AP Physics 1: Algebra-Based FRQ Room
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AP Physics 1: Algebra-Based Free Response Questions
The best way to get better at FRQs is practice. Browse through dozens of practice AP Physics 1: Algebra-Based FRQs to get ready for the big day.
Acceleration and Deceleration in a Race
A sprinter accelerates from rest and then decelerates to a stop during a race. Analyze the different
Acceleration Calculation from Tabulated Data
Using the table of velocity data below, answer the following kinematics questions.
Analysis of Position vs. Time Graph for Kinematic Insights
A student obtained a Position vs. Time graph with a quadratic relationship. Answer the following que
Analyzing Experimental Data: Uniform Acceleration
An experiment measures the position of a cart moving along a track under uniform acceleration. The f
Analyzing Position vs Time Graph
A student tracks the motion of an object along a straight track and records its position over time.
Angled Motion Analysis: Component Breakdown
A ball is thrown with an initial speed of 20 m/s at an angle of 30° above the horizontal. Analyze it
Angles and Vectors: Airplane Navigation
An airplane flies 400 km due north and then 300 km due east. Answer the following:
Calculating Vector Sums: Displacement in Two Dimensions
Two displacement vectors for an object are given. Vector A has a magnitude of 5 m at an angle of 30°
Car Acceleration and Deceleration Analysis
A car accelerates uniformly from rest with an acceleration of $$3\ m/s^2$$ for 5 s, then travels at
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
Constant Acceleration: Inclined Plane Experiment
A researcher conducts an experiment with a cart on a frictionless inclined plane. The cart starts fr
Determining Acceleration in a Free Fall Drop Experiment
In a school laboratory drop experiment, the following data was recorded: | Height (m) | Time (s) |
Distance and Displacement Analysis
An object follows a path with several segments as outlined in the table. The object moves from point
Distance and Displacement Analysis in a Motion Experiment
In a motion experiment, an object moves following a path represented by the provided position vs tim
Everyday Vector and Scalar Quantities
Consider the following physical quantities: mass, displacement, time, speed, and temperature. Identi
Experiment on Motion with Resistive Forces
A block is observed sliding on a rough horizontal surface where friction (a resistive force) affects
Experiment on Uniform Acceleration
A student conducts a laboratory experiment to study uniform acceleration of a cart on a track. The f
Free Fall Acceleration Verification
Design a controlled experiment to verify the acceleration due to gravity (using $$g = 9.81 \text{ m/
Free Fall from a Building
An object is dropped from rest from the top of a 45 m tall building.
Free Fall Motion Analysis
An object is dropped from rest and allowed to fall under the influence of gravity. The distances fal
Identifying Vector vs. Scalar Quantities
A table lists several physical quantities recorded during an experiment. Classify each quantity as e
Instantaneous versus Average Velocity from a Velocity-Time Graph
Analyze the velocity vs. time graph provided in the stimulus to compare instantaneous and average ve
Interpreting a Visual Diagram: Position vs. Time Graph Analysis
Below is a diagram intended to represent a position vs. time graph for an object undergoing interval
Investigating Non-Uniform Acceleration through Experimental Data
A researcher collects time and velocity data for an object experiencing non-uniform acceleration. Th
Jogger's Path Analysis: Distance and Displacement
A local news article reports that a jogger's displacement during his run was equal to the total dist
Kinematics of a Two-Part Journey
A runner completes a race in two segments at different speeds. Analyze the runner's overall kinemati
Measuring Displacement in Complex Paths Using Smartphone GPS Data
Design an experiment that utilizes smartphone GPS data to measure both the total distance traveled a
Motion on a Curved Path: Distance vs. Displacement
An object travels along a circular track, covering a distance of 100 m and eventually returning to i
Motion with Reaction Time Delay
A sprinter has a reaction delay of 0.2 s. After the delay, he accelerates uniformly from rest at $$a
Motion with Reverse Direction: Distance vs. Displacement
This question examines situations where an object’s path results in a different distance traveled co
Non-uniform Acceleration Analysis
An experiment records the motion of an object experiencing non-uniform acceleration. The velocity vs
Position vs Time Graph Analysis
A position vs. time graph for an object in one-dimensional motion is provided. Answer the following
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 and Prediction
A projectile is launched with an initial speed of $$20\ m/s$$ at a certain angle above the horizonta
Projectile Motion Experiment
A projectile is launched from ground level with an initial speed of $$20 \; m/s$$ at an angle of $$3
Projectile Motion with Ramp Launch
A car drives off a ramp with a speed of 15 m/s at an angle of 20° above the horizontal. The end of t
Projectile Range Variability: Data Analysis and Evaluation
A student conducted several projectile launches at varying angles, yielding the following data: | L
Relative Motion in Parallel Tracks
A researcher analyzes the relative motion of two trains moving on parallel tracks. Train A travels e
Scalar Quantities in Energy Calculations
Consider an object with a mass of 3 kg moving with a speed of 4 m/s. Evaluate its kinetic energy and
Speed versus Velocity
Examine and compare the concepts of average speed and average velocity.
