motion of two trains moving on parallel tracks. Train A travels e

Relative Motion of Two Cyclists

Two cyclists start from the same location but travel in perpendicular directions. Analyze their rela

River Navigation: Vector Addition and Resultant Displacement

A boat is attempting to cross a river. Its speed relative to the water is 5 m/s heading due north, w

Runner's Route Analysis: Distance vs. Displacement

A runner follows a specific route as shown in the provided diagram. Starting at point A, the runner

Scalars vs. Vectors: Identifying Quantities

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

Surface Friction Experiment: Effects on Motion

Students design an experiment to study how surface friction affects the motion of a sliding block al

Transition from Uniform to Non-Uniform Acceleration

Design an experiment to investigate the conditions under which an object transitions from uniform to

Uniform Acceleration Analysis Using BIG FIVE Equations

A car starting from rest accelerates uniformly. Data for a trial is provided below. Use the provided

Uniform Acceleration with Variable Initial Velocities

Two vehicles start moving with different initial velocities but share the same constant acceleration

Uniformly Accelerated Motion with the BIG FIVE Equations

This question requires you to apply the BIG FIVE equations of motion to analyze uniformly accelerate

Uniformly Accelerated Motion: Car Scenario

A car starting from rest accelerates uniformly. Using the BIG FIVE kinematic equations, answer the f

Vector Addition and Subtraction in Motion

A student is studying the effect of multiple displacement vectors on the overall movement of an obje

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

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

Analyzing Forces in a Multi-Directional Collision

Two objects collide at an angle, causing forces to act in multiple directions. A researcher is taske

Analyzing Impulse in a Collision

During a collision experiment, the force exerted as a function of time is recorded, and the graph be

Analyzing Net Force vs. Acceleration Graph

A lab experiment records various net force values acting on an object along with its resulting accel

Applied Force Direction and Acceleration

Design an experiment to investigate how the angle at which a force is applied affects the accelerati

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

Center of Mass and Tipping Point Experiment

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

Characterizing Friction on a Sloped Surface

An experiment measured the acceleration of blocks sliding down inclined planes with different coeffi

Circular Motion and Centripetal Force

A small mass of 0.2 kg is attached to a string and rotated in a horizontal circle of radius 0.5 m at

Collision Dynamics: Elastic vs Inelastic

Examine collisions to understand the differences between elastic and inelastic interactions.

Comparing Free-Body Diagrams of Different Systems

Consider three scenarios: a stationary car on a hill, an elevator accelerating upward, and a rocket

Comprehensive Analysis of Force Equilibrium in a Bridge Model

A model bridge is constructed with various supports and struts. Force sensors are attached to measur

Dynamic Response of a Spring-Connected Mass System

A mass $$m$$ is attached to a spring with a spring constant $$k$$ and is displaced by a distance $$x

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 12: Circular Motion and Centripetal Force

A student sets up an experiment to measure the centripetal force by rotating a mass attached to a st

Dynamics FRQ #17: Two-Block Spring System

Two blocks of masses 2.0 kg and 3.0 kg are connected by a light spring with a spring constant of 200

Dynamics in Non-Inertial Frames

Study the behavior of objects observed from non-inertial reference frames.

Dynamics of a Car with Air Resistance

A car of mass 1000 kg accelerates from rest under a constant engine force of 3000 N. In addition, it

Dynamics of a Cart on a Frictional Track

In a laboratory experiment, a researcher uses a cart moving on a horizontal track to study the relat

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 Sports Car: Acceleration and Friction

A sports car with a mass of $$m = 1500 * kg$$ is designed to accelerate from rest to $$30 * m/s$$ in

Dynamics of Circular Motion

A car with a mass of 1500 kg is navigating a flat, circular curve with a radius of 50 m. The car tra

Dynamics Problem 15: Equilibrium and Net Force

A horizontal beam is held in static equilibrium by several forces acting on it. The forces include a

Equilibrium in a Loaded Beam System

A uniform beam of length 10 m is supported at both ends. A 200 N weight is placed 3 m from the left

Equilibrium on an Inclined Plane with Static Friction

A block rests on an inclined plane which makes an angle \(\theta\) with the horizontal. The block is

Experimental Design for Measuring Inertial Mass

Propose an experiment to measure the inertial mass of various objects using a force sensor and a mot

Exploring the Limits of Newton’s Laws

Newton's laws work well under many conditions but have limitations.

