Reply
Mon 18 Jul, 2005 10:24 am
Two forces of 130 and 150 pounds yields a resultant force of 170 pounds. Find, to the nearest 10 minutes or nearest tenth of a degree, the measure of the angle between the ORIGINAL two forces.
I applied the law of cosines by saying a = 130, b= 150 and c = 170 to find the angle but did not find the correct answer.
You found the angle between one of the original forces and the resultant force. You have to add two of those angles together to get the angle between the two original forces. Draw a picture and you will immediately see what I mean.
Let the x axis lie along the force of 150 degrees.
Let the angle between the forces be Q.
170 = SQRT{ [150 + 130cos(Q)]^2 + [130sin(Q)]^2 }
170 = SQRT{ (150)^2 + 2(150)(130)cos(Q) +[130cos(Q)]^2 + [130sin(Q)]^2 }
170 = SQRT{ (150)^2 + 2(150)(130)cos(Q) + (130)^2}
(170)^2 = (150)^2 +(130)^2 +2(150)(130)cos(Q)
28900 = 22500 + 16900 + 39000cos(Q)
-10500 = 39000cos(Q)
-.26923 = cos(Q)
Q = 105.618 degrees (from the force of 150)
okay
I want to thank both of you for your notes.
Stumble It!
Tweet This
Bookmark on Delicious
Share on Facebook
Share on MySpace