Momentum One Dimension Collision Model

The motion of a body of mass m and velocity v is described by a vector quantity known as momentum p where

p = m v

When objects collide, whether trains, cars, billiard balls, shopping carts, or your foot and the sidewalk, the results can be complicated. Yet even in the most chaotic of collisions, as long as there are no net external forces acting on the colliding objects, one principle always holds and provides an excellent tool for understanding the collision. That principle is called the conservation of linear momentum which states that

The total momentum of a system remains constant provided that no external resultant force acts on the system

For two bodies colliding linearly, it is written mathematically as a vector equation

Total initial momentum = total final momentum

m

_{1}.u

_{1} + m

_{2}.u

_{2} = m

_{1}.v

_{1} + m

_{2}.v

_{2}If external forces (such as friction) are ignored, the total momentum of two carts prior to a collision (left side of equation) is the same as the total momentum of the carts after the collision (right side of equation).

Collisions are classified into elastic (or perfectly elastic), inelastic and completely inelastic.

There is also a concept of kinetic energy of a moving body is stated mathematically by the following equation:

KE1 = ½ m

_{1}.v

_{1}2

Main Simulation View

The simulation has 2 collision carts on frictionless floor and wheels.

Sliders

Explore the sliders allows varying the variables .

* mass of cart ONE, mass_1, m

_{1} in kg

* initial velocity of cart ONE, u

_{1} in m/s

* mass of cart TWO, mass_2, m

_{2} in kg

* initial velocity of cart TWO, u

_{2} in m/s

Radio Buttons

Allows for selecting what kind of collision is simulated.

A Perfectly elastic collision is defined as one in which both conservation of momentum and conservation of kinetic energy are observed

A Perfectly Inelastic collision is defined as one in which conservation of momentum is observed but the colliding carts stick together after collision with kinetic energy loss

Checkboxes

show: velocity, for visualizing the velocity vector

plot momentum vs time graph, for different representation of data for momentum of cart 1, 2 and both.

plot kinetic energy vs time graph, for different representation of data for kinetic energy of cart 1, 2 and both.

paused when collide, for visualizing the change in the velocity u

_{1} and u

_{2} to v

_{1} and v2

_{}fast simulation, for cases where the velocity are low and repeat learners can spend time more usefully collecting and analysing data.

hint: COM, for the equation of conservation of momentum

hint: COKE, or the equation of conservation of kinetic energy

Buttons

Play

Step Back

Step Forward

Initialize

Reset

have their usual meaning.

known bug is the Step Back button implementation, please fix it if you can and email me the improved source XML.

Credits:

The Momentum 1D Collision model was created by created by lookang using the Easy Java Simulations (EJS) version 4.2 authoring and modeling tool. An applet version of this model is available on the NTNU website

. Shout our thanks to the Ejs community namely, Francisco Esquembre , Fu-Kwun Hwang and Wolfgang Christian for their professional learning community support. You can examine and modify this compiled EJS model if you run the model (double click on the model's jar file), right-click within a plot, and select "Open EJS Model" from the pop-up menu. You must, of course, have EJS installed on your computer. Information about EJS is available at: http://www.um.es/fem/Ejs/ and in the OSP comPADRE collection http://www.compadre.org/OSP/.

Leveraging on Easy Java Simulation tool and Open Source computer simulation library to create interactive d...

Leveraging on Easy Java Simulation tool and open source computer simulation library to create interactive d...

virtual laboratory simulation for One Dimension collision of two carts allowing inquiry learning for elastic and inelastic studies.

Thanks To Professor Fu-Kwun Hwang for guidance and Professor Francisco Esquembre for EJS and the open source digital library source codes.

My java interactive digital media applet

http://home.phy.ntnu.edu.tw/~lookang/EJS_4.1_081216/Collision1Dwee.html

http://home.phy.ntnu.edu.tw/~lookang/EJS_4.1_090115/Collision1Dwee.html newer

http://home.phy.ntnu.edu.tw/~lookang/EJS_4.1_090208/Collision1Dwee01.html

Good applet model reference:

http://www.walter-fendt.de/ph14e/collision.htm

License:

http://creativecommons.org/licenses/by-sa/3.0/sg/

Original code from by Prof. Paco

F:EasyJavaSimulationEJS_4.1_081216EJS_4.1workspacesourceusersmurciafemphysicsmechanicsCollision1D.xml

1 D collision for analysis with Elastic and Inelastic Collision by lookang

Collision 1D

This is a simulation of a one-dimensional collision of two rigid disks.

It is a simple example of the event-handling features of the ODE solvers in Easy Java Simulations.

**source code**

download the *.jar for using the applet on standalone without internet connection.

**if you want to recompile without errors with the worksheet graphics, download the 1.4MB jar, expand it, copy the folder Collision1Dwee01 into the source folder location, it should recompile nicely with all graphics available! **

Modifications done are:

1. rigid rectangles

2. added wheels

3. added floor

4. added panel for inputs

5. added coefficient of restitution e, http://en.wikipedia.org/wiki/Inelastic_collision

6. added plot of KE vs t and Momentum vs t

7. change look for object 1 is RED and object 2 is blue

8. added checkbox for view of plot

9. added buttons of elastic and inelastic selection

10. change buttons to open-source physics.org default ones

11. added deterministic equations C.O.K.E. and C.O.M.

