3.4 Elastic Collisions Lab
Interactive Lab: Elastic Collisions Lab
Follow this link to the Collision Lab, complete the lab below. Note that you will be asked to complete a similar task in Lesson 1.3 of Assignment 2.
Problem
Is momentum conserved in a linear collision?
Procedure
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Perform three different collisions using the Collision 1D Simulator, and complete the data tables in the Observations section.
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For clarity on the simulator, toggle "more data"
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Adjust the mass values of the balls by deleting the values in the table and then entering the values below.
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The following equations will be required to complete the tables:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8710;«/mo»«mover»«mi»v«/mi»«mo»§#8594;«/mo»«/mover»«mo»=«/mo»«msub»«mover»«mi»v«/mi»«mo»§#8594;«/mo»«/mover»«mrow»«mi»f«/mi»«mi»i«/mi»«mi»n«/mi»«mi»a«/mi»«mi»l«/mi»«/mrow»«/msub»«mo»-«/mo»«msub»«mover»«mi»v«/mi»«mo»§#8594;«/mo»«/mover»«mrow»«mi»i«/mi»«mi»n«/mi»«mi»t«/mi»«mi»i«/mi»«mi»a«/mi»«mi»l«/mi»«/mrow»«/msub»«mo»§#160;«/mo»«mspace linebreak=¨newline¨»«/mspace»«mo»§#8710;«/mo»«mover»«mi»p«/mi»«mo»§#8594;«/mo»«/mover»«mo»=«/mo»«msub»«mover»«mi»p«/mi»«mo»§#8594;«/mo»«/mover»«mrow»«mi»f«/mi»«mi»i«/mi»«mi»n«/mi»«mi»a«/mi»«mi»l«/mi»«/mrow»«/msub»«mo»-«/mo»«msub»«mover»«mi»p«/mi»«mo»§#8594;«/mo»«/mover»«mrow»«mi»i«/mi»«mi»n«/mi»«mi»t«/mi»«mi»i«/mi»«mi»a«/mi»«mi»l«/mi»«/mrow»«/msub»«/math»
Observations
Record your observations for the three collisions in a table similar to the example below.Collision 1 (Example data)
| Object |
mass (kg) |
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle indentalign=¨center¨ mathsize=¨16px¨»«msub»«mover mathcolor=¨#FFFFFF¨»«mi mathvariant=¨bold¨»v«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mrow mathcolor=¨#FFFFFF¨»«mi mathvariant=¨bold¨»i«/mi»«mi mathvariant=¨bold¨»n«/mi»«mi mathvariant=¨bold¨»i«/mi»«mi mathvariant=¨bold¨»t«/mi»«mi mathvariant=¨bold¨»a«/mi»«mi mathvariant=¨bold¨»l«/mi»«/mrow»«/msub»«mspace linebreak=¨newline¨»«/mspace»«mfenced mathcolor=¨#FFFFFF¨»«mfrac bevelled=¨true¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«/mfenced»«/mstyle»«/math» | «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨16px¨»«mstyle indentalign=¨center¨»«msub»«mover mathcolor=¨#FFFFFF¨»«mi mathvariant=¨bold¨»v«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mi mathvariant=¨bold¨ mathcolor=¨#FFFFFF¨»final«/mi»«/msub»«mspace linebreak=¨newline¨»«/mspace»«mfenced mathcolor=¨#FFFFFF¨»«mfrac bevelled=¨true¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«/mfenced»«/mstyle»«/mstyle»«/math» | «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨16px¨»«mstyle indentalign=¨center¨»«mo mathvariant=¨bold¨ mathcolor=¨#FFFFFF¨»§#8710;«/mo»«mover