Tension Rope and Blocks Problem

[DaveTan]

Homework Statement

Two blocks, each with weight w, are held in place on a frictionless incline as shown in Figure. In terms of w and the angle a of the incline, calculate the tension in the rope connecting the blocks

Homework Equations

T = mg

The Attempt at a Solution

I cannot for figure out why the answer is Wsin(a)! I thought that since Tsin(a) = mg, T = w/sin(a)

 

[Coffee_]

You have to look at the forces that are pulling along the surface. The force pulling downwards the slope is $F_d=mgsin(a)$, the force pulling up is just the tension $T$. For the block to be not moving along the slope these two have to be equal to each other.

 

[gneill]

Homework Statement

Two blocks, each with weight w, are held in place on a frictionless incline as shown in Figure. In terms of w and the angle a of the incline, calculate the tension in the rope connecting the blocks

Homework Equations

T = mg

The Attempt at a Solution

I cannot for figure out why the answer is Wsin(a)! I thought that since Tsin(a) = mg, T = w/sin(a)

Hi DaveTan, Welcome to Physics Forums.

Take a close look at the geometry of a block on a slope. The weight W = Mg forms the hypotenuse of the force triangle:

 

[DaveTan]

Thanks! But shouldn't tension be pointing in the other direction? So towards the top-right instead of bottom left?

 

[haruspex]

Thanks! But shouldn't tension be pointing in the other direction? So towards the top-right instead of bottom left?

Tension acts both ways (as does compression). The force it exerts on B will be up and to the right, that on A down and to the left.
By the way, the reason your original approach went wrong is that the vertical forces include a component of the normal force.