AP Physics 1: Algebra-Based FRQ Room

Acceleration and Deceleration in Sprinting

A sprinter accelerates uniformly from rest to a maximum speed of 8 m/s in 4 s, maintains that speed

Air Resistance Effects on Projectile Motion

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

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 Velocity-Time Graph

A velocity-time graph is provided showing the motion of an object.

Analyzing Position vs Time Graph

A student tracks the motion of an object along a straight track and records its position over time.

Analyzing Variable Acceleration

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

Angled Motion: Design and Analysis

A cannon fires a projectile with an initial speed of $$50 m/s$$ at an angle of $$40^{\circ}$$ above

Angled Motion: Water Fountain

Water is projected from a fountain at an initial speed of \(15\,m/s\) at an angle of \(45^\circ\) wi

Average Speed Calculation Using Motion Sensor Data

Using the experimental data collected from a motion sensor, analyze the object's movement with regar

Calculating Car Stopping Distance and Reaction Time Effects

Analyze the stopping distance of a car incorporating both braking and driver reaction time.

Centripetal Motion Error

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

Circular Motion: Distance and Displacement on a Track

A researcher studies the motion of a car moving on a circular track with a fixed radius of $$r = 50$

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

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

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

Comprehensive Analysis Using the BIG FIVE Equations

A toy car starting from rest accelerates uniformly in a straight line. The experiment records time,

Deriving the Relationships Among the BIG FIVE Equations

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

Determining Displacement from Variable Velocity Data

A series of measurements of an object's velocity at different times is given in the table below. Usi

Determining Maximum Height in Projectile Motion Experimentally

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

Dimensional Analysis and Equation Derivation

Consider the displacement equation $$s = ut + \frac{1}{2}at^2$$. Answer the following parts.

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 and Displacement Analysis in a Motion Experiment

In a motion experiment, an object moves following a path represented by the provided position vs tim

Energy Considerations in Projectile Motion

A projectile of mass 0.5 kg is launched with an initial speed of $$18\ m/s$$ at an angle of $$45^\ci

Free Fall Experiment and Error Analysis

An experiment is conducted to measure the acceleration due to gravity using free fall.

Free Fall from a Building

An object is dropped from rest from the top of a 45 m tall building.

Friction in Inclined Plane Experiment Error

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

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 Analysis: Position, Velocity, and Acceleration

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

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 Runner’s Position vs. Time Graph

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

Interpreting Motion Graphs: Position, Velocity, and Acceleration

This question focuses on interpreting various aspects of motion graphs. Refer to the provided positi

Investigating Circular Motion: Displacement vs. Distance

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

Investigating the Effect of Surface Type on Friction and Acceleration

A cart is allowed to roll on different surface types and its acceleration is measured. The objective

Investigating the Impact of Air Resistance on Projectile Motion

Air resistance can significantly affect projectile motion. Design an experiment to investigate how a

Investigating Vector Addition in Force Analysis

A claim in a recent study stated that "all forces can be added simply by summing their magnitudes."

Kinematics of a Toy Car: Acceleration and Deceleration

Design an experiment to analyze the acceleration and deceleration patterns of a toy car on a track.

Methods for Calculating Displacement

Design a controlled experiment to compare two different methods for calculating displacement: one us

Momentum and Force in Collisions Experiment

In a collision experiment on an air track, a moving cart collides with a stationary block. A force s

Momentum and Impulse Error

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

Motion Sensor and Staircase Displacement Experiment

In this experiment, a motion sensor is used to track a subject as they walk up and down a flight of

Motion Under Gravity: Effects of Air Resistance

This question explores the differences between ideal free fall and motion under the influence of air

Multiple Vectors: Navigating a Hilly Terrain

A hiker embarks on a trek with three distinct segments: 4 km east, 3 km north, and 5 km west. Answer

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

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 Period Measurement Error

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

Position vs Time Graph Analysis

A position vs time graph for an object is provided. Analyze the graph to identify periods of constan

Position vs. Time Graph Experiment

A position versus time graph of a moving object is provided (see graph stimulus). You are required t

Position vs. Time Graph Interpretation

A position versus time graph for an object in motion is provided. The graph shows a non-linear (curv

Projectile Motion Analysis

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

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 Experiment: Angle of Launch

Design an experiment to investigate how the angle of launch affects the range of a projectile. Your

Projectile Motion Trajectory Experiment

A student launches a projectile at an angle from a table and uses video analysis to measure its time

