Asked by titi

force of 125 N pulls due west on a body, and a second force pulls N 28.79 W. The resulta force is 212 N. Find the second force and the direction the resultant.
Answered by Reed
Who is "jonnathan"?
Answered by Steve
suppose we say that vectors
<b>u</b> = force of 125 N pulls due west
<b>v</b> = force of magnitude v pulls N 28.79 W
<b>r</b> = resultant force is 212 N at angle b

expressing those in x-y coordinates,

<b>u</b>+<b>v</b> = <b>r</b>
<-125,0> + <-v sin 28.79,v cos28.79> = <212 cosb, 212 sinb>
<-125,0> + <-0.482v,0.876v> = <212 cosb, 212 sinb>

That means that

-125 - 0.482v = 212 cosb
0.876v = 212 sinb

solving, we get
v = 121.281
b = 30

so,
the 2nd force is 121.281N
the resultant acts at W30N

You can also solve by drawing the diagram. If we label the sides u,v,r and the angles U,V,R, then we have

u = 125
r = 212
U = 118.79°

sinR/r = sinU/u
Now, having U and R, V is easy, since they sum to 180°. Then
v^2 = u^2+r^2 - 2ur cosV
Answered by Saitama
Steve's diagram explanation is false:
SinR/212 = Sin118.79/125 results in...

Sin^-1(212Sin118.79/125) = ERROR
There are no AI answers yet. The ability to request AI answers is coming soon!