mathcolor=¨#FFFFFF¨»«mi mathvariant=¨bold¨»v«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mspace linebreak=¨newline¨»«/mspace»«mfenced mathcolor=¨#FFFFFF¨»«mfrac bevelled=¨true¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«/mfenced»«/mstyle»«/mstyle»«/math» | «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle indentalign=¨center¨»«msub»«mover mathcolor=¨#FFFFFF¨»«mi mathvariant=¨bold¨»p«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mrow mathcolor=¨#FFFFFF¨»«mi mathvariant=¨bold¨»i«/mi»«mi mathvariant=¨bold¨»n«/mi»«mi mathvariant=¨bold¨»i«/mi»«mi mathvariant=¨bold¨»t«/mi»«mi mathvariant=¨bold¨»i«/mi»«mi mathvariant=¨bold¨»a«/mi»«mi mathvariant=¨bold¨»l«/mi»«/mrow»«/msub»«mspace linebreak=¨newline¨»«/mspace»«mfenced mathcolor=¨#FFFFFF¨»«mrow»«mi mathvariant=¨bold¨»k«/mi»«mi mathvariant=¨bold¨»g«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mfrac bevelled=¨true¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«/mrow»«/mfenced»«/mstyle»«/math» | «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨16px¨»«mstyle indentalign=¨center¨»«msub»«mover mathcolor=¨#FFFFFF¨»«mi mathvariant=¨bold¨»p«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mrow mathcolor=¨#FFFFFF¨»«mi mathvariant=¨bold¨»f«/mi»«mi mathvariant=¨bold¨»i«/mi»«mi mathvariant=¨bold¨»n«/mi»«mi mathvariant=¨bold¨»a«/mi»«mi mathvariant=¨bold¨»l«/mi»«/mrow»«/msub»«mspace linebreak=¨newline¨»«/mspace»«mfenced mathcolor=¨#FFFFFF¨»«mrow»«mi mathvariant=¨bold¨»kg«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mfrac bevelled=¨true¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«/mrow»«/mfenced»«/mstyle»«/mstyle»«/math» | «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨16px¨»«mstyle indentalign=¨center¨»«mo mathvariant=¨bold¨ mathcolor=¨#FFFFFF¨»§#8710;«/mo»«mover mathcolor=¨#FFFFFF¨»«mi mathvariant=¨bold¨»p«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mspace linebreak=¨newline¨»«/mspace»«mfenced mathcolor=¨#FFFFFF¨»«mfrac bevelled=¨true¨»«mrow»«mi mathvariant=¨bold¨»k«/mi»«mi mathvariant=¨bold¨»g«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»m«/mi»«/mrow»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«/mfenced»«/mstyle»«/mstyle»«/math» |
|---|---|---|---|---|---|---|---|
| blue | 4.0 | +8.0 | -0.86 |
-8.86 | +32 | -3.44 | -35.44 |
| green |
9.0 | 0 | +3.94 | +3.94 | 0 | +35.46 | +35.46 |
You should see an interesting connection between the changes in momentum of each mass: the changes in momentum should be equal, but the opposite. For example, if the blue mass has an increase in momentum, then the green mass has a decrease in
momentum by the same amount. This connection leads us to an important concept about momentum and what happens to the total momentum of a system in a collision.
Notice the following shorthand way of talking about the sum of the momenta of the blue and green masses. The capital Greek letter sigma (Σ) is often used to denote sums.
