Tension in a rope due to hanging mass

[jegues]

Homework Statement

See figure attached for problem statement as well as my FBD.

Homework Equations

The Attempt at a Solution

I know how to relate the wave speed to the tension in the string.

$$v = \sqrt{\frac{\tau}{\mu}}$$

So as tension increases, so does the wave speed.

But how are the tensions in these two scenarios identical?

I think I can reason it out with words but I'd like to have the math to back it up.

Can someone clarify?

 

[ehild]

The masses are in rest. What does it mean for the tensions in all cases?

ehild

 

[ashishsinghal]

since net force on each block = 0, T = mg

 

[jegues]

Yes, but does the wall exert a force as well? Also, what happens in the case of the two blocks, they both pull down with a force a mg, so to the do tension forces oppose each other on the rope?

 

[ehild]

There is one tension in one rope and it acts along the rope, at both ends. A force equal to the tension acts upward to the block and on the right at the wall. The wall acts only to the rope according to Newton's third law. In case of two blocks, the forces acting on both blocks are the same and equal to the tension in the rope.

ehild

 

[ashishsinghal]

in am massless string the tension is same throughout and acts along its length at the end points (same as in a spring) . the wall will exert a force on the rope and not on the block.

 

[jegues]

There is one tension in one rope and it acts along the rope, at both ends. A force equal to the tension acts upward to the block and on the right at the wall. The wall acts only to the rope according to Newton's third law. In case of two blocks, the forces acting on both blocks are the same and equal to the tension in the rope.

ehild

Is this what the forces look like then?

See figure attached.

 

[ehild]

It is right, Jeques, but you need the magnitude of the tension. From your drawing you can only conclude that T-T =0 and Twall-T =0 Draw the forces acting on the blocks with arrows starting at the blocks. That is what a free-body diagram means.

ehild