Uniform Acceleration and Displacement of a Car
A car starting from rest accelerates uniformly at 5 m/s² for 10 seconds. Analyze this motion using k
Uniformly Accelerated Motion: Car Launch Experiment
A car starts from rest and accelerates uniformly at $$5 m/s^2$$ for 10 seconds. Using the equations
Uniformly Accelerated Motion: Deriving Equations
Derive the kinematic equation for displacement under uniform acceleration, $$s = ut + \frac{1}{2}at^
Validating Newton's Second Law
Design an experiment to investigate the relationship between net force and acceleration as stated in
Vector Addition and Resultant Displacement in a Scavenger Hunt
A hiker participates in a scavenger hunt and follows a path composed of multiple directional segment
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: 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 and Scalar Quantities
Answer the following questions regarding vector and scalar quantities in physics.
Vector and Scalar Quantities Comparison
This question addresses identifying and differentiating between vector and scalar quantities in phys
Vector Components: Ballistic Launch Analysis
A researcher observes a ball being thrown from the ground with an initial speed $$v_0 = 20$$ m/s at
Vector Representation and Component Analysis
A diagram is provided that represents three displacement vectors drawn from the same origin. The dia
Vector vs. Scalar Classification
A list of physical quantities is provided. Classify each as either a vector or a scalar quantity and
Verification of the Equation $$v = u + a*t$$
Design an experiment using a motion sensor on an inclined plane to verify the linear relationship de
Wind Effects on Projectile Trajectories: A Comparative Analysis
An experiment investigated the effect of wind on projectile motion. A graph compares the theoretical
Acceleration vs. Net Force Graph Analysis
A series of experiments are conducted where various net forces are applied to an object of constant
Airtrack Dynamics and Inertial Mass Determination
Investigate the relationship between mass and acceleration on an airtrack, and determine an object’s
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 System Equilibrium on a Rough Surface
A block is placed on a horizontal rough surface. A gradually increasing horizontal force is applied
Applied Force Direction and Acceleration
Design an experiment to investigate how the angle at which a force is applied affects the accelerati
Center of Mass and Tipping Point Experiment
A composite object consisting of two connected masses is placed on an inclined plane to determine th
Comparing Gravitational and Inertial Mass in a Vacuum
An experiment is conducted in a vacuum chamber to test the equivalence of gravitational and inertial
Critical Analysis of an Experiment on Air Resistance in Free Fall
A study reports that when air resistance is taken into account, the acceleration of objects in free
Critical Evaluation of an Experiment on Energy Dissipation in Colliding Cars
A media report claims that in a rear-end collision, nearly all the kinetic energy of the vehicles is
Designing a Multi-Factor Experiment for Vehicle Safety Dynamics
Design a comprehensive experiment to investigate how various forces (such as friction, tension, and
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 14: Inertial vs. Gravitational Mass Comparison
A student designs an experiment to compare inertial mass with gravitational mass. The procedure invo
Dynamics FRQ #10: Multi-Force Vector Analysis
A 6.0 kg object is acted upon by three forces in a horizontal plane: a 12 N force directed east, a 9
Dynamics in a Two-Dimensional Force System
A 5 kg block is subjected to two forces: Force A of 20 N at 30° above the horizontal and Force B of
Dynamics in Non-Inertial Frames
Study the behavior of objects observed from non-inertial reference frames.
