AP Physics 1: Algebra-Based FRQ Room

Acceleration and Deceleration Phases in Vehicle Motion

A car accelerates uniformly from rest to 40 m/s in 8 s and then decelerates uniformly to 0 m/s in 4

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

Angled Motion: Maximum Height Experiment

Design an experiment to determine how the launch angle affects the maximum height reached by a proje

Average Speed vs. Average Velocity on a Circular Track

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

Car Braking Experiment: Uniform Deceleration Analysis

A physics lab performed an experiment on a car braking to a stop. The data collected is summarized i

Comparative Analysis of Scalar and Vector Quantities

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

Comparative Analysis of Speed and Velocity Measurements

A radar system records both the speed and displacement of a vehicle over time. Answer the following

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 Vector and Scalar Quantities

Design an experiment to demonstrate the difference between vector and scalar quantities using motion

Comparison of Speed and Velocity in Different Trials

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

Comprehensive Analysis Using the BIG FIVE Equations

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

Critical Evaluation: Misinterpretation of Speed vs. Velocity

A popular online article claims that because speed and velocity share the same units (m/s), they con

Deriving and Comparing Kinematic Equations

An object’s position as a function of time is given by $$x(t) = 5*t^2 - 3*t + 2$$. Answer the follow

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

Elevator Motion Analysis

An elevator in a multi-story building exhibits varying motion: starting from rest, accelerating, mov

Energy Considerations in Projectile Motion

In a projectile motion experiment, energy conservation principles are used to predict the maximum he

Experimental Design: Projectile Range and Launch Angle

This question asks you to design an experiment to investigate how the launch angle affects the range

Field Trip Navigation Vector Analysis

During a school field trip, students travel between three stops along a curvy route. The actual path

Free Fall Experiment Analysis

In a free fall experiment, an object is dropped from rest. Its fall is recorded in the table below.

Graphical Analysis of Position vs. Time: Identification and Correction of Errors

Below is a schematic diagram of a position vs. time graph that is intended to represent the motion o

Identifying Scalar and Vector Quantities

Answer the following questions regarding scalar and vector quantities:

Impact of Initial Velocity on Projectile Trajectories

Two projectiles, A and B, are launched from the same height with an angle of 45° but with different

Interpreting a Position vs. Time Graph for Acceleration

Using the provided position vs. time graph, analyze the object's acceleration.

Interpreting Complex Motion Graphs

Examine the Position vs. Time graph provided, which shows two distinct segments of motion, and analy

Investigating Circular Motion: Displacement vs. Distance

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

Investigating Free Fall and Gravity

In a free-fall experiment, objects are dropped from various known heights and the time taken to fall

Investigating Scalar and Vector Quantities: Speed vs. Velocity

Design a laboratory experiment to measure an object's speed and velocity using motion sensors and ti

Investigation of Newton's Second Law: Force, Mass, and Acceleration

A student sets up an experiment on a low-friction track where a cart is attached to a hanging mass v

Kinematics of a Two-Part Journey

A runner completes a race in two segments at different speeds. Analyze the runner's overall kinemati

Misinterpreting Position vs. Time Graphs

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

Momentum and Impulse Error

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

Motion Analysis in Air and Underwater

A ball is thrown in air and underwater, and its displacement and time of travel are measured. The fo

Multi-Dimensional Motion Analysis

A drone flies in a horizontal plane following this path: it flies 8 m north, then 6 m east, then 3 m

Multi-Dimensional Projectile Motion Analysis

In this advanced experiment, a projectile is launched in a two-dimensional plane and its motion is r

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

Multi-Phase Motion Experiment: Comprehensive Analysis of Acceleration, Velocity, and Displacement

A complex motion experiment recorded the path of an object exhibiting three distinct phases: acceler

Non-Uniform Acceleration and Displacement

An object's velocity changes in a non-uniform manner over time. Given the velocity function $$v(t)=t

Nonuniform Acceleration: Piecewise Motion

An object starts from rest and undergoes a two-phase motion. In Phase 1, it accelerates uniformly at

Pendulum Period Measurement Error

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

Position, Velocity, and Acceleration Graph Analysis Experiment

In a physics lab, a motion sensor records the position versus time of a moving object. The resulting

