Lab
Conservation of Momentum in Two-Dimensions
Printer Friendly Version
In this lab we will investigate conservation of linear momentum in two-dimensions by allowing a large metal ball bearing to roll down an incline and collide obliquely with a stationary, smaller ball bearing. Afterwards we will calculate the total kinetic energy of both balls before and after the collision to determine what percentage of the energy was lost during the collision.
Equipment Needed
As shown in the above picture, each group will need a ramp, white paper, carbon paper, large ball bearing, small ball bearing, a ruler and a protractor.
Experimental Procedure
Place the carbon paper ("inky side up" under the white target paper. Place the flat portion of the ramp on top of the white paper and use a pen to mark its edges.
Next place the small ball bearing slightly off to the side of the ramp so that the large ball bearing will strike it off-center after rolling down the ramp.
After the ball bearings collide, they will leave tracks on the BACK of your white target paper. Notice that you will be viewing a mirror image, that is, the small ball bearing's track will be on the bottom and the large ball bearing's track will be on the top.
Your next step will be to "connect the dots" for each track. Drawing your lines back until they cross.
Once the intersection has been found, you will use a protractor to draw in the "x-axis" for the collision. this is a line which is perpendicular to the front edge of the ramp which passes through the intersection of the tracks.
Next use a protractor to measure the angle that each track makes to your "x-axis." Read your protractor CAREFULLY to one-decimal place. Record your measurements on your target paper.
Refer to the following information for the next five questions.
Data
How high was the top of the ramp above the top of the table in cm?
What was the mass of the large ball bearing in grams, m
_{L}
?
What was the mass of the small ball bearing in grams, m
_{S}
?
At what angle did the large ball bearing leave the collision,
q
_{L}
?
At what angle did the small ball bearing leave the collision,
q
_{S}
?
Using conservation of energy methods, determine the velocity of the large ball bearing when it reached the bottom of the ramp, prior to its collision with the small ball bearing.
The velocity of the large ball bearing (in m/sec) when it reached the bottom of the ramp, v
_{ramp base}
, was
Refer to the following information for the next two questions.
Velocity Analysis
In this lab, each of the ball bearings leaves the collision at a unique angle and speed. To determine just how fast each one is moving, we will need to look at the equations for conservation of momentum in both the x- and y-directions.
Since the large ball bearing did NOT have any
y-momentum
prior to the collision, conservation of momentum tells us that the y-components of the momenta of the ball bearings after the collision must be equal and opposite; that is, they must add to zero.
Since you know the values for both of the ball bearings' masses (m
_{L}
and m
_{S}
) as well as the angles that their paths made to the x-axis (
q
_{L}
and
q
_{S}
) you can simplify this equation to one that only has two unknowns, v
_{fL}
and v
_{fS}
with their necessary coefficients. We will refer to that equation as
Equation #1
.
As far as the
x-momenta
are concerned, we can write a similar equations using the values for the horizontal components of each ball bearing. Remember that the large ball entered the collision moving completely in the x-direction.
Once again, you know the values for both of the ball bearings' masses (m
_{L}
and m
_{S}
) as well as the angles that their paths made to the x-axis (
q
_{L}
and
q
_{S}
) you can simplify this equation to one that only has two unknowns, v
_{fL}
and v
_{fS}
and their necessary coefficients. We will refer to this equation as
Equation #2
.
Now you must use simultaneous equations to solve for v
_{fL}
and v
_{fS}
. There are two easy methods:
The first method is called the
substitution method
and involves solving the first equation for v
_{fL}
in terms of v
_{fS}
and substituting its expression in to the second equation, giving you an equation with only v
_{fS}
. Find v
_{fS}
. Substituting v
_{fS}
back into the first equation, solve for v
_{fL}
.
The second method is called the
addition-subtraction method
and it involves matching the coefficients of either v
_{fL}
or v
_{fS}
so that you can either add the system to eliminate the variable or subtract the system. Once you know one value, substituting it back into either of the original equations will give you the correct value for the second variable.
What is the value of v
_{fL}
in m/sec?
What is the value of v
_{fS}
in m/sec?
Refer to the following information for the next five questions.
To finish our analysis, we need to calculate the total kinetic energy before the collision and the total kinetic energy after the collision and see how they compare.
Remember that the total KE before the collision is actually the large ball bearing's potential energy at the top of the ramp.
Recall the both ball bearings are translating as well as rotating across the target paper. So their kinetic energies need to include expressions for both KE
_{translational}
and KE
_{rotational}
.