Friction and Motion Experiment

A car of mass $$m$$ decelerates on a roadway due to kinetic friction. The experiment measures the ca

Friction on a Horizontal Surface

A 10 kg block is pushed along a horizontal surface. An applied force of $$30\ \text{N}$$ acts on the

FRQ5: Dynamics on an Inclined Plane

A cart is allowed to slide down a nearly frictionless inclined plane at varying angles. Study the da

FRQ7: Pulley System Dynamics with Tension

In a two-mass pulley system, acceleration measurements were taken for different mass configurations.

FRQ14: Reaction Forces in Collisions

During collision experiments between carts, force sensors measured the forces acting on each cart. A

Impulse and Momentum in Collisions

During collisions, the impulse delivered to an object is closely related to its change in momentum.

Inclined Plane Experiment: Investigating Frictional Forces

A group of students claims that the coefficient of static friction for a wood block on an inclined p

Investigating Inertial Mass through Force Application Experiments

A student runs an experiment to measure inertial mass by applying different known forces to an objec

Investigating Newton's Third Law through Collision Forces

In an experiment, two objects collide and sensors record the forces experienced by each object over

Investigating Variable Mass in Rocket Propulsion

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

Lunar Rocket Dynamics

A rocket on the Moon (where $$g_{moon} = 1.62\; m/s^2$$) has a mass of 500.0 kg and is propelled upw

Measuring Gravitational vs. Inertial Mass Experiment

Design an experiment to demonstrate the equivalence of gravitational mass and inertial mass.

Motion on a Frictionless Surface

A block of mass $$m$$ rests on a frictionless horizontal surface. Initially, it is at rest. A small

Net Force Analysis with Multiple Forces

An object of mass $$m$$ is subjected to three forces: $$F_1 = 10\ \text{N}$$ east, $$F_2 = 5\ \text{

Newton’s Law of Acceleration in Varying Media

A projectile is fired horizontally through air and then enters a denser medium.

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 Dynamics and Torque Equilibrium

A lever is in equilibrium with forces applied at various distances from the pivot. The provided diag

Suspended Object and Tension Analysis

An object of mass $$m = 10.0\; kg$$ is suspended by two ropes fastened to the ceiling. The two ropes

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 Force Analysis in a Pulley System

A researcher investigates a system of two masses connected by a string over a frictionless pulley, w

Torque and Rotational Equilibrium

A uniform beam with a length of 10 m and a mass of 20 kg is hinged at one end. It is maintained in e

Translational and Rotational Dynamics in Rolling Motion

Examine the dynamics of rolling motion by differentiating between translational and rotational compo

Analyzing Satellite Motion

A space agency collects data on satellite orbital parameters. The data table shows the orbital radiu

Analyzing Tension Forces in a Swinging Bucket

A bucket attached to a rope is swung in a vertical circle. The tension in the rope varies at differe

Analyzing Variations in Centripetal Acceleration with Changing Speed

This problem requires you to examine how centripetal acceleration varies with speed for an object in

Calculating Centripetal Force in a Rotating Space Station

A rotating space station is designed to simulate Earth-like gravity by providing centripetal acceler

Comparative Analysis: Gravitational Force vs Electric Force

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

Designing a Lab Experiment on Centripetal Force

In this problem, you will outline a laboratory experiment to measure centripetal force.

Effect of Friction in Circular Motion

A car with a mass of $$1000 \;kg$$ navigates a flat circular track. The friction between the tires a

Evaluating Centripetal Force in a Car Turning a Curve

A study on car dynamics on curved roads provided data on car speeds, curve radii, and the correspond

Evaluating the Limitations of the Uniform Circular Motion Model

Uniform circular motion models assume constant speed and neglect external disturbances. (a) List and

Experimental Validation of Gravitational Law

Free-fall experiments were conducted at various altitudes to measure gravitational acceleration. The

Force Analysis in a Banked Curve

This problem involves analyzing the forces acting on a vehicle negotiating a banked curve, where an

Orbit Simulation: Satellite Motion and Gravitational Force

Design a simulation-based experiment to study how the orbital period of a satellite changes with its

Orbital Period Analysis of a Moon

A small moon orbits a planet in a nearly circular orbit. The gravitational force provides the centri

Orbital Speed Variation in Circular Orbits

A student uses a computer simulation to study the orbital speeds of satellites in circular orbits ar

Planetary Orbital Period Comparison

Consider two planets orbiting the same star. Using Newton’s law of universal gravitation and circula

Radius Change and its Effect on Centripetal Acceleration

A car travels at a constant speed of 20 m/s around a circular track. Answer the following:

Rotational Dynamics of a Car on a Circular Track

A student simulates the motion of a car on a circular track to study centripetal force and friction.