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-Force System: Tension, Normal, and Friction
A 4 kg block sits on a 20° inclined plane and is attached via a rope to a 2 kg hanging mass over a f
Dynamics of a Sports Car: Acceleration and Friction
A sports car with a mass of $$m = 1500 * kg$$ is designed to accelerate from rest to $$30 * m/s$$ in
Dynamics of a Spring-Loaded Cart
Design an experiment where a spring-loaded cart is launched by a compressed spring. The objective is
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 pulley system is used to study the relationship between force and acceleration. The follo
Dynamics of Colliding Objects on a Frictionless Track
In a collision experiment, two objects on a frictionless track collide and stick together. The table
Dynamics of Connected Masses on an Incline and Pulley
A 4 kg mass is placed on a frictionless inclined plane with an angle of 25°. It is connected by a li
Dynamics 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 6: Circular Motion and Friction
A car is negotiating a flat circular curve of radius $$r = 20\ m$$. The coefficient of static fricti
Dynamics Problem 9: Impulse from a Force-Time Graph
A force is applied to a small cart for a short duration, and the force varies with time. A force vs.
Dynamics Problem 19: Atwood Machine Analysis
An Atwood machine consists of two masses connected by a string over a frictionless pulley. In this s
Dynamics with Air Resistance
Investigate how air resistance affects the dynamics of falling objects.
Force Diagram and Modeling a Hanging Mass System
A mass hangs from a rope attached to a support. A researcher examines how additional loads affect th
Friction and Normal Force
Investigate the relationship between frictional force and the normal force in various scenarios.
FRQ4: Determining Mass from Acceleration Data
In an experiment, a constant net force of 20 N is applied to different masses, and the resulting acc
FRQ20: Two-Dimensional Force Vectors and Resultant Acceleration
In an experiment, forces in two dimensions were applied to a 1 kg object, and the resultant accelera
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
Two carts collide on a frictionless track. Cart A (mass $$m_A = 2 * kg$$) is moving at $$3 * m/s$$,
Investigating Action-Reaction Forces
In an experiment, two carts in contact on a track, equipped with force sensors, record the forces ex
Investigating Newton's Third Law through Collision Forces
In an experiment, two objects collide and sensors record the forces experienced by each object over
Moment of Inertia and Angular Acceleration
Examine the dynamics of rotational motion by exploring the relationship between net torque, moment o
Newton's First Law in Everyday Contexts
Newton's First Law, the law of inertia, explains the persistence of motion. Apply this concept to ev
Newton’s Third Law in a Collision Event
A study on collisions between hockey pucks claims that the forces measured during the impact do not
Newton's Third Law in Ice Skating
Two ice skaters with masses of 50.0 kg and 70.0 kg push off from each other on a frictionless ice su
Newton's Third Law in Rebounding Collisions
A ball is dropped from a height and rebounds off a rigid surface.
Projectile Motion and Dynamics Analysis
An object is launched into projectile motion. Neglect air resistance and assume that gravity is the
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: Influence of Newton's Laws
A projectile is launched with an initial velocity $$v_0$$ at an angle $$\theta$$. Analyze its motion
Skateboarder Acceleration: Evaluating Net Forces
A local sports science investigation reports that the acceleration of a skateboarder on a smooth sur
Tension Analysis in a Stationary Object
A mass is hanging from a rope attached to a ceiling. Consider the forces acting on the mass when it
Tension Forces in a Pulley System
A student examines a simple pulley system with two connected masses. The table below shows the measu
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
Advanced Analysis of Centripetal Force Miscalculation
A student conducts a detailed investigation into the dynamics of an object in uniform circular motio
Analyzing Angular Motion and Period
A rotating object moves in a circle with a constant radius. Its period, T, is the time required to 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 $$\omega$$.