Projectile Launch Experiment with Misapplied Gravity Components

In this projectile motion experiment, a student uses a spring-loaded cannon to launch a ball at an a

Projectile Motion Analysis

A ball is thrown with an initial speed of $$20 \;m/s$$ at an angle of $$30^\circ$$ above the horizon

Projectile Motion Analysis

A projectile is launched with an initial speed of $$20 \; m/s$$ at an angle of $$30^\circ$$ above th

Projectile Motion Analysis

A ball is thrown with an initial speed of $$20\ m/s$$ at an angle of $$30^\circ$$ above the horizont

Projectile Motion Analysis

A projectile is launched from ground level under the given conditions.

Projectile Motion Analysis

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

Projectile Motion Angle Error

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

Projectile Motion with Air Resistance

Develop an experiment to investigate the effect of air resistance on projectile motion by comparing

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: Angle Dependence

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

Railgun Motion Analysis: Evaluating Claims About High-Speed Acceleration

A research group claims that their railgun experiment achieved a uniform acceleration of $$1000\ m/s

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

Scalars vs. Vectors: Identifying Quantities

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

Speed vs. Velocity Concepts

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

Uniform Acceleration with the BIG FIVE Equations

A car accelerates uniformly from rest.

Uniformly Accelerated Motion in a Car

A car accelerates uniformly from a complete stop with an acceleration of $$2 \; m/s^2$$. Answer the

Vector Addition in Displacement Analysis

Two displacement vectors are given: one with a magnitude of 5 m directed east and another with a mag

Acceleration vs. Net Force Graph Analysis

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

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

Analysis of Forces during a Car Crash

A 1200 kg car moving at 20 m/s crashes into a stationary barrier and comes to rest in 0.25 s. Use im

Applying Newton's Second Law

Investigate Newton's Second Law through both theoretical derivation and experimental data.

Atwood Machine Dynamics Investigation

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

Centripetal Force in Circular Motion

Explore the dynamics of circular motion and the associated centripetal force acting on an object.

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

Deceleration in a Braking Car Experiment

A student investigates the deceleration of a car during braking. The velocity vs. time graph below s

Designing a Safety Mechanism in Vehicle Dynamics

In a car collision scenario, forces experienced by passengers can be extremely high over a short tim

Determining Net Force from Component Forces

A force sensor measures the components of the forces acting on an object. The data below represent t

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

Dynamic Analysis of a Swinging Pendulum

A simple pendulum with length $$L = 1.2 * (m)$$ and mass $$m = 0.4 * (kg)$$ is displaced to an angle

Dynamics Experiment 2: Pulley System Tension Measurement

A student conducts an experiment with a two-mass pulley system to measure the acceleration and tensi

Dynamics Experiment 3: Action-Reaction Force Analysis

A student sets up an experiment using two carts colliding on a frictionless track to study action-re

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 9: Free Fall Acceleration Measurements

A student performs an experiment to measure the acceleration due to gravity by dropping various obje

Dynamics Experiment 19: Skater Motion on a Tilted Surface

A student analyzes the dynamics of a skater gliding on a tilted surface using motion sensors to meas

Dynamics FRQ #5: Projectile Motion with Air Resistance

A ball of mass 2.0 kg is projected horizontally from a 45 m high building with an initial speed of 1

Dynamics FRQ #8: Friction on a Rough Surface

A 10.0 kg block slides on a horizontal surface. A constant 30 N force is applied, while the coeffici

Dynamics 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 in Non-Inertial Frames

A small mass is placed on a rotating laboratory platform with an angular acceleration of 0.5 rad/s²

Dynamics of a Block on an Incline with Applied Force

An experiment investigates the motion of a block on an inclined plane while an additional force is a

Dynamics of a 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 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 Tetherball Swing

A 1.0-kg tetherball is attached to a rope of length 3.0 m and is set into motion, swinging in a near

Dynamics on an Inclined Plane

A block of mass $$m$$ is placed on a frictional incline with an angle $$\theta$$ relative to the hor

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

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

Dynamics Problem 8: Multi-Force Analysis of a Suspended Sign

A sign weighing $$W = 200\ N$$ is suspended by two cables. The left cable makes an angle of $$30^\ci

Dynamics Problem 10: Mass Variation in a Rocket

In a model rocket experiment, the rocket's mass decreases over time as fuel is burned. At a particul

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

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

Effect of Air Resistance on Projectile Motion

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

Evaluating Newton's Third Law in Action-Reaction Pairs

A researcher investigates the force interactions between a person and a boat when the person jumps o

Exploring Air Drag and Its Effect on Free Fall

Design an experiment to measure the effect of air drag on the acceleration of objects in free fall.