Projectile Motion with Varying Launch Angle

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

Projectile Motion: Basketball Shot Analysis

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

Simulated Impact Test: Speed and Velocity

In a crash simulation lab, a test vehicle decelerates from a high speed and various sensors record i

Speed vs. Velocity Measurement Design

Propose an experiment to investigate the differences between speed (a scalar quantity) and velocity

Speed vs. Velocity Measurement Error

A student uses a photogate sensor to measure the speed of a cart moving along a straight track. The

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

Uniform Acceleration: Big Five Equations Validation

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

Uniformly Accelerated Motion: Deriving Equations

Derive the kinematic equation for displacement under uniform acceleration, $$s = ut + \frac{1}{2}at^

Uniformly Accelerated Motion: Free Fall Experiment

Consider a free fall experiment where a ball is dropped from rest.

Using Graphical Data to Determine Acceleration

A set of experimental data is provided in the table below showing the velocity of an object over tim

Vector Addition in Displacement Measurement Error

A student conducts an experiment where a robot moves in two distinct straight-line segments with a c

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 of Forces

A block is pulled by two forces applied at different angles. Answer the following parts.

Velocity-Time Graph Analysis

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

Acceleration vs. Net Force Graph Analysis

A series of experiments are conducted where various net forces are applied to an object of constant

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 the Forces in a Boat Maneuvering in a Current

A boat is shown navigating a river current, as depicted in the provided diagram (see stimulus). Answ

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

Data Analysis of Force and Acceleration

A table of experimental data was collected showing the net force applied to an object and its subseq

Deceleration Due to Friction

A student records the velocity of a sliding object on a horizontal surface. The velocity vs. time gr

Designing a Multi-Factor Experiment for Vehicle Safety Dynamics

Design a comprehensive experiment to investigate how various forces (such as friction, tension, and

Dynamic Analysis of an Incline with Multiple Forces

A researcher examines the motion of a block on an inclined plane that is subject to gravity, frictio

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 in Circular Motion: Banked Curve

A vehicle negotiates a banked curve without any friction. Analyze the forces acting on the vehicle.

Dynamics Lab: Force-Acceleration Relationship

In a lab experiment, students measure the acceleration of a frictionless dynamics cart under various

Dynamics of a Suspended Mass: Tension Analysis

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

Dynamics of a Two-Mass Pulley System

A two-mass system is set up with mass $$m_1 = 4 ~kg$$ on a horizontal surface that has kinetic frict

Dynamics of Projectile Motion

A projectile launcher is set up to launch objects at varying angles while keeping the initial speed

Dynamics Problem 4: Box Pushing on a Rough Surface

A box of mass $$m = 10\ kg$$ is pushed along a horizontal surface. The applied force is $$F_{app} =

Dynamics Problem 17: Dynamics of a Swinging Pendulum

Consider a simple pendulum consisting of a small bob suspended by a light string. Although energy co

Dynamics Problem 19: Atwood Machine Analysis

An Atwood machine consists of two masses connected by a string over a frictionless pulley. In this s

Effect of Incline Angle on Normal Force

A student measures the normal force acting on an object placed on an inclined plane at various angle

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 Dynamics: Understanding Work and Force

A researcher studies the work done on an object as it is pushed up a ramp. The investigation examine

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

Experiment: Measuring Coefficient of Kinetic Friction

In a laboratory experiment, a 2.0 kg wooden block is pulled along a horizontal table by a constant f

Experimental Determination of Object Mass using Acceleration Data

A cart on a nearly frictionless track is pulled by a constant force in several experiments. The acce

Frictional Forces in a Collision Experiment

In a collision experiment, friction plays a key role in the dissipation of kinetic energy.

FRQ2: Projectile Motion Analysis Using a Velocity-Time Graph

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

Gravitational vs. Inertial Mass Experiment

A student designed an experiment using a spring scale and a pulley system to compare gravitational m

Impact of Air Resistance on a Projectile

A ball is launched horizontally from the top of a cliff with height $$h = 45 * (m)$$. Two experiment

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

Impact of Non-Inertial Frames on Newton's Laws

When observing motion in a non-inertial frame, fictitious forces appear in the analysis of dynamics.

Impulse and Changing Motion

An object experiences a time-varying force. Analyze the effect of this force on the object’s motion.

