Finding the Tension in terms of weight and the angle of incline

[Yosty22]

Homework Statement

Two blocks, each with weight ω, are held in place by a frictionless incline.
In terms of ω and the angle θ of the incline, calculate the tension of the rope connecting the two blocks.

Homework Equations

ƩF=ma

The Attempt at a Solution

Since it is on a tilted incline, with angle θ, I made the x and y-axis tilted for the free body diagram. This means that ω, the weight, can be broken down into components ω_x, which is parallel to the tension, and ω_y, perpendicular to tension. In this case, I assumed that all forces acting in the x-direction (parallel to the tension) were ω_x and T. I then used the equation ƩF=ma_x and plugged in values and solved for T. First, I put "ωsinθ" in place of ω_x, making the equation ωsinθ+T=ma. Solving for T, I get T=ma-ωsinθ. Is this correct? It looks a little odd to me.

 

[tms]

I think something is missing in the statement of the problem. How can a frictionless incline hold anything in place?

 

[lep11]

I think something is missing in the statement of the problem. How can a frictionless incline hold anything in place?

No, they are held in place by tension.

 

[lep11]

Homework Statement

Since it is on a tilted incline, with angle θ, I made the x and y-axis tilted for the free body diagram. This means that ω, the weight, can be broken down into components ω_x, which is parallel to the tension, and ω_y, perpendicular to tension. In this case, I assumed that all forces acting in the x-direction (parallel to the tension) were ω_x and T. I then used the equation ƩF=ma_x and plugged in values and solved for T. First, I put "ωsinθ" in place of ω_x, making the equation ωsinθ+T=ma. Solving for T, I get T=ma-ωsinθ. Is this correct? It looks a little odd to me.

Since the blocks are held in place there is no acceleration so ma=0⇔ƩF_x=0. And remember, there are two blocks.

 

[tms]

No, they are held in place by tension.

I can't picture the setup.

 

[Yosty22]

Sorry guys, this is the setup. I have looked at it a few more times and still get the same thing. Am I doing something wrong?

 

[tms]

Since the blocks are not moving, what is the acceleration?

 

[Saxby]

Your answer above is wrong.

It may help to tell you that the tension in that rope would only depend on the mass of B (and not A). Remember the tension in string is equal to the force with which gravity is pulling the mass down the slope.