Forces in Equilibrium

Analyze a system in static equilibrium and determine unknown forces acting on it.

FRQ13: Tension Effects in a Two-Mass Pulley System

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

FRQ14: Reaction Forces in Collisions

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

Inertia Effects during Sudden Deceleration

A moving cart on a nearly frictionless track suddenly stops when hitting a barrier, and unsecured ob

Investigating Acceleration in Circular Motion

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

Investigating Circular Motion and Centripetal Force

A mass is attached to a string and swung in a circle on a horizontal plane. The researcher investiga

Investigating Collisions: Momentum and Newton's Third Law

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

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 Gravity with a Simple Pendulum

Design an experiment using a simple pendulum to measure the acceleration due to gravity and analyze

Measuring Inertial Mass Experimentally

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

Motion on a Frictionless Surface

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

Newton's Third Law in Collisions

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

Newton's Third Law: Analysis of Action-Reaction Forces

A collision experiment is conducted where two objects interact over a short interval of time. A grap

Projectile Motion and Launch Angle Optimization

Design an experiment to study projectile motion by varying the launch angle, with the aim of determi

Projectile Motion Dynamics

A researcher investigates projectile motion by launching a ball horizontally from a known height. Th

Projectile Motion: Influence of Newton's Laws

A projectile is launched with an initial velocity $$v_0$$ at an angle $$\theta$$. Analyze its motion

Static vs. Kinetic Friction Experiment

Investigate the differences between static and kinetic friction through definitions, experimental da

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

Analyzing Data: Impact of Variable Speed on Centripetal Force

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

Analyzing Gravity Measuring Apparatus Data

A student builds a gravity measuring apparatus that relies on timing the free fall of a small ball t

Centripetal Acceleration Due to Earth's Rotation

At the equator, a point on Earth's surface experiences centripetal acceleration due to the planet's

Centripetal Acceleration Measurement Analysis

In an experiment to measure centripetal acceleration, a mass is swung in a circle with a constant sp

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

Centripetal Force in a Circular Motion Experiment

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

Comparing Gravitational and Electric Force Effects

A series of experiments compare the magnitudes of gravitational and electric forces between pairs of

Comparing Observed and Predicted Acceleration in Circular Motion

In an experiment, the observed centripetal acceleration was compared with the theoretical prediction

Conservation of Angular Momentum in Variable Radius Circular Motion

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

Deriving the Relationship between Force, Mass, and Circular Motion

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

Effect of Charge Distribution on Electric Forces

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

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

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

Free-Fall Versus Circular Motion Analysis

Compare the dynamics of free-fall motion and uniform circular motion. (a) Derive the equations gover

Gravitational Force in Planetary Orbits

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

Integration of Gravitational and Electric Field Effects

In a laboratory setup, a test object is placed in a region where both gravitational and electric fie

Investigating the Effect of Mass Variation on Circular Motion

Two objects with different masses travel at the same speed along the same circular path. Analyze the

Investigating the Role of Radius in Uniform Circular Motion

A student investigates how the radius of a circular path affects centripetal acceleration while keep

Mass Dependence in Centripetal Force

Two objects with different masses are attached to identical strings and swung in circular motion at

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

Measuring Uniform Circular Motion: Data Analysis

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

Orbit Simulation: Satellite Motion and Gravitational Force

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

Pendulum Gravitational Acceleration Measurement

A student sets up an experiment using a simple pendulum to measure the gravitational acceleration, g

Pendulum Motion in a Vertical Circle

A pendulum bob of mass 2 kg is attached to a string of length 3 m and moves in a vertical circle. At

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: Torque and Angular Acceleration

A solid disk of radius 0.5 m and mass 10 kg is subjected to a tangential force applied at its rim, c

