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 Distance and Displacement from a Position-Time Graph

A position vs. time graph is provided below, depicting the motion of a particle along a straight lin

Analysis of Motion Using Position vs. Time Graphs

Using a provided position vs. time graph for an object in motion, analyze the intervals where the ob

Analyzing a Cyclist's Journey

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

Analyzing Acceleration from a Velocity-Time Graph

This question involves calculating and interpreting acceleration from a velocity-time graph. Refer t

Analyzing Changing Vectors: Two-Dimensional Motion

A drone takes off and follows a multi-leg flight path in a horizontal plane. The flight path consist

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

Calculating Acceleration with Changing Motion

A particle moves along a straight line with its velocity given by the function $$v(t) = 3 * t - 0.5

Calculations of Speed and Velocity from Experimental Data

The table below shows an object's position at various times during an experiment. Use the data to co

Car Acceleration Analysis

A car starting from rest accelerates uniformly along a straight road. Sensors record the car’s motio

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

Circular Motion: Understanding Displacement in a Lap

This question addresses the apparent paradox of moving over a circular path where the distance trave

Comparative Analysis of Scalar and Vector Quantities

A researcher collects data on several physical quantities during a lab experiment: mass, displacemen

Construction and Analysis of Velocity vs. Time Graph

A student conducts an experiment to measure the velocity of an object and plots the results on a vel

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 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 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 Maximum Height in Projectile Motion Experimentally

A student performs a projectile motion experiment and records the vertical displacement of a ball ov

Displacement and Motion in a River

A boat intends to cross a river. It travels with a speed of 5 m/s due east relative to the water, wh

Distance vs. Displacement Analysis

A runner follows a rectangular path that starts at point A, moves to B, then to C, then to D, and fi

Energy Implications of Distance vs. Displacement

A roller coaster car travels a path where the total distance covered is 200 m, but its net displacem

Energy Transformations on a Roller Coaster Track

A student constructs a model roller coaster and records measurements of height and speed at several

Experimental Design: Distance vs. Displacement Lab

A researcher is designing an experiment to investigate the differences between distance and displace

Exploring Non-Uniform Acceleration Through Variable Force Application

Some systems experience non-uniform acceleration when variable forces are applied. Design an experim

Free Fall and Gravitational Acceleration

A researcher conducts a free-fall experiment by dropping a ball from different heights and recording

Free Fall Motion Analysis

An object is dropped from rest and allowed to fall under the influence of gravity. The distances fal

Frisbee Flight Dynamics

A friend throws a frisbee with an initial speed of $$12\ m/s$$ at an angle of $$45^\circ$$. Assume i

Graph Analysis: Position vs. Time

A researcher records the motion of an object and plots its position (m) versus time (s) on the graph

Graphical Interpretation: Relationship between Position, Velocity, and Acceleration

An experiment provides three graphs of an object’s motion: • Graph A: Position vs. Time • Graph B:

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 Position vs Time Graph

A position vs. time graph for a moving car is provided in the stimulus. The graph displays three dis

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

Interpreting Velocity-Time Graph with Non-Uniform Acceleration

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

Investigating Speed vs. Velocity Using Smartphone Sensors

Smartphones are equipped with sensors that can measure motion. Design an experiment where you use a

Lab Analysis of Distance vs. Displacement

In this experiment, a small cart is propelled along a straight track by a compressed spring. A motio

Misinterpreting Position vs. Time Graphs

In a laboratory investigation of a rolling ball down a ramp, students use a position sensor to recor

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

Net Displacement in Multi-Segment Motion

An object moves along three straight-line segments with different directions.

Non-uniform Acceleration Analysis

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

Non-Uniform Acceleration Investigation

A velocity vs. time graph for an object is provided where the graph is curved (non-linear). Answer t

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 Experiment to Measure Gravity

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

Pendulum Length and Period Experiment

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

Position vs Time Graph: Velocity Analysis

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

Position vs. Time Graph Analysis

Examine the following position vs time graph which is composed of two segments: an initial curved se

Projectile Motion in Sports: Analyzing a Soccer Kick

A sports article claimed that a soccer ball kicked with an initial speed of $$v_0 = 30$$ m/s at an a

Projectile Motion with Air Resistance Approximation

An experiment studies projectile motion under nearly ideal conditions. A projectile is launched with