1. What was the large ball bearing's total kinetic energy before the collision? Express your answer in Joules.
2. What was the large ball bearing's total kinetic energy after the collision? Express your answer in Joules.
3. What was the small ball bearing's total kinetic energy after the collision? Express your answer in Joules.
4. How many Joules of kinetic energy was lost during the collision?
5. What percent of the large ball bearing's original kinetic energy (Question #1) does this loss (Question #4) represent?
Related Documents
Lab:
Labs -
A Battering Ram
Labs -
A Photoelectric Effect Analogy
Labs -
A Physical Pendulum, The Parallel Axis Theorem and A Bit of Calculus
Labs -
Air Track Collisions
Labs -
Ballistic Pendulum
Labs -
Ballistic Pendulum: Muzzle Velocity
Labs -
Bouncing Steel Spheres
Labs -
Coefficient of Friction
Labs -
Coefficient of Friction
Labs -
Coefficient of Kinetic Friction (pulley, incline, block)
Labs -
Collision Pendulum: Muzzle Velocity
Labs -
Conservation of Energy and Vertical Circles
Labs -
Conservation of Momentum
Labs -
Density of an Unknown Fluid
Labs -
Falling Coffee Filters
Labs -
Force Table - Force Vectors in Equilibrium
Labs -
Impulse
Labs -
Inelastic Collision - Velocity of a Softball
Labs -
Inertial Mass
Labs -
LabPro: Newton's 2nd Law
Labs -
Loop-the-Loop
Labs -
Mass of a Paper Clip
Labs -
Mass of a Rolling Cart
Labs -
Moment of Inertia of a Bicycle Wheel
Labs -
Ramps: Sliding vs Rolling
Labs -
Relationship Between Tension in a String and Wave Speed
Labs -
Relationship Between Tension in a String and Wave Speed Along the String
Labs -
Roller Coaster, Projectile Motion, and Energy
Labs -
Rotational Inertia
Labs -
Rube Goldberg Challenge
Labs -
Spring Carts
Labs -
Static Equilibrium Lab
Labs -
Static Springs: Hooke's Law
Labs -
Static Springs: Hooke's Law
Labs -
Static Springs: LabPro Data for Hooke's Law
Labs -
Target Lab: Ball Bearing Rolling Down an Inclined Plane
Labs -
Terminal Velocity
Labs -
Video LAB: A Gravitron
Labs -
Video LAB: Ball Re-Bounding From a Wall
Labs -
Video Lab: Blowdart Colliding with Cart
Labs -
Video Lab: Cart Push #2 and #3
Labs -
Video LAB: Circular Motion
Labs -
Video Lab: Falling Coffee Filters
Labs -
Video Lab: M&M Collides with Pop Can
Labs -
Video Lab: Marble Collides with Ballistic Pendulum
Resource Lesson:
RL -
A Chart of Common Moments of Inertia
RL -
A Further Look at Angular Momentum
RL -
A Further Look at Impulse
RL -
Advanced Gravitational Forces
RL -
Air Resistance
RL -
Air Resistance: Terminal Velocity
RL -
APC: Work Notation
RL -
Center of Mass
RL -
Centripetal Acceleration and Angular Motion
RL -
Conservation of Energy and Springs
RL -
Discrete Masses: Center of Mass and Moment of Inertia
RL -
Energy Conservation in Simple Pendulums
RL -
Famous Discoveries: The Franck-Hertz Experiment
RL -
Forces Acting at an Angle
RL -
Freebody Diagrams
RL -
Gravitational Energy Wells
RL -
Hinged Board
RL -
Inclined Planes
RL -
Inertial vs Gravitational Mass
RL -
Introduction to Angular Momentum
RL -
Linear Momentum
RL -
Mechanical Energy
RL -
Momentum and Energy
RL -
Newton's Laws of Motion
RL -
Non-constant Resistance Forces
RL -
Potential Energy Functions
RL -
Principal of Least Action
RL -
Properties of Friction
RL -
Rolling and Slipping
RL -
Rotary Motion
RL -
Rotational Dynamics: Pivoting Rods
RL -
Rotational Dynamics: Pulleys
RL -
Rotational Dynamics: Rolling Spheres/Cylinders
RL -
Rotational Equilibrium
RL -
Rotational Kinematics
RL -
Rotational Kinetic Energy
RL -
Springs and Blocks
RL -
Springs: Hooke's Law
RL -
Static Equilibrium
RL -
Symmetries in Physics
RL -
Systems of Bodies
RL -
Tension Cases: Four Special Situations
RL -
The Law of Universal Gravitation
RL -
Thin Rods: Center of Mass
RL -
Thin Rods: Moment of Inertia
RL -
Torque: An Introduction
RL -
Universal Gravitation and Satellites
RL -
Universal Gravitation and Weight
RL -
What is Mass?
