Analysis of Forces Acting at Knot in Tension Rope Figure

[oldspice1212]

Two ropes are connected to a steel cable that supports a hanging weight as shown in the figure: http://tinyurl.com/93c6tn3

There are 4 forces

T1: Tension force of the left rope
T2: Tension force of the right rope
T3: Tension force of the steel cable
And an unlabelled vector

Draw a free-body diagram showing all of the forces acting at the knot that connects the two ropes to the steel cable.

I put the forces T1 on the 60 degree rope exact length and same with T2 I put that on the 40 degree rope exact length, T3 I made it going down from the 2 ropes and unlabelled force I put it as the mass of the weight going down. (This was wrong)

 

[frogjg2003]

Could you give us a picture of your force diagram?
I am assuming you put the weight of the mass as a force on the knot. It isn't. The weight only acts on the mass, and the tension of the rope balances it out.

 

[NasuSama]

Hello.

You are given the diagram. First, draw the horizontal and vertical components for both wires. Then, indicate the value for the horizontal and vertical components for both sides. You need to use trigonometry formulas for this problem.

 

[oldspice1212]

Here's my diagram

 

[frogjg2003]

Here are the problems with your diagram:
1. Tensions are always attractive, not repulsive, forces.
2. Weight only acts on masses. The knot is massless, and therefore has no weight.
3. You're concerned with the forces on the knot, not on the weight at the bottom.

It's really hard to give any more without just giving you the answer, but post your correction and we'll help you out from there.

 

[oldspice1212]

I got it wrong again err...I tried to make T1 and T2 balance by making them both go down, and T3 I made it go down from the roof to the weight, I removed unlabelled force.

 

[frogjg2003]

From the first post:
T1 is the left rope
T2 is the right rope
T3 is the steel cable (bottom rope)

Tensions are always attractive. This means that the ropes are always pulling masses towards themselves. Which direction is towards the rope for all three tensions?

We are assuming that the knot isn't moving, so all the forces have to balance out.
T1 and T2 are the only ones that act in the horizontal direction, so they have to point in opposite directions: one to the right and the other to the left.
T3 also acts in the vertical direction, so it has to balance the vertical components of T1 and T2.

 

[oldspice1212]

I don't really understand the T3, but I see what you're saying for T1 and T2.

 

[frogjg2003]

So, if T1 is pointing to the left, which way should T2 point to cancel out T1's horizontal component? And then, which way should T3 be pointing to cancel out both of their vertical components?

Now, what if T1 is pointing right?

 

[oldspice1212]

I have one attempt left, If T1 is pointing left then T2 will be pointing right and T3 will be pointing up to balance it out.

 

[frogjg2003]

If T1 is pointing left and T2 is pointing right, are they pointing up or down?

 

[oldspice1212]

they will be pointing up

 

[frogjg2003]

So if they are both pointing up, which way should T3 point so there is no net force?

 

[oldspice1212]

Down! damn it why didn't I see that before...