Projectile Motion with Angled Launch

A ball is launched with an initial speed $$v_{0} = 20 m/s$$ at an angle $$\theta = 30^\circ$$ with r

Projectile Motion with Varying Launch Speeds

A researcher investigates how changes in the launch speed $$v_0$$ affect the range of a projectile l

Projectile Motion: Basketball Shot Analysis

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

Ramp Acceleration Measurement Error

A student constructs an experiment to investigate the acceleration of a toy car down an inclined ram

Relative Motion of Two Cyclists

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

Time-Dependent Acceleration Analysis

A car's acceleration is given by the function $$a(t)=3-0.5*t$$ for $$0 \leq t \leq 6 \; s$$. Analyze

Understanding the Impact of Initial Conditions in Uniform Acceleration

Two objects, A and B, are subject to uniform acceleration. Object A is released at t = 0 with an ini

Uniform Acceleration and Displacement of a Car

A car starting from rest accelerates uniformly at 5 m/s² for 10 seconds. Analyze this motion using k

Uniform and Non-Uniform Acceleration: Evaluating a Claim

A claim has been made that the BIG FIVE equations of motion can be applied even when an object exhib

Validation of Projectile Motion Equations

In an experiment on projectile motion, measured ranges and theoretical ranges were recorded for thre

Vector Addition in Two-Dimensional Displacement

An object moves in two stages: first, it travels 6 m at an angle of 30° above the horizontal; then,

Vector Addition: Forces on an Object

An object is subjected to two forces: one force of 10 N acting due East and another force of 15 N ac

Vector Representation and Component Analysis

A diagram is provided that represents three displacement vectors drawn from the same origin. The dia

Velocity-Time Graph Analysis

A velocity vs. time graph for a moving object is provided. The graph is described by the equation $$

Analyzing Impulse in a Collision

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

Atwood Machine Dynamics Investigation

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

Center of Mass and Tipping Point Experiment

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

Centripetal Force Analysis in a Swinging Bucket

A 2.0-kg bucket is attached to a rope and swung in a vertical circle with a radius of 1.5 m. At diff

Centripetal Force Measurement Using a Rotating Bucket

In this experiment, students fill a bucket with water and swing it in a circular path to measure the

Comparing Free-Body Diagrams of Different Systems

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

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

Determining the Coefficient of Friction from Dynamic Experiment Data

An experiment is performed where a block of mass $$m = 5 * (kg)$$ is pulled on a horizontal surface

Dynamics Experiment 17: Multi-Body System Tension and Acceleration

A student investigates a multi-body system consisting of two masses connected by a string over a pul

Dynamics Experiment 18: Fuel Ejection Effects on Spacecraft Acceleration

A student simulates rocket propulsion by attaching small masses (representing fuel) to a trolley and

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 #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 in an Amusement Park Ride

Consider an amusement park ride where a car moves along a vertical loop of radius $$r$$. The car has

Dynamics of a Car Stopping

A researcher investigates the dynamics of a car coming to a stop. A velocity vs. time graph is provi

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 Multi-Block Pulley System

Two blocks with masses $$m_1 = 4\ \text{kg}$$ and $$m_2 = 6\ \text{kg}$$ are connected by a rope ove

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 Coupled Oscillators: Mass-Spring Systems

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

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

Effect of Air Resistance on Projectile Motion

A student measures the range of a projectile launched horizontally with different initial speeds. Th

Effect of Changing Mass on a Rotating Platform Dynamics

A person stands on a frictionless rotating platform holding weights. Initially, with the weights hel

Effect of Variable Mass on Acceleration

A moving cart is subjected to a constant applied force, but additional mass is being added to the ca

Energy and Newton's Laws: Work Done Against Friction

A box of mass 8 kg is pushed over a distance of 5 m on a rough horizontal surface. The coefficient o

Evaluating Satellite Motion: Gravitational Force and Newton's Laws

A recent aerospace report claims that satellites in low Earth orbit experience slightly lower gravit

Experimental Verification of Newton's Second Law

Verify Newton's Second Law experimentally by examining the relationship between net force, mass, and

Exploring the Limits of Newton’s Laws

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

Force Analysis on a Rotating Platform

A 70 kg person stands on a rotating platform of radius 2 m. The platform rotates with an angular spe

Forces on an Inclined Plane

Analyze the dynamics of an object on an inclined plane with friction and an applied force.