Tangential Speed and Centripetal Acceleration Analysis

A student sets up an experiment to investigate the relationship between tangential speed and centrip

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

Theoretical Analysis of a Particle in a Circular Orbit under Electric Force

Consider a particle of mass $$m$$ and charge $$q$$ moving in a circular orbit under the influence of

Uniform Circular Motion in a Conical Pendulum

A conical pendulum consists of a mass attached to a string that rotates in a horizontal circle, form

Analysis of Energy in a Rolling Cylinder

A student performs an experiment in which a cylinder rolls down an inclined plane without slipping.

Analyzing Power Output in an Electric Motor

Review the experimental data for an electric motor under varying loads. Analyze the effect on work d

Bungee Jump Energy Conservation Analysis

A researcher studies the mechanics of a bungee jump. A jumper with mass $$m = 70 \; kg$$ jumps from

Calculating Power Output in a Weight-Lifting Activity

A weightlifter lifts a 50 kg weight vertically by 2 m in 5 seconds. Answer the following questions:

Calculating Work at an Angle

A sled is pulled along a horizontal surface by a rope that makes an angle of 40° with the horizontal

Calculating Work on an Inclined Surface

A 10 kg box is pushed up a frictionless ramp inclined at 30° to the horizontal using a constant forc

Comparative Analysis of Work in Different Force Directions

A researcher pushes two identical boxes under different conditions. In Case A, the force is applied

Conservation of Mechanical Energy in a Roller Coaster

In a laboratory experiment, a small model roller coaster is tested on a nearly frictionless track. T

Designing an Experiment for Work and Energy Transfer

Propose a laboratory experiment to measure the work done on an object as it is moved across a surfac

Designing an Experiment to Measure the Efficiency of Energy Transfer in a Motor

You are to design an experiment to evaluate the efficiency of an electric motor in converting electr

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 Work Done by a Variable Force from Experimental Data

A researcher conducts an experiment where a variable force is applied to move an object along a stra

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 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 Conservation in a Skate Park

A skateboarder rides in a skate park, starting at the top of a ramp, descending to the bottom, and t

Energy Loss in a Bouncing Ball

A ball is dropped from a height of 10 m and bounces back to a height of 6 m. Answer all parts.

Energy Transformation in a Pendulum

A simple pendulum of length 2 m and mass 1 kg is released from an initial angle of $$30°$$ with the

Evaluating Mechanical Energy during a Bounce

Analyze the experimental data from a bouncing ball that tracks bounce height and kinetic energy at i

Experimental Data on Potential Energy Variations

Evaluate the experimental data that shows how potential energy varies with height. Analyze the data,

Experimental Validation of the Work-Energy Theorem

Review the experimental data provided to validate the work-energy theorem. Analyze the table, choose

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 Effect of Friction on Mechanical Energy Conservation

Design an experiment to investigate how friction affects the conservation of mechanical energy in a

Graphical Analysis of a Pendulum's Mechanical Energy

A pendulum is being analyzed in the laboratory. A graph plotting its kinetic energy (KE) and potenti

Interpreting a Diagram of Mechanical Energy Conservation

A diagram is provided that shows the energy transformations of a roller coaster car as it moves alon

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 in a Roller Coaster Experiment

This question involves analyzing experimental data from a roller coaster where changes in height and

Nonconservative Forces and Energy Loss

A 2 kg sled slides down a hill of height $$5 m$$. Due to friction, the sled loses energy equivalent

Power Calculation for Lifting Equipment

A lifting crane raises a $$1000\;kg$$ load vertically by $$10\;m$$ in $$20\;s$$. Calculate the work

Power Output during Lifting Exercise

Investigate the experimental data from lifting exercises where work and power output are calculated.

Power Output of an Electric Motor

An electric motor lifts a 100 kg elevator 10 m high in 20 seconds. Answer the following:

Power Output Variability in a Walking Robot

A walking robot performs cyclic motion. In one cycle, the robot does 150 J of work in 2 seconds. Ans

Projectile Mechanical Energy Analysis

A researcher launches a projectile from ground level. The projectile has a mass of $$0.5 \; kg$$ and

Studying the Relationship between Work and Thermal Energy in Frictional Heating

In this experiment a metal block is slid across a rough surface to generate heat from friction. The

Torque, Work, and Mechanical Advantage in Using a Wrench

A mechanic uses a 0.4 m long wrench to loosen a bolt. A force is applied at an angle of 60° relative

Work and Energy in a Pulley System

In a frictionless pulley system, two masses (3 kg and 5 kg) are connected by a rope. Mass 2 (5 kg) d

Work and Energy in a Solar-Powered Lift

A solar-powered lift is used to raise a platform with a mass of $$800\;kg$$ vertically by $$15\;m$$.

