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Having done that, you can rotate the axis by the same amount in the opposite direction at the end to cause the final solution to apply to the original axes.I will present an example of this in the next section.

Example scenarios

Several examples

I will use the information in Figure 1 to analyze several scenarios involving collisions in both one dimension and two dimensions in this section.

The use of JavaScript

All of these examples could be solved using the Google calculator. However, several steps are involved and I find it easier to keep things organized andperform the steps in the correct order by using JavaScript to compute and display the solution.

Note, however, that JavaScript will only do the arithmetic for you. You must still do the algebra/trigonometry yourself. In these examples, I willusually work through the algebra in comment sections and switch to actual code when it is time to compute and display one or more values.

One-dimensional scenarios

The first one-dimensional scenario involves an automobile accident.

The rear end car crash

The description as well as the solution to the problem are shown in Listing 1 .

Listing 1 . The rear end car crash.
<!---------------- File JavaScript01.html ---------------------><html><body><script language="JavaScript1.3">/* This script simulates car #2 rear-ending car #1 in aone-dimensional elastic collision while car #1 was stopped. The script computes and displays the speed of car #2immediately before the collision under the assumption that car #1 was moving at 20 m/s just after the collision.Using conservation of momentum alone, we have two equations, allowing us to solve for two unknowns.m1*u1x + m2*u2x = m1*v1x + m2*v2x m1*u1y + m2*u2y = m1*v1y + m2*v2yUsing conservation of kinetic energy for the elastic case gives us one additional equation, allowing usto solve for three unknowns. 0.5*m1*u1^2 + 0.5*m2*u2^2 = 0.5*m1*v1^2 + 0.5*m2*v2^2Variables: m1, m2, u1, u2, v1, v2, a1, a2, b1, b2*/ document.write("Start Script</br>"); //Solve for u2 and v2 for an elastic collisionvar m1 = 1500;//kg var m2 = 2000;//kg//Velocities before the collision var u1 = 0;//meters per second - standing stillvar u2;//unknown value to be determined //Velocities after the collisionvar v1 = 20;//meters/second var v2;//unknown value to be determined//Angles var a1 = 0;//car was not movingvar a2 = 0;//moving straight ahead var b1 = 0;//moving straight aheadvar b2 = 0;//moving straight ahead //Convert angles to radiansA1 = a1*Math.PI/180; A2 = a2*Math.PI/180;B1 = b1*Math.PI/180; B2 = b2*Math.PI/180;//Compute and print the x and y components of velocity u1x = u1*Math.cos(A1)u1y = u1*Math.sin(A1) //u2x = u2*Math.cos(A2)//unknown//u2y = u2*Math.sin(A2)//unknown v1x = v1*Math.cos(B1)v1y = v1*Math.sin(B1) //v2x = v2*Math.cos(B2)//unknown//v2y = v2*Math.sin(B2)//unknown document.write("x and y components of velocity</br>"); document.write("u1x = " + u1x.toFixed(3) + "</br>"); document.write("u1y = " + u1y.toFixed(3) + "</br>"); document.write("v1x = " + v1x.toFixed(3) + "</br>"); document.write("v1y = " + v1y.toFixed(3) + "</br>"); document.write("==============================="+ "</br>"); /*Prepare the equations for use in solving the problem. Given the following three equationsm1*u1x + m2*u2x = m1*v1x + m2*v2x m1*u1y + m2*u2y = m1*v1y + m2*v2y0.5*m1*u1^2 + 0.5*m2*u2^2 = 0.5*m1*v1^2 + 0.5*m2*v2^2 Eliminate all of the components for which the above printoutshows zero or for which the given values show zero. 0 + m2*u2x = m1*v1x + m2*v2x0 + m2*u2y = 0 + m2*v2y 0 + 0.5*m2*u2^2 = 0.5*m1*v1^2 + 0.5*m2*v2^2Although it isn't totally obvious from the equations, at this point we need to recognize that because all velocities aredefined to occur along the x-axis, all of the terms in the middle equation above that deals with the y-component ofvelocity must be zero. Therefore, we can eliminate that equation entirely.We also need to recognize that because there are no velocity components along the y-axis, the velocity components alongthe x-axis are actually the magnitudes of those velocity components. Thus, u2x = u2.Now we will make the substitutions and eliminate terms with a value of 0 in the process, yieldingm2*u2 = m1*v1 + m2*v2 0.5*m2*u2^2 = 0.5*m1*v1^2 + 0.5*m2*v2^2Substituting known values into the two equations yields 2000*u2 = 1500*20 + 2000*v22000*u2^2 = 1500*20*20 + 2000*v2^2 Simplifying the two equations yieldsu2 = 15 + v2 u2*u2 = 300 + v2*v2Now we need to eliminate one equation through substitution v2 = u2 - 15u2*u2 = 300 + (u2 - 15)*(u2 - 15) u2*u2 = 300 + u2*u2 - 30*u2 +225u2*u2 - 300 - u2*u2 + 30*u2 -225 = 0 u2*u2 - u2*u2 + 30*u2 - 300 -225 = 030*u2 - 525 = 0 30*u2 = 525*/ //Compute and print the first speed valuedocument.write("Speed values</br>"); u2 = 525/30;document.write("u2 = " + u2.toFixed(2) + " m/s</br>"); /*Substituting this value back into an earlier energy equation yieldsv2*v2 = u2*u2 - 300; *///Compute and display the second speed value v2 = Math.sqrt(u2*u2 - 300);document.write("v2 = " + v2.toFixed(2) + " m/s</br>"); document.write("==============================="+ "</br>"); //Check the answers for conservation of momentumdocument.write("Check for conservation of momentum</br>"); var mou = m1*u1 + m2*u2;var mov = m1*v1 + m2*v2; document.write("mou = " + mou.toFixed(0) + " Kg*m/s</br>"); document.write("mov = " + mov.toFixed(0) + " Kg*m/s</br>"); document.write("==============================="+ "</br>"); //Check the answer for elastic collisionvar keIn = 0.5*m1*u1*u1 + 0.5*m2*u2*u2; var keOut = 0.5*m1*v1*v1 + 0.5*m2*v2*v2;document.write("Check for conservation of energy</br>"); document.write("keIn = " + keIn.toFixed(0)+ " Kg*m^2/s^2</br>"); document.write("keOut = " + keOut.toFixed(0)+ " Kg*m^2/s^2</br>"); document.write("End Script");</script></body></html>

Questions & Answers

so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
what is the k.e before it land
what is the function of carbon nanotubes?
I'm interested in nanotube
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
what is system testing
what is the application of nanotechnology?
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
anybody can imagine what will be happen after 100 years from now in nano tech world
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
silver nanoparticles could handle the job?
not now but maybe in future only AgNP maybe any other nanomaterials
I'm interested in Nanotube
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Accessible physics concepts for blind students. OpenStax CNX. Oct 02, 2015 Download for free at https://legacy.cnx.org/content/col11294/1.36
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