Free-Fall Motion and Acceleration Detection via Sensor

Students conduct an experiment to measure the acceleration due to gravity by dropping a small object

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

FRQ19: Elevator Dynamics: Tension and Acceleration

An experiment on an elevator involves measuring the cable tension for different elevator masses and

Gravitational Mass vs. Inertial Mass Experiment

Students designed an experiment to compare gravitational mass and inertial mass using separate proce

Impact of Force Angle on Net Force Magnitude

A student investigates how the angle between two applied forces affects the net force acting on an o

Impulse and Momentum in Collisions

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

Inertia in Motion

This question explores Newton's First Law and the concept of inertia. A 0.50 kg hockey puck slides o

Investigating Circular Motion on a Banked Curve

A car negotiates a banked curve with radius $$r = 50 * (m)$$ and bank angle $$\theta = 20^\circ$$. A

Investigating Inertia and Mass Relationship

A researcher conducts an experiment to study how the inertia of an object (its resistance to acceler

Investigating Normal Force Variations on an Uneven Surface

An object moves along an uneven, curved path such as a roller coaster loop where the normal force ch

Investigation of Normal Force Variation on Curved Surfaces

Students use a dynamics cart to travel along a curved track to examine how the normal force changes

Measuring Gravitational Acceleration with a Simple Pendulum

Design an experiment using a simple pendulum to determine the local acceleration due to gravity (g).

Newton's Third Law in Collisions

A diagram illustrating two carts colliding on a frictionless track is provided (see stimulus). Each

Projectile Motion Dynamics

A projectile is launched from a catapult at an angle of $$45^\circ$$ with an initial speed of 20 m/s

Pulley System Verification of Newton’s Second Law

A student uses a pulley system in which a cart on a track is connected to a hanging mass. Different

Quantitative Analysis of Tension in a Dual-Pulley System

In a dual-pulley system experiment, it was claimed that the tensions measured in the rope deviate fr

Relationship Between Applied Force and Acceleration

A student performs an experiment on a single object by applying different forces and measuring the r

Rotational Dynamics in a Spinning Disc

A student studies the rotational dynamics of a spinning disc by measuring its angular acceleration u

Variable Force and Acceleration Graph Analysis

In a dynamics experiment, the acceleration of an object is recorded as a function of time under a va

Verifying Newton's Second Law in a Lab Experiment

In a lab experiment, a cart on a frictionless track is subjected to different applied forces. The ac

Analyzing Force Equilibrium in Circular Motion

An experiment measures the tension in a rope used to swing a ball in a circular path at varying spee

Ball on a String: Uniform Circular Motion Analysis

A student sets up an experiment to analyze uniform circular motion using a ball attached to a string

Calculating Centripetal Force in a Rotating Space Station

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

Centripetal Force and Friction in Car Dynamics

An automobile of mass 1200 kg is rounding a flat curve of radius 80 m at a speed of 15 m/s. The fric

Comparative Analysis of Gravitational and Electric Forces

In a laboratory experiment, two identical small spheres each have a mass of $$0.1 \;kg$$ and carry a

Comparative Analysis: Gravitational Force vs Electric Force

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

Conical Pendulum Analysis

A conical pendulum consists of a mass $$m$$ attached to a string of length $$L$$, swinging in a hori

Conical Pendulum Analysis

A conical pendulum consists of a small bob of mass m attached to a string of length L, making a cons

Constructing an Experiment to Measure Gravitational Acceleration

A student aims to measure the gravitational acceleration 'g' by designing an experiment that combine

Designing a Free-Fall Experiment

A student aims to measure the gravitational acceleration (g) using a free-fall experiment with a mot

Designing a Lab Experiment on Centripetal Force

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

Effect of Charge Distribution on Electric Forces

An insulating rod with a non-uniform charge distribution is studied by measuring the electric force

Energy Considerations in Vertical Circular Motion

A mass of $$2.0 \;kg$$ is attached to a string of length $$2.0 \;m$$ and is whirled in a vertical ci

Escape Velocity Derivation

A satellite must achieve escape velocity to break free from a planet’s gravitational field. Using en

Experiment on Mass Dependence in Centripetal Force

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

Free-Body Diagram for Circular Motion in a Loop-the-Loop

A roller coaster car of mass 500 kg navigates a loop-the-loop with a radius of 12 m. Answer the foll

Friction and Circular Motion on a Flat Curve

A car negotiating a circular turn on a flat road relies on static friction to provide the necessary