Work and Energy in Circular Motion

Analyze the experimental data from a vertical loop where an object's speed is recorded at different

Work and Power: Variable Force Analysis

An experiment is conducted in which a variable force is applied to an object over a displacement. Th

Work Done on an Inclined Plane Experiment

Using experimental data from pushing a box on various inclined planes, analyze how the angle of incl

Work on an Inclined Plane with Friction

A 2 kg block slides down a 30° inclined plane that is 4 m long. The coefficient of kinetic friction

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 in a Kinetic Friction Scenario

A $$2\;kg$$ block slides across a rough surface. It starts with an initial velocity of $$5\;m/s$$ an

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 Collision Experiment Analysis

In an air track experiment, a researcher studies collisions by recording the mass and velocity of a

Amusement Park Ride Collision Analysis

Two ride cars at an amusement park, each with a mass of $$500\,\text{kg}$$, are moving along the sam

Analysis of a Perfectly Inelastic Collision

Consider a 2.0 kg cart moving at 4.0 m/s that collides with a 3.0 kg cart at rest, and the two carts

Collision Analysis: Conservation of Momentum

In a collision experiment, two carts on a frictionless track are recorded. The following table provi

Elastic Collision Analysis

A researcher investigates an elastic collision between two gliders on an air track. The experiment t

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

Exploring the Limits of Momentum Conservation

In real-world systems, no system is perfectly isolated. Consider a nearly isolated system where smal

Explosive Separations and Momentum Distribution

A device at rest explodes into three fragments. Data for two fragments is provided, and the momentum

Force-Time Graph with Multiple Intervals

An object's force–time graph has three intervals: from $$0\,s$$ to $$1\,s$$ the force is constant at

Impulse, Momentum, and Safety: Automobile Crash Analysis

Design an experiment or simulation to evaluate how automobile safety features (such as airbags and c

Inelastic Collision Investigation

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

Inelastic Collision Momentum Analysis

Two objects collide and stick together in a perfectly inelastic collision. The table below provides

Inelastic Collision: Objects Sticking Together

A 2 kg cart moving at $$8\,\text{m/s}$$ collides with a 3 kg cart moving at $$4\,\text{m/s}$$ in the

Mid-air Collision Analysis

Two gymnasts collide mid-air and stick together. Gymnast A has a mass of $$55$$ kg and is moving at

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 in Explosions

A projectile of mass 1.2 kg is moving horizontally at 20 m/s when it explodes into two fragments. On

Momentum in Sports Collisions

In a contact sport, two players collide head-on. Player 1 has a mass of $$80\,kg$$ and runs at $$5\,

Momentum Measurement Error in Cart Collision Experiment

In this experiment, students attempted to measure the momentum of a cart on a frictionless track. Th

Momentum Transfer in Sports Equipment: Bat and Ball Dynamics

A sports equipment engineer aims to optimize bat design by examining how different bat materials aff

One-Dimensional Collision and Momentum Conservation

On a frictionless surface, Object 1 (mass = 2 kg) is moving east at 3 m/s, and Object 2 (mass = 3 kg

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 mini rocket expels mass to propel itself forward. Consider a rocket with an initial mass $$m_r = 0

Comparative Dynamics: Pendulum vs. Mass-Spring System

Compare the dynamics of a simple pendulum and a mass-spring oscillator.

Conservation of Energy in SHM

An experiment monitored the kinetic and potential energies of a mass-spring system undergoing simple

Coupled Oscillators and Energy Transfer

When two mass-spring oscillators are coupled by a weak spring, energy can be exchanged between them,

Damped Oscillations in a Mass-Spring System

A mass-spring oscillator subject to damping is described by the equation $$x = A e^{-b*t}\cos(ω*t)$$

Determining the Impact of Air Resistance on Amplitude Decay in SHM

An experiment records the amplitude of a damped oscillator over successive cycles in the presence of

Effect of Spring Constant on Oscillatory Motion

In a series of experiments, a mass-spring system is tested using springs with different spring const

Effects of Gravitational Variation on Pendulum Motion

Analyze how changes in gravitational acceleration affect the period of a pendulum.