Inclined Plane Dynamics Experiment

A group of students designed an experiment to measure the acceleration of a dynamics cart on an incl

Inertia in Motion

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

Investigating Air Resistance in Free Fall

While studying free-fall motion, a researcher investigates the effect of air resistance on the accel

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 Collisions: Momentum and Newton's Third Law

A researcher studies collisions between two gliders on an air track to examine momentum conservation

Investigating Gravitational Mass

A series of experiments are conducted to compare gravitational mass and inertial mass. In one experi

Investigating Motion on an Inclined Plane

A student studies a frictionless object's acceleration on an inclined plane by measuring acceleratio

Motion on an Inclined Plane

A block is placed on a frictionless inclined plane that makes an angle $$\theta$$ with the horizonta

Multi-Stage Motion Under Changing Forces

A student performs an experiment where an object is subjected to different constant forces in two di

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 in Collisions

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

Projectile Motion and Dynamics Analysis

An object is launched into projectile motion. Neglect air resistance and assume that gravity is the

Projectile Motion Dynamics

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

Projectile Motion Dynamics with Air Resistance

A projectile is launched horizontally, and its horizontal displacement is measured at different time

Rocket Propulsion and Variable Mass

A toy rocket of mass 2 kg produces a constant thrust force of 10 N in space with negligible external

Rotational Dynamics in a Spinning Disc

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

Tension and Acceleration in a Pulley System

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

Testing Hooke's Law in a Spring-Mass System

A student investigates the relationship between force and displacement in a spring-mass system. The

Vector Decomposition on an Incline

An object of mass \(m\) rests on a \(30^\circ\) inclined plane. Decompose the gravitational force in

Work-Energy Principle in Dynamics

Examine the application of the work-energy theorem in dynamic systems.

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

Angular to Linear Kinematics in Circular Motion

A point on a rotating disk moves in a circle of radius $$r$$ at a constant angular speed $$\omega$$.

Ball on a String Dynamics

A ball of mass $$m = 0.2\,kg$$ is attached to a string of length $$L = 1.5\,m$$ and is swung so that

Banked Curve Analysis

A car is negotiating a banked curve on a frictionless road. In such a scenario, the normal force and

Calculating Gravitational Acceleration on an Unknown Planet

An experiment measures gravitational acceleration $$g$$ at various altitudes above the surface of an

Car on a Circular Track: Maximum Speed Analysis

A car of mass $$m$$ negotiates a circular turn of radius $$r$$ on a level road. The maximum static f

Centripetal Force in a Rotating Amusement Park Ride

An amusement park ride consists of a rotating circular platform. A rider with a mass of $$70 \;kg$$

Comparative Analysis of Gravitational and Electric Forces

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

Comparing Gravitational and Electric Force in Microscale Systems

In a laboratory experiment, two microscale spheres are suspended near each other. Each sphere has a

Comparing Gravitational and Electric Forces

Two scenarios are considered on a lab bench: (1) two small spheres, each of mass 0.1 kg, are 0.5 m a

Comparing Methodologies: Damped Pendulum versus Free Fall for g Measurement

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

Deriving the Relationship between Force, Mass, and Circular Motion

Using the concept of centripetal acceleration, derive the formula that relates centripetal force to

Designing a Circular Motion Laboratory Experiment

Design an experiment to study the relationship between centripetal acceleration and radius for an ob

Designing a Controlled Experiment to Distinguish Gravitation from Electromagnetism

A scientist wishes to design an experiment to distinguish gravitational forces from electric forces

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.

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

Impact of Radius Variation on Uniform Circular Motion

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

Investigating the Impact of Air Resistance on Circular Motion Experiments

A student performing an experiment on uniform circular motion notices that the measured centripetal

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

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

Design an experiment to measure the gravitational acceleration $$g$$ (near 9.81 m/s^2) using free-fa

Measuring Uniform Circular Motion: Data Analysis

In a laboratory experiment, the centripetal force acting on a mass in circular motion was measured f

Non-Uniform Circular Motion: Incorporating Tangential Acceleration

An object on a circular track is accelerating, meaning its speed is increasing along with its circul

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 Mechanical Energy Analysis

An object in a circular orbit around a planet has both kinetic energy and gravitational potential en

Orbital Mechanics and Kepler's Third Law Applications

A moon orbits a planet in a nearly circular orbit. Using gravitational force as the source of centri

Satellite Orbit Dynamics

A satellite of negligible mass orbits Earth in a circular orbit of radius $$r$$. The gravitational f

Surface Gravity on Mars vs. Earth

Mars has a mass of approximately 0.107 times the mass of Earth and a radius approximately 0.532 time

Uniform Circular Motion: Centripetal Force Calculation

This question explores the basic principles of uniform circular motion and how centripetal force is

Bungee Jump Energy Conservation Analysis

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

Crane Lifting with Force Angle

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

Determining Work with Nonconservative Forces

A 3 kg block is placed on a 10 m high frictional ramp and is released from rest. It slides down the

