Trouble with the concept of tension....

[haruspex]

Ft-10N=1*a

No. That equation says -10N is the force A is exerting on the ground. Your equations lead to A exerting a force -15N on the rope and B exerting a force +15N on it.

 

[kkps]

You realize that thread is 2 years old. That said, your free body diagram is incorrect. If the rope is the only entity that exerts a force on A and B, the direction of the force on A is from A to B and the direction of the force on B is from B to A. These two are equal and opposite according to Newton's third law.

10N<-A---ROPE---B->20N
is not different from
<-A(say 1Kg)hanging on a rope on left of pulley---ROPE---B(say 2Kg)hanging on a rope on right of pulley
this is same as Atwood machine problem
of course, we can add force on ground etc. to problem and complicate, but it is not needed to solve the problem IMO
I think it can be solved by my simple free body diagram which are drawn similar to Atwood machine solution
and, of course, i am assuming massless rope to simplify

>You realize that thread is 2 years old
yes, but i think someone will still search for this, and i think the question was not answered well

 

[kkps]

No. That equation says -10N is the force A is exerting on the ground. Your equations lead to A exerting a force -15N on the rope and B exerting a force +15N on it.

please see my answer to kuruman. A is pulling on rope with 10N to left, B is pulling on rope with 20N to right. we do not have to add Ground in picture, A is somehow generating 10N, B 20N. Then we can translate the question to an Atwood machine problem

I have still not answered the "rope with mass" part of the original question. I am working on it

 

[kkps]

You should open a new thread. Your answer makes little sense to me.

My answer is treating the problem like an Atwood machine problem. I think I forgot to mention that I am treating the string as massless. I am working on a simple explanation for the "string with mass" case. I think this thread is a good interaction, though there is lot of unnecessary confusion in the discussion. But the original question is a doubt anyone could have

 

[PeroK]

there is lot of unnecessary confusion in the discussion.

Which you've just added to! Your solution is conceptually wrong, as it violates Newton's third law, which I think has already been pointed out.

 

[kkps]

Which you've just added to! Your solution is conceptually wrong, as it violates Newton's third law, which I think has already been pointed out.

can you explain why this question cannot be simplified to an Atwood machine question as I pointed out in reply to kuruman? After that, can you explain why my solution is conceptually wrong and how it violates Netwon's third law?

FBD of A
10N<-A->15N A is moving to right with a=5, if m of A=1kg

FBD of B
15N<-B->20N B is moving to right with a=5, if m of B=1kg

FBD of rope
15N<-Rope(massless)->15N

what force is not balanced violating third law?

 

[PeroK]

what force is not balanced violating third law?

B cannot be pulling on the string with $20N$ and the string pulling back with $15N$. That violates Newton's third law.

 

[haruspex]

A is pulling on rope with 10N to left, B is pulling on rope with 20N to right

That is the proposition in post #1. It appears to be a situation invented by the student, not a problem he or she was given.
If the rope has zero mass then it is not physically possible, and if you start with an impossible combination of facts you can deduce anything.

 

[haruspex]

we do not have to add Ground in picture

In post #68 you described your equations as based on free body considerations for A and B. Necessarily that means your are considering all horizontal forces on those bodies, namely, the force from the ground and the force from the rope.

If your FBD has the force of tension and the force of a person pulling, what is the body those two forces are acting on?

You seem not to understand the concept of an FBD.

 

[kkps]

B cannot be pulling on the string with $20N$ and the string pulling back with $15N$. That violates Newton's third law.

to make it simple, translate the question to this:
A(1Kg)hanging on a rope on left of pulley---massless ROPE---B(2Kg)hanging on a rope on right of pulley
in the above (pulley) case, the entire system (A-rope-B) will fall to right

This is an Atwood machine problem
The original question is exactly same as I see it
solution to above Atwood problem is: a=5, Ft=15

>B cannot be pulling on the string with $20N$ and the string pulling back with $15N$.
it is very much possible. that is what causes motion!

 

[kkps]

That is the proposition in post #1. It appears to be a situation invented by the student, not a problem he or she was given.
If the rope has zero mass then it is not physically possible, and if you start with an impossible combination of facts you can deduce anything.

you are trying to prove that the question makes no sense, but the question makes a lot of sense to the original poster. I am trying to understand what the original poster meant, and answer the intent of the original poster.

Most textbooks have similar questions where, say, A pulls something to left. All that the student has to consider to answer the question is that there is a force to left. There is no need to consider where the force is coming from, the type of shoes he is wearing, the surface he is standing on (ice vs slush), etc.

Imagine you are in a classroom and the teacher has asked this question, and imagine the teacher walked away. You would answer the question making some assumptions yourself, rather than heckling the teacher with more questions. I am taking this approach

Also, zero mass of rope is used in all basic textbooks in all such problems. if you add mass, your answer is not going to be much different . I will post that answer soon

 

[kkps]

In post #68 you described your equations as based on free body considerations for A and B. Necessarily that means your are considering all horizontal forces on those bodies, namely, the force from the ground and the force from the rope.