Artificial Gravity in a Rotating Space Station
A rotating space station creates artificial gravity through centripetal acceleration. Answer the fol
Banked Curve Analysis
A car is negotiating a banked curve on a frictionless road. In such a scenario, the normal force and
Calculating Centripetal Force in a Rotating Space Station
A rotating space station is designed to simulate Earth-like gravity by providing centripetal acceler
Car Dynamics on a Circular Track
A car is rounding a circular curve with a constant speed. The car’s speed is 20 m/s and the radius o
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 Ball on a String
A ball of mass $$m$$ is attached to a string and swung in a horizontal circle of radius $$r$$ at a c
Centripetal Force in a Roller Coaster Loop
This problem analyzes the forces acting on a roller coaster car as it navigates a vertical loop.
Charged Particle in Circular Orbit
A stationary charged sphere with charge $$Q = 5.0 \times 10^{-6} \;C$$ is fixed at the center of a f
Circular Track Dynamics
A car of mass $$m = 1500\,kg$$ moves on a circular track of radius $$r = 50\,m$$ at a constant speed
Determining the Gravitational Constant G Using a Torsion Balance
Design an experiment using a torsion balance to measure the gravitational constant $$G$$. Your desig
Effect of Friction in Circular Motion
A car with a mass of $$1000 \;kg$$ navigates a flat circular track. The friction between the tires a
Effect of Magnetic Forces on Uniform Circular Motion
Design an experiment to investigate how an applied magnetic field influences the circular motion of
Electric Force Experiment Analysis
In an experiment, two charged spheres interact with each other. The electric force between them is e
Energy Considerations in Circular Motion: Kinetic and Potential Energy Analysis
Design an experiment to measure the kinetic and potential energy of an object undergoing uniform cir
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
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
Experimental Validation of Gravitational Law
Free-fall experiments were conducted at various altitudes to measure gravitational acceleration. The
Gravitational and Electric Forces Comparison
In a laboratory experiment, students investigate both gravitational and electric forces between two
Gravitational vs Electric Force Experiment: Conceptual Error Analysis
A group of students designs an experiment to compare gravitational and electric forces acting on sma
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
Mass Dependence in Centripetal Force
Two objects with different masses are attached to identical strings and swung in circular motion at
Measuring Uniform Circular Motion: Data Analysis
In a laboratory experiment, the centripetal force acting on a mass in circular motion was measured f
Momentum and Circular Motion
An object in circular motion experiences steady forces that maintain its path, while an external imp
Multiple Forces in Circular Motion: Combined Gravity and Tension
A pendulum bob of mass 0.8 kg is swung in a vertical circle using a string of length 3 m. Assume the
Orbital Mechanical Energy Analysis
An object in a circular orbit around a planet has both kinetic energy and gravitational potential en
Orbital Motion and Gravitational Forces
A satellite of mass $$500 \;kg$$ is orbiting the Earth at an altitude of $$300 \;km$$ above the Eart
Pendulum Gravitational Acceleration Measurement
A student sets up an experiment using a simple pendulum to measure the gravitational acceleration, g
Pendulum Period Variations and Gravitation
A pendulum clock is used to measure local gravitational acceleration by observing its period. The pe
Projection of Circular Motion onto SHM
Uniform circular motion can be used to model simple harmonic motion (SHM) when projected onto a diam
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
Satellite Orbit Dynamics
A satellite of negligible mass orbits Earth in a circular orbit of radius $$r$$. The gravitational f
Satellite Orbital Motion: Gravitational and Centripetal Force
A satellite orbits the Earth in a circular path. In such an orbit, the gravitational force provides
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 $$r
Transition from Circular to Projectile Motion
This problem investigates the transition of motion from uniform circular to projectile motion when t
Uniform Circular Motion Fundamentals
A 2.0 kg mass is attached to a string and whirled in a horizontal circle of radius 0.50 m at constan
Uniform Circular Motion: Tension and Gravity in a Conical Pendulum
A conical pendulum consists of a mass m attached to a string of length L, swinging in a horizontal c
Water Park Slide Centripetal Dynamics
