Force at Equilibrium: How to Solve X and Y Components of Tension

[GOPgabe]

Homework Statement

I have an actual image which is quite better than my poor descriptive skills

Homework Equations

The X and Y components of each tension must balance.

The Attempt at a Solution

I thought if F3 weighs 200N then that mean the X component of Fw1 must equal
Fw1 tan(35)=200. Clearly I was wrong based on the answer. How would I proceed from here? Any help would be much appreciated.

 

[kuruman]

At the point where the three ropes meet, the sum of all the horizontal forces is zero and the sum of all the vertical forces is zero. This gives you two equations and you have two unknowns.

 

[GOPgabe]

At the point where the three ropes meet, the sum of all the horizontal forces is zero and the sum of all the vertical forces is zero. This gives you two equations and you have two unknowns.

I think I got it now, just one question. Are you supposed to add the vertical components of both of the systems in order to get the weight of F_w1?

 

[kuruman]

I think I got it now, just one question. Are you supposed to add the vertical components of both of the systems in order to get the weight of F_w1?

I am not sure what you mean by "both systems". Your system in this case is the knot where all three ropes are tied together. There are three forces acting on it, and the sum of these forces is zero.

 

[rwisz]

As a scientist, it is important to approach problems like these with a systematic and analytical mindset. Let's break down the problem into smaller parts and use the given information to determine the X and Y components of tension.

First, let's identify all the forces acting on the system. We have three forces: F1, F2, and F3. F1 is pointing upwards at a 35 degree angle, F2 is pointing downwards at a 50 degree angle, and F3 is pointing downwards vertically.

Next, let's draw a free-body diagram to visualize the forces and their directions. Label the X and Y components for each force, using trigonometry to determine their magnitudes.

Now, we know that the system is at equilibrium, which means that the net force in the X and Y directions must be equal to zero. This gives us two equations: ΣFx = 0 and ΣFy = 0. We can use these equations to solve for the unknown X and Y components of tension.

For the X direction, we have:

ΣFx = F1x + F2x = 0

F1x = -F2x

F1x = -F2cos(50)

F1x = -F2(0.6428)

F1x = -0.6428F2

Similarly, for the Y direction, we have:

ΣFy = F1y + F2y - F3 = 0

F1y + F2y = F3

F1y + F2sin(50) = F3

F1y = F3 - F2sin(50)

F1y = F3 - F2(0.7660)

F1y = F3 - 0.7660F2

Now, we can use the given information that F3 = 200N to solve for the X and Y components of tension. Substituting this value into our equations, we get:

F1x = -0.6428F2

F1y = 200 - 0.7660F2

We can now solve for F2 by setting these two equations equal to each other:

-0.6428F2 = 200 - 0.7660F2

0.1232F2 = 200

F2 = 200/0.1232

F2 = 162