How Do You Solve a Non-Equilibrium Pulley System with a 154 Degree Angle?

[ashley2024]

Homework Statement

Find the tension in the following system (see image).

Relevant Equations

Fnet = ma, Ff = uFn,

Please note that the system is not in equilibrium, and that tension must be solved for the instant where the angle is 154 degrees.

My attempt (correct ans is Ft = 626N)

 

[haruspex]

$a_1=a_2$? Sure?

 

[ashley2024]

$a_1=a_2$? Sure?

Nope, but I don't really have any other ideas.

 

[haruspex]

Nope, but I don't really have any other ideas.

There is a simple relationship between the two, just not quite that simple.
Start with positions. If m is x from the vertical through M, the knot is y below the horizontal through m, the string connecting them has length L, and it is at θ to the vertical, write expressions for x and y and differentiate twice.

 

[ashley2024]

There is a simple relationship between the two, just not quite that simple.
Start with positions. If m is x from the vertical through M, the knot is y below the horizontal through m, the string connecting them has length L, and it is at θ to the vertical, write expressions for x and y and differentiate twice.

Would this be similar to the related rates problems? Since the ropes have fixed length, it seems similar to the ladder problem where you have to differentiate its rate as it falls...

 

[Lnewqban]

Please note that the system is not in equilibrium...

Welcome, Ashley!

What makes you state that?

 

[ashley2024]

Welcome, Ashley!

What makes you state that?

The teacher who gave this problem.

 

[Lnewqban]

The teacher who gave this problem.

Then, the tension in the V=shaped wire should be the minimum to keep masses #1 sliding toward each other.
We could then, disregard the value of the force exerted by the falling mass #2, since we know that it is plenty to have induced and to keep the sliding movements of both masses #1.
Therefore, calculating T2 seems not to be necessary.
As the system is geometrically symmetrical, there is a unique value for T1.

 

[ashley2024]

Interesting! But I don't understand why it would be the minimum though? Since its asking for the tension when the angle is 154, I assumed that the tension could be still in the process of changing.

 

[haruspex]

But I don't understand why it would be the minimum though

It isn't. Don’t be distracted by that.

 

[haruspex]

Would this be similar to the related rates problems? Since the ropes have fixed length, it seems similar to the ladder problem where you have to differentiate its rate as it falls...

Yes.