Satellite Orbital Mechanics

A small satellite of mass $$m = 500\,kg$$ is in a circular orbit around a planet of mass $$M = 5.97

Tension and Acceleration in Circular Motion

A 0.5 kg ball is attached to a string and is swung in a horizontal circle at a constant speed of 4 m

Air Resistance Impact on Energy Conversion

In this experiment, a student drops a small ball from a fixed height in two conditions: one in a nea

Analysis of Power in an Oscillatory System

A mass-spring system oscillates with a mass of $$2 kg$$ attached to a spring of constant $$200 N/m$$

Analyzing the Work-Energy Theorem through a Spring Launch Experiment

In this experiment, a spring launcher propels a mass horizontally. The spring is compressed a known

Comparative Analysis of Work in Different Force Directions

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

Comparing Lifting Mechanisms

Two methods are used to lift a 100 kg mass by 5 m. In method 1, the mass is lifted directly with a v

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 on a Frictionless Incline

A $$3\;kg$$ block is released from rest at a height of $$5\;m$$ on a frictionless inclined plane. Us

Determining the Influence of Mass on Work Done

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

Effective Force Measurement in a Pulley Experiment

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

Efficiency Analysis of a Mechanical System

A machine requires an input energy of $$5000\;J$$ and produces a work output of $$3200\;J$$. Calcula

Energy Conservation in a Mass-Spring Oscillator

A mass-spring oscillator with a mass of 0.5 kg and a spring constant of 200 N/m is investigated. The

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

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

Evaluating Mechanical Energy during a Bounce

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

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 Effects of Applied Angle on Work Done

In this experiment, a student drags a sled across a flat surface while varying the angle at which th

Investigating Power Variations in Electric Motor-Driven Lifts

An electric motor is used to power a lift that raises a load at constant speed. The experiment recor

Investigating the Relationship Between Force, Displacement, and Power Output Using an Electric Motor

Design an experiment to measure how efficiently an electric motor converts electrical energy into me

Investigating the Work-Energy Theorem with Multiple Forces

A 5 kg object is subjected simultaneously to two forces on a horizontal surface: an applied force of

Kinetic Energy and Braking Force

A vehicle of mass $$1200 kg$$ is traveling at $$20 m/s$$ and comes to a stop over a distance of $$40

Mechanical Energy in a Bouncing Ball

A ball with a mass of $$0.2\;kg$$ is dropped from a height of $$2\;m$$. On the first bounce, it reac

Mechanical Work in a Pulley System

A bucket with a mass of 10 kg is lifted from a well using a pulley system with an efficiency of 80%.

Ramp Experiment for Work-Energy Theorem

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

Work Done at an Angle

A force of 100 N is applied to a crate at an angle of 40° above the horizontal, moving the crate 5 m

Work Measurement Under Non-Uniform Acceleration

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

Work-Energy Theorem and Friction

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

Analyzing Momentum in a Rocket Launch

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

Basic Momentum and Impulse: Data Analysis

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

Calculating Linear Momentum and Impulse

In this problem, you will calculate linear momentum and impulse for a moving object and relate impul

Coefficient of Restitution in Collisions

A 1.0 kg ball moving at 8 m/s collides head-on with a 1.0 kg ball moving at -2 m/s. After the collis

Collision with Energy Absorption via Spring Mechanism

A 3 kg block moving at $$10\,\text{m/s}$$ collides with a spring attached to a wall. The block compr

Comparative Collision Dynamics

Two identical balls are thrown toward a rigid wall from the same height at a speed of $$9$$ m/s. One

Data Analysis of Collision from Velocity Graph

The velocity vs. time graph for Glider A during a collision on an air track is provided. Assume Glid

Data Analysis of Elastic versus Inelastic Collisions

A series of collision experiments were performed and the momentum values before and after collisions

Determining the Coefficient of Restitution using Collision Data

A ball is dropped from a height and bounces off a hard surface. Using the recorded drop heights and

Experimental Uncertainty in Momentum Measurements

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

Explosive Separations and Momentum Distribution

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

Ignoring Elastic Deformation Effects in Impulse Measurements

In this experiment, two blocks collide after being launched by a spring-loaded mechanism, and impuls

Impact of Bat on Ball: Momentum Transfer

A baseball of mass $$0.145\,kg$$ is hit by a bat. The ball approaches the bat at $$30\,m/s$$ and lea

Impulse Analysis from Crash Test Data

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

Impulse from a Force-Time Graph

An object is subjected to a varying force generated over a 4-second interval as a function of time.