Energy Transformation in a Pendulum

In a pendulum experiment, a 1.5 kg bob is released from a certain height and swings down. At the low

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

Evaluating the Work-Energy Theorem in a Car's Braking Process

A 1200 kg car decelerates uniformly from an unknown initial speed to rest over a distance of 50 m. I

Exploring Mechanical Advantage and Energy Transfer in a Compound Pulley System

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

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

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

Investigating the Impact of Variable Force Application on Work Done

Design an experiment to study how variable force application (i.e., when the force is not constant)

Mechanical Energy in a Roller Coaster

A roller coaster car of mass $$800 kg$$ starts from rest at the top of a hill $$30 m$$ high. Answer

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 and Efficiency in an Electric Motor

An electric motor receives 5000 J of input energy over 10 seconds and produces 3500 J of useful mech

Ramp Experiment for Work-Energy Theorem

In this experiment, a student studies the work-energy theorem by letting a cart slide down an inclin

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

Time-Dependent Power Output Analysis

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

Variable Force Work Calculation

An object is acted upon by a variable force given by $$F(x)=10 - 0.5 * x$$ (in Newtons), where $$x$$

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-Energy Theorem in Collisions

A 4 kg cart moving at 3 m/s collides with a fixed spring, compressing it by 0.2 m. The spring consta

Analyzing Rebounding Basketball

A basketball of mass $$0.62 \ kg$$ is dropped from a certain height. Just before impact, its speed i

Basic Momentum and Impulse Calculation

Consider a 2.5 kg object moving with a velocity of 3.0 m/s eastward. A constant force of 5.0 N is ap

Billiard Ball Elastic Collision

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

Car Braking and Impulse

A car of mass $$1200\,kg$$ traveling at $$25\,m/s$$ comes to a complete stop by braking over a time

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

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

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

Exploring the Limits of Momentum Conservation

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

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

Fragmenting Projectile: Momentum Analysis

A projectile with a mass of $$10\,kg$$ explodes in mid-air into two fragments. Before the explosion,

Impulse Analysis from Crash Test Data

During a vehicle collision test, the force experienced by the test dummy is recorded over time. Use

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

Measurement Errors in Momentum Experiments

A lab report on momentum measurements describes various experiments. Answer the following: (a) Iden

Momentum Analysis in a Variable Mass System: The Leaky Cart

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

Momentum and Energy in a Diver's Jump

A diver with a mass of $$70\,kg$$ jumps off a platform and enters the water at a speed of $$3.0\,m/s

Momentum Conservation in Explosions

A 10 kg object at rest explodes into two fragments. One fragment, with a mass of 6 kg, is observed t

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

Projectile Collision with Moving Object

A 0.2 kg projectile is fired horizontally at 50 m/s and collides with a 0.8 kg block moving to the r

Rocket Propulsion and Momentum Conservation

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

Rocket Propulsion: Conservation of Momentum

A rocket initially has a total mass of 1000 kg. During an engine burn, it ejects 100 kg of fuel at a

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,

Traffic Safety and Momentum in Multi-Car Collisions

A traffic safety study reconstructs a multi-car collision where several vehicles collide and move to

Underestimating the Role of Impulse in Variable Force Applications

In this experiment, a cart is subjected to a force from a mechanical actuator designed to change its

Adapting SHM for Seismic Measurement

Seismometers use principles of SHM to detect and measure ground motion. Consider a design using a ma

Amplitude Dependency and Maximum Acceleration in SHM

In SHM, the acceleration is given by $$a(t) = -A*\omega^2 \cos(\omega*t + \phi)$$. (a) Explain mat

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

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 Oscillatory Motion in a Fluid

Examine how an oscillating object behaves in a fluid medium compared to in air, particularly focusin

Comparative Study: Mass-Spring System vs. Pendulum

Compare a mass-spring oscillator and a simple pendulum, noting that both systems exhibit simple harm

Damped Oscillations and Energy Loss

Real systems often experience damping where a damping force proportional to the velocity causes ener

Designing an SHM Experiment

Design an experiment to study the effect of varying the spring constant (k) on the period (T) of a m

Effect of a Change in Spring Constant on Oscillation Frequency

An experiment measured the frequency of a mass-spring oscillator for different spring constants. Ana

Effect of Amplitude on SHM System

A researcher investigates the effect of varying amplitude in a spring-mass system while keeping the

Effect of Spring Constant on Oscillatory Motion

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

Effect of Spring Constant Variation on Oscillation

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

Effect of Temperature on Material Properties in Oscillatory Motion

Temperature can affect the properties of materials, including the spring constant of a metal spring,