At a water park, a curved slide features a circular arc section with a fixed radius of $$r = 5\,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 Mechanical Energy Conservation in a Pendulum
A pendulum with a 2 kg bob is released from a height of 1.5 m above its lowest point. Answer the fol
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
Calculating Work at an Angle
A sled is pulled along a horizontal surface by a rope that makes an angle of 40° with the horizontal
Conservation of Mechanical Energy in a Roller Coaster
In a laboratory experiment, a small model roller coaster is tested on a nearly frictionless track. T
Designing an Experiment to Measure the Efficiency of Energy Transfer in a Motor
You are to design an experiment to evaluate the efficiency of an electric motor in converting electr
Determination of Power Output in a Vertical Lift
A researcher measures an athlete’s performance lifting a 50 kg weight vertically upward by 2 m in 5
Efficiency and Power Loss in a Mechanical System
Examine the experimental data of a mechanical system that measures input energy, output energy, and
Energy Analysis of a Spring-Mass System
A 2 kg mass is attached to a spring with a spring constant of 100 N/m and is pulled 0.3 m from its e
Energy Conservation in a Skate Park
A skateboarder rides in a skate park, starting at the top of a ramp, descending to the bottom, and t
Energy Dissipation in a Bouncing Ball
A 0.5 kg ball is dropped from a height of 5 m and subsequently bounces back to a height of 3.5 m. An
Energy Transformation in a Roller Coaster
A roller coaster car with a mass of 500 kg starts from rest at the top of a 20 m high hill and desce
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
Impact of Air Resistance on Energy Conservation
In an experiment, two objects—a smooth sphere and a flat plate—are dropped from a height of 15 m. Th
Interpreting a Displacement vs. Time Chart for Work and Power
A constant horizontal force of $$50 N$$ is applied to a block. The following table shows the displac
Investigating Work Done on a Spring: Variable Force Analysis
Design an experiment to measure the work required to compress a spring, where the force applied is v
Investigation of Work on an Inclined Plane
A group of students conducts an experiment to analyze the work done on a block sliding on a friction
Lifting a Dumbbell at an Angle
A person lifts a 10 kg dumbbell from the floor by applying a force at an angle of 30° above the hori
Pendulum Energy Conservation and Nonconservative Forces
In this experiment, a student sets up a pendulum and measures its maximum height and the speed at it
Roller Coaster Energy Analysis
A roller coaster car of mass 500 kg is released from rest at a height of 30 m. Compute its speed at
Rolling Motion and Energy Distribution
A solid cylinder (mass = 4 kg, radius = 0.2 m) rolls without slipping down an incline of height 5 m.
Work and Power in a Hydraulic Lift
A hydraulic lift raises a car with a mass of $$1200\,kg$$ a vertical distance of $$2.0\,m$$ in $$10\
Work and Power: Variable Force Analysis
An experiment is conducted in which a variable force is applied to an object over a displacement. Th
Work at an Angle: Experimental Analysis
A recent experiment measures the work done on a block when a force is applied at different angles re
Work Done Lifting a Weight
A person lifts a 50 kg weight vertically upward by 2 m. Use $$g = 9.8\,m/s^2$$. Answer the following
Work-Energy Analysis in a Car Braking System
A car with a mass of $$1200\;kg$$ is traveling at $$25\;m/s$$ when the brakes are applied, generatin
2D Momentum Conservation Analysis
In a two-dimensional collision, two objects exhibit the following velocities (in m/s) before and aft
Automotive Crumple Zone Analysis
Engineers are analyzing the performance of crumple zones in automobiles during collisions. A car of
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: Elastic vs Inelastic
In a collision experiment, two carts with masses $$m_1 = 1$$ kg and $$m_2 = 2$$ kg are used. In one
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
Comparing Elastic and Inelastic Collisions
Two objects undergo collisions under different conditions. Experiment 1 features an elastic collisio
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
Erroneous Application of Momentum Conservation in Explosive Separations
In this experiment, an object is exploded into two fragments by a small charge, and the velocities o
Evaluating Momentum in Multi-Stage Collisions
A system of three objects (A, B, and C) on a frictionless track undergoes sequential collisions. Dat
Explosive Separation in a Projectile
A projectile of total mass 5.0 kg explodes mid-air into two fragments. One fragment has a mass of 3.