Impulse in Sports Performance

In sports such as baseball, the brief, high-force impact between the bat and ball generates an impul

Impulse Integration with Variable Force

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

Impulse-Momentum Theorem: Graph Analysis

A force-time graph is provided showing the force exerted on an object during a collision. Use the gr

Impulsive Force in Car Crash Safety Design

In automotive safety design, engineers reduce occupant injury by increasing the collision duration.

Investigating Collision Outcomes on an Air Track

Design an experiment on an air track to study the outcomes of collisions between carts. Answer the f

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

Misreading Sensor Data in a Projectile Collision Experiment

In this experiment, a projectile is launched and its velocity is recorded by a motion sensor to anal

Momentum and Safety Design in Car Crashes

Modern cars use design features like airbags and crumple zones to manage the impulse experienced dur

Momentum Change Due to Friction

A 5.0 kg block is sliding on a horizontal surface and comes to rest due to kinetic friction over a p

Momentum Conservation in Rotational Collisions on a Rotating Platform

An experiment involves a ball landing on a rotating platform, thereby transferring linear momentum i

Momentum in Two-Dimensional Collisions

Two objects collide in a two-dimensional setting. Object A (mass = 2 kg) moves east at 6 m/s, and Ob

Momentum Transfer in a Baseball Collision

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

Momentum Transfer in a Baseball Collision

A baseball (mass $$0.145\,\text{kg}$$) is pitched toward a batter at $$40\,\text{m/s}$$. Upon being

Neglected Frictional Effects in Momentum Experiment

In this experiment, two carts are set to collide on a track that is assumed to be frictionless. The

Sequential Collisions on a Frictionless Track

A 2 kg cart moving at $$3\,\text{m/s}$$ collides elastically with a stationary 3 kg cart. After the

Solving for Final Momentum in a Multi-Collision System

Consider a system with three objects undergoing sequential collisions. Object A (mass = 2 kg, veloci

Traffic Safety and Momentum in Multi-Car Collisions

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

Two-Dimensional Collision Analysis

Two objects collide on a frictionless surface. Object A with mass $$2\,\text{kg}$$ is moving east at

Understanding Momentum in Car Crash Reconstruction

In accident reconstruction, conservation of momentum is a key principle. Consider two vehicles: Car

Amplitude Effects on Energy

A researcher examines how changes in amplitude affect the total mechanical energy of a mass-spring s

Analyzing Nonlinear Restoring Forces

A study has observed that for large displacements, the restoring force deviates from Hooke's Law in

Comparing Displacement Functions

Consider the two displacement functions for a mass-spring system: $$x_1(t)= A*cos(ω*t+φ)$$ and $$x_2

Determining Phase Constant in SHM

A mass-spring oscillator is described by the displacement equation $$x(t) = A \cos(\omega*t + \phi)$

Determining the Spring Constant from Oscillation Data

A series of experiments measured the period of oscillation for different masses attached to the same

Effect of Mass Variation on Oscillation Parameters

An investigation is conducted in which the mass attached to a spring in an SHM system is varied, whi

Effect of Spring Constant on Oscillation

The spring constant (k) affects the angular frequency and period of oscillation in a mass-spring sys

Energy Conservation in SHM

A mass-spring system undergoing SHM has an amplitude of $$A = 0.20 m$$ and a spring constant of $$k

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

Analyze the force exerted by a spring on a mass undergoing simple harmonic motion using Hooke's law.

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: Displacement vs. Time

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

Interpreting and Correcting a Faulty SHM Diagram

An experimental setup diagram for a mass-spring system in SHM is provided. The diagram attempts to i

Mass-Spring Oscillator Energy Analysis

A block attached to a horizontal spring is oscillating in SHM. Consider a system with mass m and spr

Non-Ideal Effects in SHM

Real oscillatory systems often deviate from ideal SHM due to friction and air resistance. Consider a

Oscillatory Motion with Variable Amplitude

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

Pendulum Motion and Period Analysis

A simple pendulum with small oscillations obeys the period equation $$ T = 2\pi * \sqrt{\frac{L}{g}}

Phase Difference in SHM

In SHM, displacement, velocity, and acceleration are sinusoidal functions of time with specific phas

Rotational SHM: Physical Pendulum

An experiment is conducted with a physical pendulum, where a rigid body swings about a fixed pivot.