Graphical Analysis of Circular Motion Experiment

An experiment was conducted to measure the centripetal acceleration of an object moving in a circle

Gravitational Acceleration across Different Celestial Bodies

Consider two planets with the following data provided in the table. Answer the following:

Gravitational Force in Planetary Orbits

This problem explores the gravitational force acting on satellites by using Newton's law of universa

Investigating Centripetal Force using a Conical Pendulum

Design an experiment using a conical pendulum to investigate the relationship between the pendulum’s

Investigating the Relationship between Speed, Radius, and Centripetal Force

In an experiment, a student collects data on the centripetal force acting on an object in circular m

Mass on a String Undergoing Vertical Circular Motion

A ball attached to a string is swung in a vertical circle of radius $$r$$. (a) Draw free-body diagra

Orbital Dynamics: Balancing Gravitational and Centripetal Forces

This problem examines the conditions required for a satellite to remain in a stable circular orbit b

Orbital Speed and Escape Considerations

A satellite of mass $$m = 400\,kg$$ is in circular orbit around Earth at a radius of $$r = 7.0 \time

Relationships Between Period, Radius, and Speed

A student analyzes uniform circular motion and wishes to relate the period $$T$$ of motion to the ra

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.

Satellite Orbit and Free-fall

A 500-kg satellite is orbiting the Earth at an altitude of 300 km above the Earth's surface. Assume

Tension in a Swinging Object

A ball of mass $$m = 0.5\,kg$$ is attached to a string and swung in a vertical circle of radius $$r

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

Transition from Circular to Projectile Motion

This problem investigates the transition of motion from uniform circular to projectile motion when t

Visual Analysis of a Uniform Circular Motion Diagram

A diagram is provided that illustrates a ball on a string undergoing uniform circular motion. (a) Pr

Analysis of Work with Variable Force and Angle

An object is pulled along a horizontal surface using a rope. However, both the magnitude of the appl

Comparing Work and Efficiency in Lifting Methods

In a study comparing two lifting methods, one using a mechanical crane and the other manual human li

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

Effects of Force Direction on Work Calculations

A sled is pulled 15 m by a force of 40 N applied at different angles. Answer the following: (a) Cal

Energy Conversion in a Pendulum Swing

A simple pendulum consists of a $$1\;kg$$ mass suspended from a $$2\;m$$ string. It is pulled aside

Energy Dissipation in a Collision

Analyze the experimental data from an inelastic collision that shows changes in kinetic energy befor

Energy Transformations in Pendulum Motion

A pendulum bob of mass 0.5 kg is released from a 30° angle relative to the vertical. Answer the foll

Evaluating the Role of Angle, Friction, and Distance in Work Calculations

Propose an experiment to evaluate how the angle of an applied force, friction, and the displacement

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

Inclined Plane Energy Conservation

A 4 kg block is released from rest at the top of a frictionless incline that is $$10 m$$ long and ma

Interpreting a Free-Body Diagram of a Block on an Incline

Below is a free-body diagram intended to represent a block on an inclined plane. The diagram shows t

Investigating Energy Losses in Real-World Applications

Design an experiment using a toy car track to quantify mechanical energy losses during motion, where

Investigating Work Done on a Spring: Variable Force Analysis

Design an experiment to measure the work required to compress a spring, where the force applied is v

Investigation of Mechanical Energy in a Roller Coaster Model

A model roller coaster is built and data are collected on the speed of the coaster at different poin

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

Non-Conservation of Mechanical Energy due to Air Resistance

Review the experimental data showing loss in total mechanical energy due to air resistance. Analyze

Power Calculation Error in a Weight-Lifting Machine

In a biomechanics lab, a student evaluates the power output of a weight-lifting machine. The machine

Power Consumption in a Conveyor Belt System

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

Quantitative Analysis of Frictional Work

Examine the provided data which quantifies work done by friction on surfaces of varying roughness. A

Rolling Motion and Energy Distribution

A solid cylinder (mass = 4 kg, radius = 0.2 m) rolls without slipping down an incline of height 5 m.

Time-Dependent Power Output Analysis

A weightlifter's performance is recorded over an 8-second interval. The following data shows the wor

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 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 by Variable Forces

A variable force given by $$F(x) = 20 * x$$ (in N) acts on a block as it moves from x = 0 m to x = 2

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-Energy Considerations in Car Crash Analysis

During a car crash, a 1200 kg car traveling at 15 m/s comes to a stop over a displacement of 2 m. An

Air Track Collision Experiment Analysis

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

Airbag Impact and Impulse Analysis

During a car crash, an airbag deploys and exerts a time-varying force on the occupant. The force vs.

