Effect on net torque and net force on spools

[dl447342]

Homework Statement

Determine whether spool A in the diagram below will strike the floor to the left of the x, where the x is initially directly below spool A and likewise for spool B.

Determine which of the students is correct in the second picture below and determine newton's second laws.

Relevant Equations

Torque = moment of inertia * angular acceleration, net force = mass * acceleration (newton's second law).

I think both spools will land about at the spot x (there aren't any horizontal forces causing them to land away from the x).

Also, I think student 2 might be the closest to being correct, but I'm not sure if they're entirely correct; isn't it possible that force doesn't only go to translational and rotational acceleration (E.g. some force can be used for thermal energy)?

Or maybe student 3 is right too? Isn't that the statement of Newton's second law?

For the equations, I think one should get the following (here $\alpha$ is the angular acceleration of spool A, $m$ is the mass of each spool, and $a_A, a_B$ are the accelerations of the center of masses of spools A and B, $I$ is the moment of inertia of spool $A$, $\tau_{net}$ is the net torque on spool A, and $R$ is the radius of spool A):

$I\alpha = RT = \tau_{net}$

$mg - T = ma_A$

$mg = ma_B$

 

[kuruman]

I think both spools will land about at the spot x (there aren't any horizontal forces causing them to land away from the x).

"About"? Why not at X since there aren't any horizontal forces? None of the students mentioned point X. There is no reasoning connecting their statements to "will the spool strike the floor to the left of point X?" and no explicit answer to that question. Therefore, it is not clear whether they believe that the spool will strike at X or not. Providing statements, whether correct or incorrect, without establishing their relevance to the question asked, is an incomplete answer. Your answer is complete in that regard although a bit wishy washy.

 

[haruspex]

"About"? Why not at X since there aren't any horizontal forces? None of the students mentioned point X. There is no reasoning connecting their statements to "will the spool strike the floor to the left of point X?" and no explicit answer to that question. Therefore, it is not clear whether they believe that the spool will strike at X or not. Providing statements, whether correct or incorrect, without establishing their relevance to the question asked, is an incomplete answer. Your answer is complete in that regard although a bit wishy washy.

The question as stated in the image does not ask about landing at x or otherwise, so I would guess that comes in a later part of the question. Consequently, there is no reason for the given student statements to address that.

So for now, let's just consider the student statements.
@dl447342 , what physical law considers parts of forces being "used up"?

 

[kuruman]

The question as stated in the image does not ask about landing at x or otherwise, so I would guess that comes in a later part of the question. Consequently, there is no reason for the given student statements to address that.

So for now, let's just consider the student statements.
@dl447342 , what physical law considers parts of forces being "used up"?

In the part of the question that is already posted, we are asked to "Draw an extended free body diagram at an instant after they are released but before they hit the floor." That has been done by OP.

Next we are given three student statements without any instructions on what to do with them. Are we supposed to find which are True and which are False? Are we supposed to fix errors in these statements? Furthermore, we are not told why the students provided these statements and what we are supposed to do with them. If we are to go by the question as stated and not bother with point X, then let's not bother considering the students' statements either.

 

[haruspex]

In the part of the question that is already posted, we are asked to "Draw an extended free body diagram at an instant after they are released but before they hit the floor." That has been done by OP.

Next we are given three student statements without any instructions on what to do with them. Are we supposed to find which are True and which are False? Are we supposed to fix errors in these statements? Furthermore, we are not told why the students provided these statements and what we are supposed to do with them. If we are to go by the question as stated and not bother with point X, then let's not bother considering the students' statements either.

The three statements appear to be in response to a question like "how and why does the tension in the string affect the acceleration of the mass centre". I feel no need for that to have been explicit in the question.

 

[kuruman]

The three statements appear to be in response to a question like "how and why does the tension in the string affect the acceleration of the mass centre". I feel no need for that to have been explicit in the question.

That could be. The question is entitled "Distinguishing the effect of net torque and net force." If I were soliciting answers from students using this setup as reference, I would ask "What is the same and what is different in the motion of the two spools after release but before landing?"

Nevertheless, I feel the need to know what one is supposed to do with the students' statements. I don't see why you think we should consider just the image and not the two paragraphs that start with "Determine ..." in the homework statement posted by the OP.

 

[dl447342]

That could be. The question is entitled "Distinguishing the effect of net torque and net force." If I were soliciting answers from students using this setup as reference, I would ask "What is the same and what is different in the motion of the two spools after release but before landing?"

Nevertheless, I feel the need to know what one is supposed to do with the students' statements. I don't see why you think we should consider just the image and not the two paragraphs that start with "Determine ..." in the homework statement posted by the OP.

For the students' statements, I meant to say that you're supposed to determine which are true and which are false.

 

[haruspex]

For the students' statements, I meant to say that you're supposed to determine which are true and which are false.

Can you answer my question in post #3?

 

[dl447342]

Can you answer my question in post #3?

Isn't the physical law the conservation of energy?

 

[haruspex]

Isn't the physical law the conservation of energy?

That's energy. The student's answer refers to using up force.
I suspect the answer could be made valid with a bit of elaboration, but it won't do as it stands.