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5.9 N ......... 4.9 N
.....α\... .../ ß
-------- \ . /---------
...........V 4.9 N
(It wasn't clear from your description whether the two angled forces act upward or downward, but if they're going to be in equilibrium with the weight, they should be upward.)
we're in static equilibrium - the body is not accelerating. From the
vector version of F = ma, that means that the net vector force is zero.
If the vector force is zero, that means that orthogonal components of
the net vector force are zero. So, we take the horizontal and vertical
directions (which are orthogonal), find the net force components in
those directions, and set them equal to zero. We need to define the
positive and negative directions for those components, so let's say that
the positive x direction is to the right, and the positive y direction
In the x direction, the weight has no component. The 5.9 N force component acts in the -x direction, with magnitude -5.9 N * cos α. The 4.9 N force component acts in the +x direction, with magnitude +4.9 * cos ß. So, the sum of forces in the x direction (which is equal to zero) is
ΣFx = -5.9 N * cos α + 4.9 N * cos ß = 0
In the y direction, the weight acts in the negative direction, with magnitude -9.6 N. The other forces act in the +y direction, with magnitude 5.5 N * sin α and 6.4 N * sin ß. So, the sum of forces in the y direction (which is equal to zero) is
ΣFy = -4.9 N + 4.9 N * sin α + 4.9 N * sin ß = 0
So, we have 2 equations, and 2 unknowns, and we can solve. Let's start with the first equation.
-5.9 N * cos α + 4.9 N * cos ß = 0
5.9 * cos α = 4.9 * cos ß
cos α = (4.9 / 5.9) * cos ß
Please let me know if you need any clarification. I'm always happy to answer your questions.
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