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 Elastic Collision Using Graph Data

A high-speed camera records the velocities of two objects involved in an elastic collision. The grap

Analyzing Momentum in a Rocket Launch

Rocket propulsion is explained using conservation of momentum. Consider a rocket that ejects fuel to

Assumption of Uniform Mass Distribution in a Pendulum Collision

In this experiment, a pendulum bob is released from a fixed height to collide with a stationary targ

Basic Momentum and Impulse: Data Analysis

In an experiment, three objects with differing masses and velocities were launched horizontally. The

Billiards Collision Analysis

In a game of billiards, a cue ball collides with a stationary target ball. Data regarding the masses

Collision Analysis on a Low-Friction Track

In a laboratory experiment, two carts (A and B) on a low-friction track undergo a collision. You are

Collision Analysis Using Conservation Laws

In a laboratory experiment, two pendulum bobs collide. One bob (mass = 0.5 kg) is moving at 3 m/s an

Collision and Rebound in a Roller Coaster Car

A 300-kg roller coaster car traveling at $$10 \ m/s$$ collides with a safety bumper and comes to a s

Design an Experiment to Verify Momentum Conservation

Design a controlled laboratory experiment to verify the law of conservation of linear momentum. Your

Designing a Lab Experiment to Measure Impulse

You are tasked with designing an experiment to measure the impulse delivered to a cart during a coll

Designing an Air Track Experiment for Momentum Conservation

A student plans to verify momentum conservation using an air track and gliders. The experiment invol

Diver's Momentum and Water Impact

A diver with a mass of $$70 \ kg$$ jumps off a diving board with a horizontal component of velocity

Effect of Mass Variation on Momentum

Consider a collision between two objects with different masses. The data are given in the table belo

Experimental Analysis of Momentum Transfer

An experiment using carts on an air track measured momentum before and after collisions to test mome

Failing to Account for Impulse Duration Variability in Dynamic Collisions

In this experiment, a moving cart collides with a spring-loaded mechanism intended to alter its mome

Flawed Timing Measurements in a Cart Collision Experiment

In this experiment, two carts on an air track collide, and photocell timers are used to measure the

Impulse Analysis in Variable Mass Systems

A cart moving on a frictionless track collects rainwater, causing its mass to increase over time. A

Impulse Applied to Varying Masses

In a physics lab, a constant impulse of $$10$$ Ns is applied separately to two objects of different

Impulse in Variable Force Experiment

In an experiment, a student applies a variable force to a cart. The force-time graph, provided as a

Impulse Integration with Variable Force

A variable force is applied to an object, and the resulting force vs. time graph is given below. Use

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

Momentum and Impulse in Circular Motion

Consider an object moving in uniform circular motion. A brief tangential force is applied, deliverin

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 a Variable Mass System

A small rocket of initial mass 50 kg (including fuel) is moving at 30 m/s in deep space with no exte

Momentum in Two-Dimensional Collisions

Two pucks collide on a frictionless air table, resulting in two-dimensional motion. Answer the follo

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

Over-Simplified Analysis of Two-Dimensional Collisions

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

Pendulum Collision and Energy Transformation

A pendulum bob of mass $$0.8\,kg$$ swings into a stationary block of mass $$1.2\,kg$$ that hangs on

Perfectly Inelastic Collision: Stuck Together Objects

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

Sports Collision: Soccer Heading Impact

A soccer ball with mass $$0.43 \ kg$$ is moving at $$15 \ m/s$$ toward a player's head. Upon impact,

Analysis of Phase Constant in SHM

For a mass-spring oscillator described by $$x(t)=A\cos(\omega t+\phi)$$, consider that at \(t=0\) th

Calculating Energy Loss in a Damped Oscillator

In a damped oscillator, the amplitude decays over time due to energy dissipation. (a) Derive the ex

Comparative Analysis of SHM Systems

Consider a mass-spring system and a simple pendulum, both undergoing simple harmonic motion under id

Effect of Amplitude on Force in SHM

Examine the relationship between amplitude and the restoring force in a mass-spring oscillator.