RL -
Work
RL -
Work and Energy
Worksheet:
APP -
Big Fist
APP -
Family Reunion
APP -
Puppy Love
APP -
The Antelope
APP -
The Baton Twirler
APP -
The Box Seat
APP -
The Jogger
APP -
The Pepsi Challenge
APP -
The Pet Rock
APP -
The Pool Game
APP -
The Raft
APP -
The See-Saw Scene
CP -
Action-Reaction #1
CP -
Action-Reaction #2
CP -
Center of Gravity
CP -
Conservation of Energy
CP -
Conservation of Momentum
CP -
Equilibrium on an Inclined Plane
CP -
Falling and Air Resistance
CP -
Force and Acceleration
CP -
Force and Weight
CP -
Force Vectors and the Parallelogram Rule
CP -
Freebody Diagrams
CP -
Gravitational Interactions
CP -
Incline Places: Force Vector Resultants
CP -
Incline Planes - Force Vector Components
CP -
Inertia
CP -
Mobiles: Rotational Equilibrium
CP -
Momentum
CP -
Momentum and Energy
CP -
Momentum and Kinetic Energy
CP -
Momentum Practice Problems
CP -
Momentum Systems and Conservation
CP -
Net Force
CP -
Newton's Law of Motion: Friction
CP -
Power Production
CP -
Satellites: Circular and Elliptical
CP -
Static Equilibrium
CP -
Tensions and Equilibrium
CP -
Torque Beams
CP -
Torque: Cams and Spools
CP -
Work and Energy
NT -
Acceleration
NT -
Air Resistance #1
NT -
An Apple on a Table
NT -
Apex #1
NT -
Apex #2
NT -
Center of Gravity
NT -
Center of Gravity vs Torque
NT -
Cliffs
NT -
Elliptical Orbits
NT -
Escape Velocity
NT -
Falling Rock
NT -
Falling Spheres
NT -
Falling Sticks
NT -
Friction
NT -
Frictionless Pulley
NT -
Gravitation #1
NT -
Gravitation #2
NT -
Head-on Collisions #1
NT -
Head-on Collisions #2
NT -
Ice Boat
NT -
Momentum
NT -
Ramps
NT -
Rolling Cans
NT -
Rolling Spool
NT -
Rotating Disk
NT -
Sailboats #1
NT -
Sailboats #2
NT -
Satellite Positions
NT -
Scale Reading
NT -
Settling
NT -
Skidding Distances
NT -
Spiral Tube
NT -
Tensile Strength
NT -
Terminal Velocity
NT -
Tug of War #1
NT -
Tug of War #2
NT -
Two-block Systems
WS -
Advanced Properties of Freely Falling Bodies #1
WS -
Advanced Properties of Freely Falling Bodies #2
WS -
Advanced Properties of Freely Falling Bodies #3
WS -
Calculating Force Components
WS -
Charged Projectiles in Uniform Electric Fields
WS -
Combining Kinematics and Dynamics
WS -
Distinguishing 2nd and 3rd Law Forces
WS -
Energy Methods: More Practice with Projectiles
WS -
Energy Methods: Projectiles
WS -
Energy/Work Vocabulary
WS -
Force vs Displacement Graphs
WS -
Freebody Diagrams #1
WS -
Freebody Diagrams #2
WS -
Freebody Diagrams #3
WS -
Freebody Diagrams #4
WS -
Introduction to Springs
WS -
Kinematics Along With Work/Energy
WS -
Lab Discussion: Gravitational Field Strength and the Acceleration Due to Gravity
WS -
Lab Discussion: Inertial and Gravitational Mass
WS -
Moment Arms
WS -
Moments of Inertia and Angular Momentum
WS -
net F = ma
WS -
Potential Energy Functions
WS -
Practice: Momentum and Energy #1
WS -
Practice: Momentum and Energy #2
WS -
Practice: Uniform Circular Motion
WS -
Practice: Vertical Circular Motion
WS -
Ropes and Pulleys in Static Equilibrium
WS -
Rotational Kinetic Energy
WS -
Standard Model: Particles and Forces
WS -
Static Springs: The Basics
WS -
Torque: Rotational Equilibrium Problems
WS -
Vocabulary for Newton's Laws
WS -
Work and Energy Practice: An Assortment of Situations
WS -
Work and Energy Practice: Forces at Angles
TB -
Basic Torque Problems
TB -
Center of Mass (Discrete Collections)
TB -
Moment of Inertia (Discrete Collections)
TB -
Rotational Kinematics
TB -
Rotational Kinematics #2
TB -
Systems of Bodies (including pulleys)
TB -
Work, Power, Kinetic Energy
PhysicsLAB
Copyright © 1997-2020
Catharine H. Colwell
All rights reserved.
Application Programmer
Mark Acton