0.18 Phy1160: force and motion -- momentum, impulse, and conservation  (Page 11/14)

 Page 11 / 14

1. Enter the following into the Google calculator and press Enter to produce the results shown.

• convert 2205 lb to kg = 1000.17118 kilograms
• convert 33.6 mph to m/s = 15.020544 meters / second
• 1000 kg*15 m/s = 15000 m kg / s

Therefore, the initial momentum = 15000*kg*m/s at 0 degrees

2. 1000 kg*30 m/s = 30000 m kg / s at 0 degrees

3. 2000 kg*15 m/s = 30000 m kg / s at 0 degrees

4. 2000 kg*30 m/s = 60000 m kg / s at 0 degrees

Change in momentum due to change in speed and direction

A car with a weight of 10000 newtons is moving in a direction of 90 degrees at 40m/s. After going around a curve in the road, the car is moving in a direction of 0 degrees at 20 m/s. What is the change in momentum of the car?

Solution:

While this problem could be solved using the Google calculator, because of the number of steps involved, JavaScript is probably a better approach.

The solution script for this problem is shown in Listing 1 .

Listing 1 . Solution script.
```<!---------------- File JavaScript01.html ---------------------><html><body><script language="JavaScript1.3">//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("Start Script</br>"); var weight = 10000//Nvar g = 9.8// m/s^2 //Find the mass of the carvar mass = weight/g;// kg var ang1 = 90;//initial angle in degreesvar ang2 = 0; //final angle in degrees var speed1 = 40;//initial speed in m/svar speed2 = 20;//final speed in m/s var ang1r = ang1*Math.PI/180;//initial angle in radiansvar ang2r = ang2*Math.PI/180;//final angle in radians //Remember, momentum is a vector quantity and momenta must// be added and subtracted using vector arithmetic. //Compute the components of the change in momentum.var P1x = mass * speed1 * Math.cos(ang1r); var P1y = mass * speed1 * Math.sin(ang1r);var P2x = mass * speed2 * Math.cos(ang2r); var P2y = mass * speed2 * Math.sin(ang2r);var deltaPx = P2x-P1x;//change in horizontal component var deltaPy = P2y-P1y;//change in vertical component//Compute the magnitude of the change in momentum using // the Pythagorean theorem.var deltaPm = Math.sqrt(deltaPx*deltaPx + deltaPy*deltaPy); //Compute the angle of the change in momentum usiing// trigonometry. var deltaPa = getAngle(deltaPx,deltaPy);document.write("The givens." + "</br>"); document.write("weight = " + weight.toFixed(0)+ " kg</br>"); document.write("speed1 = " + speed1.toFixed(0)+ " m/s</br>"); document.write("angle 1 = " + ang1.toFixed(0)+ " degrees</br>"); document.write("speed2 = " + speed2.toFixed(0)+ " m/s</br>"); document.write("angle 2 = " + ang2.toFixed(0)+ " degrees</br>"); document.write("Computed mass." + "</br>"); document.write("mass = " + mass.toFixed(0) + " kg</br>"); document.write("Components of momentum vectors." + "</br>"); document.write("P1x = " + P1x.toFixed(0) + "</br>"); document.write("P1y = " + P1y.toFixed(0) + "</br>"); document.write("P2x = " + P2x.toFixed(0) + "</br>"); document.write("P2y = " + P2y.toFixed(0) + "</br>"); document.write("Components of momentum change vectors."+ "</br>"); document.write("deltaPx = " + deltaPx.toFixed(0) + "</br>"); document.write("deltaPy = " + deltaPy.toFixed(0) + "</br>"); document.write("Magnitude and angle of change vector."+ "</br>"); document.write("deltaPm = " + deltaPm.toFixed(0)+ " m kg/s</br>"); document.write("deltaPa = " + deltaPa.toFixed(0)+ " degrees</br>"); document.write("End Script");</script></body></html>```

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