If your FBD has the force of tension and the force of a person pulling, what is the body those two forces are acting on?

You seem not to understand the concept of an FBD.

please see post #80
IMO, post #1 is asking the same question as shown in the diagram of post #80
(as I mentioned in post #81, some simplification of original question can be applied to give a meaningful answer without further questioning - force from ground etc. are irrelevant to the original problem)

 

[jbriggs444]

you are trying to prove that the question makes no sense, but the question makes a lot of sense to the original poster. I am trying to understand what the original poster meant, and answer the intent of the original poster.

If the original poster intends a massless rope then the question posits an impossible scenario according to Newton's second law. $\sum F = ma$. $m = 0$ so $\sum F = 0$.

If the original poster intends a rope with mass then the scenario is possible.

Both possibilities have been contemplated in already. For instance, see post #6 which contemplates a massless rope and #8 which looks at both scenarios -- a rope with or without mass.

The possibility of A pulling on the rope with 20N and the rope pulling on A with 15N is a direct violation of Newton's third law and is nonsense.

 

[PeroK]

if you add mass, your answer is not going to be much different . I will post that answer soon

Please don't!

 

[kuruman]

Let's examine and interpret the equations in your drawing. You have

Equation 1: Ft - 10 = 1*a
Here Ft is the tension, 10 (N) is the weight of the mass on the left and 1*a is mass*acceleration

Equation 2: Ft - 20 = 1*(-a)

Here Ft is the tension, 20 (N) is the weight of the mass on the right and 1*(-a) $\dots~$ is what ? If the mass is 2 kg, the term should be 2*(-a) to be correct. Then one has
Ft - 10 (N) = a
Ft - 20 (N) = -2a
If the first equation is doubled and added it to the second, one gets
3 Ft - 40 (N) = 0 ⇒ Ft = 40/3 (N) = 13.3 (N) and that is the correct tension in the string connecting the masses. More generally, $$F_T=\frac{2m_1m_2}{m_1+m_2}g.

 

[haruspex]

B cannot be pulling on the string with 20N

Indeed, it is not. Gravity pulls on B with 20N, but if B is accelerating at 5m/s², B only pulls on the string with 15N, same as the tension.

What if we let A's mass dwindle to zero? B will be in free fall, so no tension, but according to your reasoning it is still pulling on the string with 20N.

 

[haruspex]

Please don't!

Well, it would be interesting to see that, and take the limit as the rope's mass tends to zero.

 

[kuruman]

Indeed, it is not. Gravity pulls on B with 20N, but B is accelerating at 5m/s², so B only pulls on the string with 15N, same as the tension.

For $m_1 = 1$ kg and $m_2 = 2$ kg, the acceleration is $$a=\frac{m_2-m_1}{m_2+m_1}g=\frac{1}{3}g$$and the tension is 13$\frac{1}{3}$ N as indicated in post #85.

 

[haruspex]

For $m_1 = 1$ kg and $m_2 = 2$ kg, the acceleration is $$a=\frac{m_2-m_1}{m_2+m_1}g=\frac{1}{3}g$$and the tension is 13$\frac{1}{3}$ N as indicated in post #85.

Thanks. I made the mistake of assuming @kkps's numbers were correct, just the interpretation that was wrong. I've edited it to avoid making that assumption.

 

[kuruman]

To @kkps :
Here is a multiple choice question to help you sort this out.
Two teams are engaged in a tug o' war as shown in the figure below. The team on the left is pulling on the rope with a force of 100 N and the team on the right with a force of 200 N. A force gauge is attached to the rope as shown. What does the gauge read?

(A) 100 N
(B) 150 N
(C) 200 N
(D) The people on the left read 100 N and the people on the right read 200 N.
(E) This question makes no physical sense.

Hint: How would your answer change if the right side of the gauge were attached to an immovable wall instead of being pulled by the team on the right? What about swapping the left team with the immovable wall?

 

[kkps]

Let's examine and interpret the equations in your drawing. You have

View attachment 316230
Equation 1: Ft - 10 = 1*a
Here Ft is the tension, 10 (N) is the weight of the mass on the left and 1*a is mass*acceleration

Equation 2: Ft - 20 = 1*(-a)

Here Ft is the tension, 20 (N) is the weight of the mass on the right and 1*(-a) $\dots~$ is what ? If the mass is 2 kg, the term should be 2*(-a) to be correct. Then one has
Ft - 10 (N) = a
Ft - 20 (N) = -2a
If the first equation is doubled and added it to the second, one gets
3 Ft - 40 (N) = 0 ⇒ Ft = 40/3 (N) = 13.3 (N) and that is the correct tension in the string connecting the masses. More generally, $$F_T=\frac{2m_1m_2}{m_1+m_2}g.

Thanks for pointing out the mistake
What I wanted to show by this example is that the following statement made by PeroK is wrong "B cannot be pulling on the string with 20N and the string pulling back with 15N. That violates Newton's third law."

In my FBD of B, there is 20N down and 13.3N up. This is similar to the question of the original poster - just that where the force comes from is different in the Atwood machine example vs the original poster's question

 

[berkeman]

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