+185 three forces of 150, 200 and 250 pounds respectively are in equilibrium. what are the angles between them?
+36916 Egads ! I do not know that I could figure this one out without a little more info......but I will try....lets put the 250 pound force on the x-axis
Forces vertical = 200 sin x & 150 sin y Since the 250 pound will not exert any vertical force because it is strictly horizontal these two must be equal and opposite THEN 200 sin x = - 150 sin y ... .(EQUATION 1)
Horizontal forces 200 cos x & 150 cos y and 250 I wil have to assume that the two smaller horizontal forces are balancing the larger 250 force
so 200 cos x + 150 cos y = 250 ... . (EQUATION 2)
We now have two equations with two unknowns and should be able to solve for the angles x and y.....
I'm missing some trig rule to figure out these two equations, BUT by successive trial and elimination (i.e interprolation) I come up with (approximately)
250 horizontal to the right
200 @ 143.77 degrees
150 @ 232 degrees Sorry.....I got STUCK !
+36916 Egads ! I do not know that I could figure this one out without a little more info......but I will try....lets put the 250 pound force on the x-axis
Forces vertical = 200 sin x & 150 sin y Since the 250 pound will not exert any vertical force because it is strictly horizontal these two must be equal and opposite THEN 200 sin x = - 150 sin y ... .(EQUATION 1)
Horizontal forces 200 cos x & 150 cos y and 250 I wil have to assume that the two smaller horizontal forces are balancing the larger 250 force
so 200 cos x + 150 cos y = 250 ... . (EQUATION 2)
We now have two equations with two unknowns and should be able to solve for the angles x and y.....
I'm missing some trig rule to figure out these two equations, BUT by successive trial and elimination (i.e interprolation) I come up with (approximately)
250 horizontal to the right
200 @ 143.77 degrees
150 @ 232 degrees Sorry.....I got STUCK !
+36916 Though I got the same answer via trial and error, I wanted to do it mathematically like you did...but you lost me between the step 4 lines from the bottom and the step 3 lines form the bottom.....how did you 'simplify' that?
Thanx !
+33616 I just used a piece of software to do it for me! However, here is the derivation:
.
+36916 Ahhhhhhh! I got to that point and it seemed like it was gonna be big a drawn out ordeal squaring both of those factors...THAT is when I 'trial and error'ed' it ! Thanx again !