Energy Loss Mechanisms in SHM

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

Error in Relating Frequency to Energy in SHM

A student investigates the relationship between frequency and total mechanical energy in a mass-spri

Exploring Non-Ideal Behaviors in SHM

In an experiment using a mass-spring system, deviations from ideal SHM are observed, including gradu

Force Analysis in SHM: Vector Representation

The restoring force in SHM is given by Hooke’s Law: $$F = -k*x$$. (a) Explain the significance of t

Forced Oscillations and Resonance

A mass-spring system is subjected to an external periodic driving force described by $$F = F_0*\cos(

Graphical Analysis of SHM Data

A mass-spring oscillator is undergoing simple harmonic motion, and experimental measurements of disp

Hooke’s Law Lab Analysis

In a laboratory experiment, a spring is stretched by attaching various weights and the following dat

Interpreting Velocity and Displacement Time Graphs in SHM

A combined graph displays both the displacement and velocity of an oscillator as functions of time.

Investigating Nonlinear Effects in Large Amplitude SHM

For a pendulum undergoing large angular displacements, the period deviates from the simple harmonic

Investigating the Role of Mass in SHM

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

Mass Dependence in a Spring Oscillator

In an experimental setup, different masses are attached to the same spring and the oscillation perio

Non-Ideal SHM: Measurement Uncertainty

Investigations of SHM in a laboratory setting are subject to various sources of measurement uncertai

Oscillating Mass on a Spring

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

Oscillations in Coupled Mass-Spring Systems

Consider a system of two masses connected by springs in series undergoing coupled oscillations. Answ

Pendulum Oscillation: Small-Angle Approximation Validity

A pendulum of length \(L=2.0\,m\) swings with a maximum angular displacement of 10°. Answer the foll

Predicting Motion in a Modified SHM System

Consider a mass-spring system in which an additional constant force is applied. Analyze how this aff

Analyzing a Damped Rotational System

Investigate a rotating disc subjected to a damping torque proportional to its angular velocity.

Angular Acceleration and Velocity

A turntable starts from rest and reaches an angular velocity of $$4 \text{ rad/s}$$ after 8 s under

Angular Kinematics Analysis

A rotating wheel starts from rest and undergoes constant angular acceleration. Use the data provided

Center of Mass in a Rotating System

A system consists of a uniform rod and two attached masses located at specified distances from a piv

Center of Mass of a Multi-Mass System

Consider a system of three masses placed along a straight line. Use the data in the table below and

Comparative Analysis of Rotational Motion in Different Systems

Two systems—a disc and a rod—are subjected to the same net torque. Their moments of inertia and corr

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

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

Conservation of Angular Momentum

A figure skater begins with an initial moment of inertia $$I_i$$ and angular velocity $$\omega_i$$.

Designing a Rotational Motion Experiment

Design an experiment to measure the moment of inertia of a solid cylinder. Outline the experimental

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

Dimensional Analysis in Rotational Motion

Verify the consistency of units in the rotational motion equation $$τ = I * α$$. Answer the followin

Energy Considerations in Rotational Motion

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

Experimental Assessment of Angular Acceleration

A rotating wheel's angular velocity is measured at various time intervals as follows:

Exploring Non-uniform Rotational Motion under Variable Torque

In an experiment, a rotating object's applied torque varied over time. The graph provided shows the

Frictional Torque on a Rotating Platform

A rotating platform initially spins at 4.0 rad/s and comes to a complete stop in 12 seconds due to f

Graph Analysis of Angular Displacement

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

Rotational Dynamics of a Car Wheel

A car wheel is modeled as a thin hoop with mass $$12 \;kg$$ and radius $$0.3 \;m$$. The engine appli

Rotational Energy and Dynamics

This question focuses on the energy aspects of rotational motion. You will calculate the rotational

Rotational Kinematics Data Analysis

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

Rotational Motion in Celestial Mechanics

This problem applies rotational motion concepts to celestial bodies. Analyze the rotation of a plane

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

Torque and Rotational Motion

A wrench with a length of $$0.4 \;m$$ is used to loosen a bolt. In part (a), a force of 80 N is appl

Torque Calculation from Provided Data Table

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

Torque-induced Precession in a Gyroscope

This problem examines the phenomenon of gyroscopic precession when an external torque is applied to

Translational vs. Rotational Motion Comparison

Compare and contrast linear (translational) motion with rotational motion based on the provided tabl