Exploring SHM in Pendulums

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

Graphical Analysis of SHM Motion

A researcher performs an experiment with a spring-mass system and records its displacement as a func

Impact of Mass Variation on Oscillation Period

Analyze how varying the mass in a mass-spring oscillator affects the period of oscillation.

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

Investigating the Role of Mass in SHM

Explore how varying the mass attached to a spring affects the dynamics of SHM, specifically focusing

Mass-Spring Oscillator Analysis

A researcher studies a mass attached to a spring on a frictionless surface exhibiting simple harmoni

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

Measurement Uncertainty in SHM Parameters

A student performs an experiment to measure the period, amplitude, and angular frequency of a mass-s

Modeling and Simulating SHM in a Laboratory Setting

A computational simulation is developed to model a mass-spring system undergoing simple harmonic mot

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

Pendulum Period Investigation

A researcher is studying the period of a simple pendulum. The period is given by $$T = 2\pi \sqrt{\f

Period and Frequency Relationship Analysis

Examine the relationship between the period and frequency of an oscillator using the provided data.

Phase Angle Influence in SHM

A set of experiments measured the initial displacement of an oscillator at time t = 0 for different

Spring Constant Variation and Oscillation Frequency

Examine how variations in the spring constant affect the oscillation frequency of a mass-spring syst

Accelerometer-Based Measurement in Rotational Motion

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

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 Acceleration from a Graph

A graph of angular velocity versus time for a rotating wheel is provided. Use this graph to determin

Angular Displacement and Arc Length Relationships

Examine the relationship between angular displacement and the arc length traversed by an object movi

Angular Kinematics Basics

This question examines fundamental concepts in angular kinematics. Use the provided formulas to comp

Center of Mass Computation for a Non-Uniform Rod

A non-uniform rod is divided into segments with differing masses. Use the data provided to determine

Center of Mass in Rotational Systems

A non-uniform bar of length 2 m has its left half weighing 3 kg and its right half weighing 5 kg. (a

Comparative Analysis of Angular Sensors and Linear Measurement Systems

A researcher is evaluating two sensor types for measuring rotational motion in an industrial machine

Comparing Rotational Inertia: Disk vs. Ring

Two objects—a solid disk and a ring—each with a mass of 1 kg and a radius of 0.5 m, are subjected to

Conservation of Angular Momentum Experiment Evaluation

A student examines the rotation of a system with no external torques and claims that angular momentu

Construction Crane Moment of Inertia

A construction crane rotates its arm while carrying loads. Two loads are positioned along the arm: o

Dynamics of a Rotating Cylinder on an Incline

A solid cylinder with mass 10 kg and radius 0.5 m is released from rest and rolls down a 30° incline

Evaluating Angular Displacement with Variable Acceleration

In an experiment using a rotating platform, the angular acceleration is not constant. Researchers cl

Graph Analysis of Angular Displacement

Consider the attached graph of angular displacement versus time for a rotating object. (a) Determine

Investigating Rotational Impulse

Design an experiment to test the rotational analog of the impulse-momentum theorem by applying a bri

Moment of Inertia and Rotational Kinetic Energy

Different objects are rotating with various moments of inertia and angular velocities. Use the data

Moment of Inertia Calculations for Simple Shapes

A thin rod of mass $$m = 2 \text{ kg}$$ and length $$L = 1.5 \text{ m}$$ is considered for rotationa

Relationship Between Angular and Linear Quantities

A rotating cylinder's motion was analyzed by measuring its angular velocity and the corresponding li

Rotating Carousel Analysis

An amusement park carousel rotates about a vertical axis. A student records the angular displacement

Rotating Chair Angular Momentum Transfer Experiment Error

A student simulates a figure skater's rotation on a rotating chair by measuring angular speed before

Rotational Collision: Turntable and Clay Ball

A turntable with a moment of inertia $$3.0 kg·m^2$$ rotates at $$5 rad/s$$. A clay ball of mass $$2

Rotational Dynamics in a Newton’s Cradle

In a modified Newton's Cradle setup, the collision of swinging spheres not only involves translation

Rotational Dynamics in Amusement Park Rides

An amusement park ride features a rotating swing platform with a radius of $$3.5 \;m$$ rotating at a

Rotational Kinematics Data Analysis

An experiment records the angular displacement of a rotating disc at different times as shown in the

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 =

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

Torque and Angular Acceleration Experiment

A series of experiments measures the relationship between applied torque and resulting angular accel

Torque Calculation from Provided Data Table

A set of experiments measures forces and lever arms for different scenarios where forces are applied