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The output
The output for this scenario is shown in Figure 4 .
Figure 4 . Output for an elastic collision between two pucks on friction-free ice. |
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Start Script
u1x = 2.00 m/su1y = 0.00 m/s
u2x = 0.00 m/su2y = 0.00 m/s
v1x = 0.50 m/sv1y = 0.87 m/s
v2x = 1.50 m/sv2y = -0.866 m/s
u1 = 2.00 m/su2 = 0.00 m/s
v1 = 1.00 m/s===============================
v2 = 1.73 m/sb2 = -30.00 degrees
===============================moux = 2.00 Kg*m/s
movx = 2.00 Kg*m/smouy = 0.00 Kg*m/s
movy = 0.00 Kg*m/smou = 2.00 Kg*m/s
mov = 2.00 Kg*m/s===============================
End Script |
Hopefully the comments in the script will be sufficient to explain the solution to this problem.
Listing 4 provides the description and the solution to a scenario involving a perfectly inelastic collision between two objects in a friction-free environmentmoving at odd angles. By odd angles, I mean that neither object is moving along either the x-axis or the y-axis, either before or after the collision.
Listing 4 . Perfectly inelastic collision between objects with odd angles. |
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<!---------------- File JavaScript03.html ---------------------><html><body><script language="JavaScript1.3">/*
Obj1 with a mass of 1 Kg and an initial velocity of 3000 m/sin a direction 67 degrees north of east collides in a perfectly
inelastic manner with Obj2, whose mass is also 1 Kg and whoseinitial velocity is 2000 m/s in a direction 45 degrees north of east.
Calculate (1) the angle of motion of the combined bodies,and (2) the magnitude of the momentum of the combined bodies
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*v2yVariables:
m1, m2, u1, u2, v1, v2, a1, a2, b1, b2*/
document.write("Start Script</br>");
var m1 = 1;//kgvar m2 = 1;//kg
var u1 = 3000;//meters per secondvar u2 = 2000;//meters per second
var v1;//unknown -- to be foundvar v2;//unknown -- to be found
var a1 = 67;//degreesvar a2 = 45;//degrees
var b1;//unknown -- to be foundvar b2;//unknown -- to be found
//Perfectly inelastic collision so v2=v1 and b2=b1//Convert angles to radians
A1 = a1*Math.PI/180;A2 = a2*Math.PI/180;
//B1 = b1*Math.PI/180;//unknown
//B2 = b2*Math.PI/180;//unknown//Compute the x and y components of velocity
u1x = u1*Math.cos(A1)u1y = u1*Math.sin(A1)
u2x = u2*Math.cos(A2)u2y = u2*Math.sin(A2)
//v1x = v1*Math.cos(B1)//unknown//v1y = v1*Math.sin(B1)//unknown
//v2x = v2*Math.cos(B2)//unknown//v2y = v2*Math.sin(B2)//unknown
/*For the special case of m2=m1=1 and v2=v1 (perfectly inelastic
collision) we can simplify the equations to the following:u1x + u2x = 2*v1x
u1y + u2y = 2*v1y*/
//Rearranging terms yieldsv1x = (u1x + u2x)/2
v1y = (u1y + u2y)/2//Knowing the x and y components of the final velocity, we can
// find the angle and magnitude asb1 = getAngle(v1x,v1y);
v1 = Math.sqrt(v1x*v1x + v1y*v1y);//Compute the momentum after the collision
var Px = v1x*(m1 + m2);var Py = v1y*(m1 + m2);
var Pmag = Math.sqrt(Px*Px + Py*Py);//Display the results
document.write("b1 = " + b1.toFixed(1) + " degrees</br>");
document.write("v1 = " + v1.toFixed(0) + " m/s</br>");
document.write("v1x = " + v1x.toFixed(0) + " m/s</br>");
document.write("v1y = " + v1y.toFixed(0) + " m/s</br>");
document.write("Px = " + Px.toFixed(0) + " Kg*m/s</br>");
document.write("Py = " + Py.toFixed(0) + " Kg*m/s</br>");
document.write("Pmag = " + Pmag.toFixed(0) + " Kg*m/s</br>");
document.write("==============================="+ "</br>");
//Check the answer for perfect inelastic collisionv2x = v1x;
v2y = v1y;v2 = v1;
var moux = u1x + u2x;var movx = v1x + v2x;
var mouy = u1y + u2y;var movy = v1y + v2y;
var mou = Math.sqrt(moux * moux + mouy * mouy);var mov = Math.sqrt(movx * movx + movy * movy);
document.write("moux = " + moux.toFixed(0) + " Kg*m/s</br>");
document.write("movx = " + movx.toFixed(0) + " Kg*m/s</br>");
document.write("mouy = " + mouy.toFixed(0) + " Kg*m/s</br>");
document.write("movy = " + movy.toFixed(0) + " Kg*m/s</br>");
document.write("mou = " + mou.toFixed(0) + " Kg*m/s</br>");
document.write("mov = " + mov.toFixed(0) + " Kg*m/s</br>");
document.write("==============================="+ "</br>");
//The purpose of this function is to receive the adjacent// and opposite side values for a right triangle and to
// return the angle in degrees in the correct quadrant.function getAngle(x,y){
if((x == 0)&&(y == 0)){
//Angle is indeterminate. Just return zero.return 0;
}else if((x == 0)&&(y>0)){
//Avoid divide by zero denominator.return 90;
}else if((x == 0)&&(y<0)){
//Avoid divide by zero denominator.return -90;
}else if((x<0)&&(y>= 0)){
//Correct to second quadrantreturn Math.atan(y/x)*180/Math.PI + 180;
}else if((x<0)&&(y<= 0)){
//Correct to third quadrantreturn Math.atan(y/x)*180/Math.PI + 180;
}else{//First and fourth quadrants. No correction required.
return Math.atan(y/x)*180/Math.PI;}//end else
}//end function getAngledocument.write("End Script");</script></body></html> |
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