SHM Displacement Analysis

A mass-spring system oscillates horizontally on a frictionless surface. The displacement is given by

SHM Energy Conservation Analysis Error

A group of students is investigating energy conservation in a mass-spring system undergoing SHM. The

SHM Kinematics in a Mass-Spring System

Consider a mass-spring system undergoing simple harmonic motion described by $$x = A \cos(ω*t+ φ)$$,

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 Rotational Energy Data

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

Analysis of Rotational Equilibrium on a Seesaw

A seesaw is in rotational equilibrium. A weight of 20 N is placed 1.0 m from the pivot on one side.

Angular Displacement from Arc Length

A car travels along a circular track with a radius of $$50 \;m$$ and covers an arc length of $$200 \

Angular Displacement from Arc Length Measurements

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

Angular Momentum Change on a Rotating Platform

A rotating platform with a moment of inertia $$5.0 kg·m^2$$ spins at $$4 rad/s$$. A 50 kg person (tr

Angular Momentum in Figure Skating

A figure skater is spinning with arms extended at an angular velocity of $$4 \;rad/s$$ and has a mom

Axis Dependency of Moment of Inertia

A solid disk of mass $$m = 3 \text{ kg}$$ and radius $$r = 0.5 \text{ m}$$ is rotated about differen

Bicycle Wheel Dynamics

A cyclist's bicycle wheel is modeled as a thin hoop having a mass of 2 kg and a radius of 0.35 m. Wh

Biomechanics of Diving: Torque and Rotation Analysis

A researcher examines the rotational dynamics of a diver performing a somersault. Initially, the div

Center of Mass vs. Geometric Center: A Rotational Dynamics Experiment

In an experiment on a non-uniform rod, mass elements are recorded at various positions along the rod

Comparing Rotational and Translational Inertia

A solid sphere (mass = 3 kg, radius = 0.2 m) and a hollow cylinder (mass = 3 kg, radius = 0.2 m) rol

Connecting Linear and Angular Motion on a Rotating Disc

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

Conservation of Angular Momentum in an Isolated System

An individual on a rotating platform changes body configuration, altering the system's moment of ine

Coupled Rotational Systems Analysis

A system consists of two disks connected by a frictionless axle. Disk X has mass $$4 \text{ kg}$$ an

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

Energy Considerations in Rotational Motion

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

Experimental Analysis of Angular Deceleration

This experiment examines angular deceleration using experimental data. Analyze the data, identify tr

Experimental Investigation of Frictional Torque

A rotating wheel is observed to slow down over time due to frictional torque. This experiment aims t

Linear and Angular Kinematics Relationship

Investigate the relationship between linear motion and angular motion by using the relation $$v = r

Modeling Translational and Rotational Dynamics

The equations of motion for translational dynamics (e.g., $$F = m a$$) have close analogies with tho

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

Rotating Disc with Friction

A disc with a moment of inertia of $$I = 1.5\, kg\cdot m^2$$ rotates with an initial angular velocit

Rotating Disk Dynamics Experiment

A uniform disk of radius $$R = 0.5$$ m and mass 2 kg is mounted on a nearly frictionless axle. A for

Rotational Collision Dynamics

Two separate rotating bodies collide and stick together. Analyze the collision using conservation of

Rotational Dynamics and Angular Impulse

An experiment applies short-duration force pulses to a rotating object, resulting in changes in its

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 Moment of Inertia in Rotational Motion

A thin rod of length $$L$$ and mass $$m$$ is pivoted about one end. An experiment claims that its mo

Uniform Circular Motion and Linear Relationship

In a controlled experiment, the linear velocity of points on a rotating wheel was measured for diffe

Using Video Analysis for Rotational Measurements

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

Variable Torque and Angular Acceleration

An object with a moment of inertia of $$I = 5.0 kg·m^2$$ is subjected to different net torques over