Expert answer:PHYS100 Lab 5 Collisions
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PHYS-100 Lab #5: Collisions
American University Physics Department
“The purpose of models is not to fit the data, but to sharpen the questions” – Samuel Karlin
Learning Objectives:
Use video tracking to analyze one-dimensional, linear motion,
Understand and measure kinematic quantities that can be used to elucidate conservation laws,
Understand elastic and inelastic collisions.
Theory:
Conservation laws are powerful tools that scientists use to analyze a
diversity of problems. Within the context of mechanics, a vast number
of problems can be solved by simultaneously conserving momentum
and mechanical energy.
Conservation of linear and angular momentum are said to be exact
laws, that is, these laws have never been shown to be experimentally
violated. Stating that momentum is conserved is the same as saying
that the initial momentum is equal to the final momentum in a closed
system of particles,
⃑ = ⃑
If there are two particles within this closed system, we may rewrite this as,
⃑1 + ⃑2 = ⃑1 + ⃑2
Suppose the two masses m1 and m2 have initial velocities v1i and v2i and final velocities v1f and v2f, respectively. If
only linear or translational momentum is considered, then the conservation of momentum may be rewritten as,
1 ⃑1 + 2 ⃑2 = 1 ⃑1 + 1 ⃑2
It is this result that we will attempt to confirm through empirical evidence.
Conservation of Energy is another exact law, but is more comprehensive in scope. Not only can energy be
contained within the movement of an object (kinetic energy), but it might also manifest itself as thermal energy,
electric energy, wave energy or chemical energy, to name just a few. For our purposes, we shall only consider
kinetic energy. In a perfectly elastic collision, total mechanical energy is conserved,
=
As we only care about the objects’ behavior immediately before and after the collision, mechanical potential
energy can be neglected. Using the definition of kinetic energy for our two particles when no external work on
the system is done we find,
1
1
1
1
2
2
2
2
=
⟹
1 ⃑1
+ 2 ⃑2
= 1 ⃑1
+ 1 ⃑2
2
2
2
2
It should be emphasized that if kinetic energy is found to be not conserved, that does not mean conservation of
energy has been violated! Instead, the interaction under scrutiny has transformed mechanical energy into
another form of energy.
In conclusion, if a collision is found to conserve both momentum and kinetic energy it is said to be perfectly
elastic. If total kinetic energy is not conserved, the collision is said to be inelastic.
Procedure:
1. Using Tracker©, analyze three collision videos:
a. Import a selected collision video.
b. Create a calibration stick and adjust it to coincide with a known length.
c. Show the coordinate axes and move the origin to an appropriate location.
d. Create a point mass and use Autotracker to track Cart Mass #1.
e. Create a second point mass and use Autotracker to track Cart Mass #2.
f. Optionally, play with the vector tools to view the carts’ velocity vectors
g. Using the tools at your disposal (namely the Tracker© Analyze tool), measure the velocity
before and after the interaction.
h. Draw a diagram, like the one depicted above, of the before and after collision for each trial with
the appropriate labels, i.e. m1, m2, v1i, v1f, v2i and v2f.
i. In a spreadsheet, record and/or calculate the following information for each of your three trials:
Trial #
Mass Cart #1 [kg]
Mass Cart #2 [kg]
Initial Velocity Cart #1 [m/s]
Initial Velocity Cart #2 [m/s]
Final Velocity Cart #1 [m/s]
Final Velocity Cart #2 [m/s]
Initial Momentum Cart #1 [kg*m/s]
Initial Momentum Cart #2 [kg*m/s]
Final Momentum Cart #1 [kg*m/s]
Final Momentum Cart #2 [kg*m/s]
Total Initial Momentum [kg*m/s]
Total Final Momentum [kg*m/s]
Change in momentum [kg*m/s]
Initial Kinetic Energy Cart #1 [J]
Initial Kinetic Energy Cart #2 [J]
Final Kinetic Energy Cart #1 [J]
Final Kinetic Energy Cart #2 [J]
Total Initial Kinetic Energy [J]
Total Final Kinetic Energy [J]
Change in Kinetic Energy [J]
Post-Lab Tasks and Questions:
Please use complete sentences when answering the following questions. Answers may be provided in a bulleted
list or in paragraph form.
1. (2 points) For each of your trials, determine if linear momentum and kinetic energy are conserved.
Describe what information you used to determine this.
2. (2 points) Assume your data suggests that linear momentum and kinetic energy are not conserved.
Describe at least three sources of discrepancy that might cause this to be so.
3. (1 point) Which, if any, of your trials were elastic? Which trials were inelastic? To what data can you
refer to justify your answer?
Lab Report Checklist:
1. (9 points) Collision data table/spreadsheet
2. (6 points) Before/after collision drawings
3. (5 points) Post-Lab Tasks and Questions*
*Though you are encouraged to answer the Post-Lab Tasks and Questions during your lab session, these tasks
may be performed outside of the formal lab period if the time allotted is insufficient. Your spreadsheet data
table and plots must be signed by your instructor before you leave lab.
Trial #
Mass Cart #1 [kg]
(left)
Mass Cart #2 [kg]
(right)
Initial Velocity Cart
#1 [m/s]
Initial Velocity Cart
#2 [m/s]
Final Velocity Cart #1
[m/s]
Final Velocity Cart #2
[m/s]
Initial Momentum
Cart #1 [kg*m/s]
Initial Momentum
Cart #2 [kg*m/s]
Final Momentum
Cart #1 [kg*m/s]
Final Momentum
Cart #2 [kg*m/s]
Total Initial
Momentum [kg*m/s]
Total Final
Momentum [kg*m/s]
Change in
momentum [kg*m/s]
Initial Kinetic Energy
Cart #1 [J]
Initial Kinetic Energy
Cart #2 [J]
Final Kinetic Energy
Cart #1 [J]
Final Kinetic Energy
Cart #2 [J]
Total Initial Kinetic
Energy [J]
Total Final Kinetic
Energy [J]
Change in Kinetic
Energy [J]
1
2
3 Cart 1: Left Cart Cart 2: Right Cart
0,521
1,01
1,01
0,523
5,23
5,13
0
0
0
0
0
0
46
26
59
62
17
49
…
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