12. added view zoom slider

13. added color change easy

14. added enable buttons only at start of simulation

15. added slider for m1 m2 v1 v2 with closest ticker for inquiry learning

16. added calculation for tcollision and tmaxleft and tmaxright

17. added enable play button only if collision occurs in the view max

18. added stepback() function by using dt = -dt with if else statement

19. added stepforward() function to replace _step() as need a way to remember dt

20. added wheelAngle to rotate the wheel

21. added mass1 and mass2 stored values after reset through a work around after considering initialise method but i decide to do the reset method.

22. added bigger arrows and texts before and after tcollision to alert learners to difference in u1, u2 and v1 ,v2

23. added before hint is shown for t < tcollision

24. added physical detection when press cart1 and cart2, to prevent overlap of carts

25. fix some bugs on enable play button for detecting collision in screen

26. known bug of u1 =0.5 and u2 = 0.5, the play button is still allow........ strange?

27. rearrange the codes for housekeeping less messy

March 11 2009

28. redesign to make look wheel more circle

29. remove hints to suit request to try without from school

30. rearrange bottom panel

31. make graphs to show by default

March 19 2009

32. added graphics of springs and velcro for elastic and inelastic collision

33. added checkbox for values of

m_{1}u_{1}=, m_{2}u_{2}= m_{1}u_{1}+ m_{2}u_{2}=,

m_{1}v_{1}=, m_{2}v_{2}= m_{1}v_{1}+ m_{2}v_{2}=,

0.5m_{1}u_{1}2= and so on to aid data analysis in worksheet activity, for pattern recognition

March 20 2009

34. added magnets for elastic and velcro for inelastic now with tooltips!

March 21 2009

35. changed to spring for elastic

36. redesign the table for values

January 21 2010

37 fixed a bug of the velcro and springs not draggable and dislocate the carts, now it is activated by on press and on exit, sensitivity at 10 to make it easily to mouse over the velcro TT and spring

January 24 2010 only Available on the standalone jar file http://www.phy.ntnu.edu.tw/ntnujava/index.php?action=dlattach;topic=831.0;attach=1628

38 modify the codes to show partial inelastic collision with an input field of e = 0

39 modify partial to Math.random()

40 remove the number of ticks and closest "false" in order to deploy as a web applet

41 added input field for velocity u1 and u2

42 the appears to be an issue of stability after using Ejs 4.2.7 to compile the source codes, i will investigate and try Ejs 4.2 to test out the codes

March 6 2010

43 made the text for graph click-able as the check-box

44 set x max to tmax as requested by leongster, improving the visual learning of interpretation of the graphs instead of auto-scale immediately

March10 2010

45 added centre of mass as inspired by tatlee08 and http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=5.msg5482;topicseen#msg5482

15 April 2010

46 Fixed an input field of e to be allow to take values from user to allow exploration of e, technique used is assign es to the field

47 made the bottom smaller to fit into the view of width = 750 when web deployed

realized guest accounts canot see attachment which makes my *.jar almost difficult to find by interested learners.

April23 2010

48 increased the sensitivity of cart1 and 2 for ease of drag of carts instead of the exact center

49 added codes to prevent the applet from jamming when the carts are placed at extreme left and right by inserting +0.001 and -0.001 into the x positions of the carts thanks to HY LEE for finding the bug.

50 fixed a calculation of tcollision, remove from evolution page, only in initialization page now because the calculation is deterministic.

18May2010

51 fixed a bug with the time due to the introduction of 49, added -0.001 and +0.001 to the left and right side of the extreme

if (x1>=(max-radius1-0.001) || x1<=(-max+radius1+0.001) || x2>=(max-radius2-0.001)|| x2<=(-max+radius1+0.001))

{

_pause();

}

52 added the worksheets and suggested answer key into the jar file for ease of scaling to other classrooms in the world

53 added portuguese language translated by ahmedelshfie, thanks!

26May2010

54 added game like assessment of learning input fields for students to check for understanding thanks to student feedback from rvhs http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=831.msg6291#msg6291

55 made color background of last column uniform

29May2010

56 finer customization of assessment for learning game feedback now recognize elastic and inelastic and partial

57 added sound effect for collision for partial and inelastic, elastic has no sound because real life use like poles of a magnet to repel simulate collision refer to http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=824.0 for sound adding

58 added data analysis tool for graphs data like tracker

59 worksheets and suggested answer all packed inside the jar, 1.6 mb file now.

15 June 2010

60 remove the "pause when collide" checkbox since it seems to not work anymore

61 width = 600 resized

31 March 2011

made all the vectors point to the right by adding Math.abs() for consistent pen paper discussion

made the table editable for clearer values though it cannot be edited, for journal paper graphics

i started doing html again in EJS4.1 16 dec 2008 version

this is another world class applet in my view, built on the strengths of open source, and contribution by great man like prof paco and prof hwang.

addition improved in next version:

a prediction of collision before showing the 2 equations of MOM and COKE because it did not collide and the equations shown are for assumed the is a collision.

any help is appreciated