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Figure 13 shows the mirror image that is contained in that file for the benefit of your assistant who will create the tactile graphicfor this exercise.
| Figure 13 . Mirror image from the file named Phy1100e1.svg. |
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Figure 14 shows a non-mirror-image version of the same image.
| Figure 14 . Non-mirror-image version of the image from the file named Phy1100e1.svg. |
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Figure 15 shows the key-value pairs that go with the image in the file named Phy1100e1.svg.
| Figure 15 . Key-value pairs for the image in the file named Phy1100e1.svg. |
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m: Tent pole exercisen: File: Phy1100e1.svg |
Equilibrium
Is the tent pole in equilibrium? If not, why not? What new force would need to be added to cause it to be in equilibrium?
You can probably solve this exercise in your head by inspection of the force vectors because they are all of the same length and they emanate outward at regularlyspaced angles around the pole.
Could be more complex
Note, however, that the scenario could be much more complicated involving force vectors with different lengths arranged at seemingly random angles aroundthe pole.
The important point is, the same general scheme would be used to solve the more complicated problem as is used to solve this simple exercise. However, thecode in the script for the more complicated version would probably be somewhat more messy.
The scheme for the solution
The solution is to compute the sum of the force vectors to determine if the resultant vector is zero. If it is not zero, the tent pole would not be inequilibrium. It would be necessary to add a new force vector with the same magnitude as the resultant vector but in adirection that is the exact opposite of the direction of the resultant vector to cause the tent pole to be in equilibrium.
Create a script
Please copy the code from Listing 1 into an html file and open the file in your browser.
| Listing 1 . Tent pole exercise. |
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<!---------------- File JavaScript01.html ---------------------><html><body><script language="JavaScript1.3">document.write("Start Script</br></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 getAnglevar resultX = 0;//magnitude in newtons
var resultY = 0;//magnitude in newtonsvar ang = 0;//degrees
var mag = 10;//newtonswhile(ang<= 270){
resultX = resultX + mag*Math.cos(ang*Math.PI/180);resultY = resultY + mag*Math.sin(ang*Math.PI/180);
ang = ang + 45;}//end while loop
var resultAng = getAngle(resultX,resultY);var resultMag = Math.sqrt(resultX*resultX +
resultY*resultY);document.write("The resultant is:" + "</br>");
document.write("Magnitude = " + resultMag.toFixed(2) +"</br>");
document.write("Angle = " + resultAng.toFixed(2) +"</br>");
document.write("</br>End Script");</script></body></html> |
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