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mo»§#8721;«/mo»«mrow»«/mrow»«/munder»«mo».«/mo»«msub»«mover»«mi»p«/mi»«mo»§#8594;«/mo»«/mover»«mrow»«mi»i«/mi»«mi»n«/mi»«mi»i«/mi»«mi»t«/mi»«mi»i«/mi»«mi»a«/mi»«mi»l«/mi»«/mrow»«/msub»«mo»=«/mo»«msub»«mover»«mi»p«/mi»«mo»§#8594;«/mo»«/mover»«mrow»«mi»i«/mi»«mi»n«/mi»«mi»t«/mi»«mi»i«/mi»«mi»a«/mi»«mi»l«/mi»«mo»§#160;«/mo»«mi»g«/mi»«mi»r«/mi»«mi»e«/mi»«mi»e«/mi»«mi»n«/mi»«mo»§#160;«/mo»«mi»b«/mi»«mi»a«/mi»«mi»l«/mi»«mi»l«/mi»«/mrow»«/msub»«mo»+«/mo»«msub»«mover»«mi»p«/mi»«mo»§#8594;«/mo»«/mover»«mrow»«mi»i«/mi»«mi»n«/mi»«mi»t«/mi»«mi»i«/mi»«mi»a«/mi»«mi»l«/mi»«mo»§#160;«/mo»«mi»o«/mi»«mi»f«/mi»«mo»§#160;«/mo»«mi»b«/mi»«mi»l«/mi»«mi»u«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»b«/mi»«mi»a«/mi»«mi»l«/mi»«mi»l«/mi»«/mrow»«/msub»«mspace linebreak=¨newline¨»«/mspace»«munder»«mo»§#8721;«/mo»«mrow»«/mrow»«/munder»«mo».«/mo»«msub»«mover»«mi»p«/mi»«mo»§#8594;«/mo»«/mover»«mrow»«mi»f«/mi»«mi»i«/mi»«mi»n«/mi»«mi»a«/mi»«mi»l«/mi»«/mrow»«/msub»«mo»=«/mo»«msub»«mover»«mi»p«/mi»«mo»§#8594;«/mo»«/mover»«mrow»«mi»f«/mi»«mi»i«/mi»«mi»n«/mi»«mi»a«/mi»«mi»l«/mi»«mo»§#160;«/mo»«mi»g«/mi»«mi»r«/mi»«mi»e«/mi»«mi»e«/mi»«mi»n«/mi»«mo»§#160;«/mo»«mi»b«/mi»«mi»a«/mi»«mi»l«/mi»«mi»l«/mi»«/mrow»«/msub»«mo»+«/mo»«msub»«mover»«mi»p«/mi»«mo»§#8594;«/mo»«/mover»«mrow»«mi»f«/mi»«mi»i«/mi»«mi»n«/mi»«mi»a«/mi»«mi»l«/mi»«mo»§#160;«/mo»«mi»o«/mi»«mi»f«/mi»«mo»§#160;«/mo»«mi»b«/mi»«mi»l«/mi»«mi»u«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»b«/mi»«mi»a«/mi»«mi»l«/mi»«mi»l«/mi»«/mrow»«/msub»«/math»
Summarize your findings regarding momentum before and after the collision in the table below.
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Collision |
Total Initial
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨16px¨»«mrow»«mstyle displaystyle=¨false¨»«munder mathcolor=¨#FFFFFF¨»«mo mathvariant=¨bold¨»§#8721;«/mo»«mrow»«/mrow»«/munder»«/mstyle»«msub»«mover mathcolor=¨#FFFFFF¨»«mi mathvariant=¨bold¨»p«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mrow mathcolor=¨#FFFFFF¨»«mi mathvariant=¨bold¨»i«/mi»«mi mathvariant=¨bold¨»n«/mi»«mi mathvariant=¨bold¨»i«/mi»«mi mathvariant=¨bold¨»t«/mi»«mi mathvariant=¨bold¨»i«/mi»«mi mathvariant=¨bold¨»a«/mi»«mi mathvariant=¨bold¨»l«/mi»«/mrow»«/msub»«mspace linebreak=¨newline¨»«/mspace»«mfenced mathcolor=¨#FFFFFF¨»«mrow»«mi mathvariant=¨bold¨»k«/mi»«mi mathvariant=¨bold¨»g«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mfrac bevelled=¨true¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«/mrow»«/mfenced»«/mrow»«/mstyle»«/math» |
Total Final
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Is Momentum Conserved?
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Conclusion
Based on the lab activity, you should have found that the total momentum is conserved in a collision within an isolated system.