Impulse and Force‐Time Analysis
An object initially at rest is subjected to a time-dependent force during an experiment. The impulse
Impulse and Momentum in Baseball Bat Design
Engineers are investigating how the mass and swing speed of a baseball bat affect the impulse delive
Impulse Applied to Varying Masses
In a physics lab, a constant impulse of $$10$$ Ns is applied separately to two objects of different
Impulse from a Time-Dependent Force
A force acting on an object varies with time according to the equation $$F(t) = 3*t$$ N for $$0 \leq
Investigating the Coefficient of Restitution
A 0.3 kg ball is dropped from a height of 2.0 m and bounces to a height of 1.2 m. The contact time w
Momentum and Safety Design in Car Crashes
Modern cars use design features like airbags and crumple zones to manage the impulse experienced dur
Momentum Change Due to Variable Force
An object with a mass of 2 kg initially moves at 2 m/s. After a variable force acts on it over a 3-s
Momentum Measurement Error in Cart Collision Experiment
In this experiment, students attempted to measure the momentum of a cart on a frictionless track. Th
Momentum Transfer in a Baseball Collision
A baseball (mass $$0.145\,\text{kg}$$) is pitched toward a batter at $$40\,\text{m/s}$$. Upon being
Momentum Transfer in a Baseball Collision
A 0.145 kg baseball is traveling at 40 m/s towards a bat. After being hit, it rebounds in the opposi
Oblique Collision in Billiards
In a game of billiards, a cue ball of mass $$0.17\,\text{kg}$$ traveling at $$2\,\text{m/s}$$ strike
Oblique Collision in Two Dimensions
Two ice hockey pucks collide on a frictionless rink. Puck A (0.15 kg) is moving southeast at 10 m/s,
Pendulum and Cart Collision Dynamics
A 2.0 kg pendulum bob is suspended and released from rest so that at its lowest point it collides wi
Rebound Motion and Momentum Change
A ball is dropped from a height and rebounds off the ground. During the collision with the ground, t
Soccer Player Collision Analysis
During a soccer match, two players collide. Player A (mass 70 kg) is running at 6 m/s and Player B (
Traffic Safety and Momentum in Multi-Car Collisions
A traffic safety study reconstructs a multi-car collision where several vehicles collide and move to
Two-Body Collision Analysis
Two vehicles collide at an intersection. Vehicle A (mass 1200 kg) is traveling east at 15.0 m/s and
Two-Dimensional Collision Analysis
On a nearly frictionless air hockey table, two pucks (mass = 0.2 kg each) collide elastically. Puck
Two-Dimensional Collision Analysis
Two hockey pucks on an air-cushioned table undergo a collision. Their initial data are provided in t
Two-Dimensional Collision Analysis
Two objects collide on a frictionless surface. Object A with mass $$2\,\text{kg}$$ is moving east at
Two-Dimensional Collision with Angular Components
Two objects on a frictionless surface collide. Object A (mass $$1.5$$ kg) is moving at $$4$$ m/s hor
Underestimating the Role of Impulse in Variable Force Applications
In this experiment, a cart is subjected to a force from a mechanical actuator designed to change its
Acceleration Derivation in SHM
Given the displacement function $$x(t)=A*cos(ω*t+φ)$$, answer the following: (a) Derive the correspo
Adapting SHM for Seismic Measurement
Seismometers use principles of SHM to detect and measure ground motion. Consider a design using a ma
Amplitude Independence of Period in SHM
In ideal simple harmonic motion, the period is independent of the amplitude. Answer the following pa
Calculating Energy Loss in a Damped Oscillator
In a damped oscillator, the amplitude decays over time due to energy dissipation. (a) Derive the ex
Comparative Analysis: Mass-Spring vs. Pendulum SHM
Two experiments are conducted: one with a mass-spring oscillator and one with a simple pendulum. Bot
Comparative Dynamics: Pendulum vs. Mass-Spring System
Compare the dynamics of a simple pendulum and a mass-spring oscillator.