Energy Analysis in a Mass-Spring System

A 0.5 kg mass attached to a spring (with spring constant k = 200 N/m) oscillates on a frictionless s

Energy Conversion in SHM

A mass-spring system undergoing simple harmonic motion has amplitude $$A$$ and spring constant $$k$$

Energy Transformation in SHM

In a mass-spring system undergoing SHM, the total mechanical energy is conserved and is partitioned

Energy Transformation in SHM

In an experiment on a mass-spring system, the following data were recorded over one complete oscilla

Investigating SHM through Electrical Analogues

Electrical circuits containing inductors and capacitors can exhibit oscillatory behavior analogous t

Large Amplitude Pendulum Analysis

For a pendulum oscillating with large amplitudes, the period deviates from the simple small-angle fo

Measurement Uncertainty in SHM Parameters

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

Misinterpretation of SHM Sinusoidal Graph Data

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

Non-Ideal SHM: Measurement Uncertainty

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

Non-linear Effects in Large Amplitude Oscillations

For a mass-spring system, the period is independent of amplitude only for small oscillations. At lar

Oscillatory Motion with Variable Amplitude

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

Pendulum Period Investigation

A simple pendulum is used to study the relationship between its length and period of oscillation.

Predicting Motion in a Modified SHM System

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

SHM and Gravitational Effects in Pendulums

Gravity plays a crucial role in pendulum motion as described by the equation $$T = 2π\sqrt{L/g}$$. A

Simple Harmonic Motion in Biological Systems

Biological systems, such as the rhythmic beating of a heart or neuron firing patterns, sometimes exh

Verification of Hooke's Law

A series of experiments measured the force exerted by a spring for different displacements. Analyze

Amusement Park Ride Safety Check

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

Analysis of Experimental Rotational Data

During an experiment, the angular position of a rotating arm was recorded at various times.

Analysis of Rotational Energy Data

An experiment measured the rotational kinetic energy of a rotating object at various angular velocit

Angular Momentum Conservation and Collisions

This problem explores conservation of angular momentum during a collision on a rotating platform.

Angular Momentum Conservation: Figure Skater

A figure skater spins with her arms extended with an initial moment of inertia $$I_i = 4.0 kg·m^2$$

Dynamics of a Rotating Disk with Applied Torque

A researcher examines a solid disk with mass $$M = 2.0\;kg$$ and radius $$R = 0.5\;m$$ that is initi

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 Conservation in Rolling Motion

A solid sphere of mass $$2 kg$$ and radius $$0.2 m$$ rolls without slipping down an incline of heigh

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

Influence of External Friction on Angular Acceleration

A student claims that increasing friction at the pivot of a rotating system significantly reduces it

Investigating Rotational Impulse

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

Lever Arm Length Impact on Angular Acceleration Experiment Error

A student studies the effect of lever arm length on angular acceleration by applying an identical fo

Load Distribution and Angular Velocity in a Space Station

A rotating space station generates artificial gravity. Initially, the station has a moment of inerti

Merry-Go-Round Rotation Measurement Error

A student analyzes the rotational motion of a merry-go-round by measuring its angular displacement a

Oscillations of a Physical Pendulum

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

Relating Angular to Linear Motion

A carousel rotates at a constant angular velocity of $$0.8 \text{ rad/s}$$. (a) Calculate the tangen

Rotational Dynamics and Frictional Torque Error

In an experiment on rotational dynamics using a spinning disk, a student applies a constant force to

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 Dynamics of a Physical Pendulum

A physical pendulum is made from a uniform rod of length $$L = 1.2\, m$$ and mass $$m = 2.0\, kg$$ p

Rotational Motion in a Physical Pendulum

Consider a physical pendulum composed of a thin rod of length $$1.2 \;m$$ and mass $$5 \;kg$$, pivot

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

Spinning Ice Skater and Angular Momentum

An ice skater performs a spin with an initial moment of inertia of 4.0 kg*m² and an angular speed of

Torque and Equilibrium on a Seesaw

A researcher is studying the rotational equilibrium of a seesaw. A 4 m long seesaw has its pivot at

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 in a Non-Uniform Beam

A 2 m long beam pivots about one end. A 3 kg mass is placed 0.5 m from the pivot on one side, and a

Torque-induced Precession in a Gyroscope

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

Using Torque to Analyze Rotational Equilibrium

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

Using Video Analysis for Rotational Measurements

Design an experiment that utilizes video analysis to measure the rotational motion of an object. You