Comparative Study: Mass-Spring System vs. Pendulum
Compare a mass-spring oscillator and a simple pendulum, noting that both systems exhibit simple harm
Comparison of Pendulum and Spring Systems
Compare the factors that affect the period of oscillation in a mass-spring system versus a simple pe
Damped Harmonic Oscillation Experiment
An experiment involving a mass-spring system is modified by attaching a damping mechanism (such as a
Effect of Damping on Oscillatory Motion
Real oscillatory systems can experience damping. Consider a damped mass-spring system with displacem
Effect of Phase Angle on SHM Motion
A researcher studies the effect of changing the phase angle $$\phi$$ in the SHM equation $$x = A \co
Energy Conversion in SHM
A mass-spring system undergoing simple harmonic motion has amplitude $$A$$ and spring constant $$k$$
Experimental Determination of Spring Constant
Using experimental data, determine the spring constant of a given spring.
Exploring SHM in Pendulums
Examine the validity of the small-angle approximation used in simple pendulum motion.
Forced Oscillations and Resonance
A mass-spring system is subjected to an external periodic driving force described by $$F = F_0*\cos(
Graphical Estimation of SHM Parameters
A researcher obtains a graph of angular displacement versus time for a pendulum. The following graph
Investigating the Impact of Changing Mass on Oscillation Frequency
A researcher increases the mass attached to a spring and records the oscillation period for each cha
Mass Variation in SHM
A series of experiments was performed using a mass-spring system with different masses. The measured
Mass-Spring Oscillator Analysis
A researcher studies a mass attached to a spring on a frictionless surface exhibiting simple harmoni
Nonlinear Effects in Pendulum Motion
For a pendulum undergoing large amplitude oscillations, the period deviates from the simple harmonic
Nonlinear Restoring Forces and Limitations of SHM
In many real systems the restoring force deviates from Hooke’s law at large displacements. (a) Expl
Pendulum Period Analysis
A simple pendulum with a length of $$L = 1.0 m$$ is undergoing small-angle oscillations under gravit
Phase Angle Determination in SHM
Determine the phase angle in a mass-spring oscillator using initial conditions.
Phase Angle Influence in SHM
A set of experiments measured the initial displacement of an oscillator at time t = 0 for different
Phase Difference and Interference in Coupled Oscillatory Systems
Two identical mass-spring oscillators, each given by $$x(t) = A \cos(\omega*t + \phi)$$, oscillate w
Photogate Oscillation Measurements
A mass-spring oscillator is timed using a photogate for 10 oscillations across four trials. The reco
Resonance and Energy Absorption in Driven Oscillators
In a driven harmonic oscillator, the amplitude is maximized at resonance where energy absorption is
Resonance in Driven Damped Oscillators
A driven, damped oscillator is described by the equation $$m\frac{d^2x}{dt^2}+b\frac{dx}{dt}+kx=F_0\
Role of Resonance in SHM
A mass-spring system is driven by an external periodic force. Although damping is neglected, answer
Small Angle Approximation in Pendulum Motion
For a simple pendulum, the small-angle approximation allows its motion to be approximated as simple
Analysis of Angular and Linear Motion on a Rotating Rod
A researcher investigates a uniform rod of length 2 m, pivoted at one end, which rotates at a consta
Angular Acceleration and Velocity
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