Why did I get two different results for the mass m2?

[Iamconfused123]

Homework Statement

Basically, as the sketch is drawn. I was given tension force and acceleration. T=42N, a=4m/s^2.
I need to find masses and force that dynamometer shows.

Relevant Equations

F=ma

I wonder why did I get two different answers for m2 using two different approaches? The correct answer is m1=3kg, m2=7kg.
So pleases if someone can take a look.

Also can someone suggest how am I supposed to find the force that dynamometer is showing?
I was thinking that it equals (m1+m2)*g, which would be 100N, but it's 84N, according to the solutions. I thought it's 100N, and as a reason for such thought would be that the rope is infinitely long and it's the same thing as having 10kg hanged on dynamometer therefore 100N

Thank you

 

[erobz]

1) Please indicate your stated positive convention.
2) Provide equations of motion for each mass given that convention.

 

[Iamconfused123]

I just used ay(m1)=-ay(m2). ay being acceleration in y direction. And I used + for ay(m1)

I didn't use any equations of motion. Just F=ma. Was I supposed to?

 

[erobz]

I just used ay(m1)=-ay(m2). ay being acceleration in y direction. And I used + for ay(m1)

I didn't use any equations of motion. Just F=ma. Was I supposed to?

You are saying you get the wrong masses one way. I assume that since you are asking you don't realize that your second method is wrong.

Do a FBD of diagram of the pulley...

 

[Iamconfused123]

I mean I know it's wrong(because solutions are more likely to be correct then me) but I don't know why is wrong.

 

[erobz]

I mean I know it's wrong(because solutions are more likely to be correct then me) but I don't know why is wrong.

Do a FBD of the pulley.

 

[Iamconfused123]

You are saying you get the wrong masses one way. I assume that since you are asking you don't realize that your second method is wrong.

Do a FBD of diagram of the pulley...

Isn't FBD of pulley just (m1+m2)*g = - F(tension). AKA weight of sum of bodies = Tension force, which is the force that dynamometer is showing

 

[erobz]

Isn't FBD of pulley just (m1+m2)*g = - F(tension). AKA weight of sum of bodies = Tension force, which is the force that dynamometer is showing

The weight of the masses are not forces that act on the pulley. What are the forces that act on the pulley? What is touching the pulley? Hint: There should be three.

 

[Iamconfused123]

no? How? They are pulling pulley down and the tension force is holding him up

 

[erobz]

no? How? They are pulling pulley down and the tension force is holding him up

Are you going to fight me the whole time or try to learn something? If you simply do a correct FBD of the pulley your questions will be answered...just like the last problem...

 

[Iamconfused123]

wait, can the pulley move? would larger mass drag pulley on one side? would that cause the dynamometer to show less then 100N because it would be under an angle?

 

[Iamconfused123]

Are you going to fight me the whole time or try to learn something? If you simply do a correct FBD of the pulley your questions will be answered...just like the last problem...

I am really not trying to prove anything, I was just "thinking out loud", much less trying to fight people who are helping me. Sorry if it sounded like that

 

[erobz]

wait, can the pulley move? would larger mass drag pulley on one side? would that cause the dynamometer to show less then 100N because it would be under an angle?

Thats not a proper FBD of the pulley. The pully "knows" nothing of the masses below it (get rid of them), just the tension in the ropes that are accelerating them.

 

[erobz]

I am really not trying to prove anything, I was just "thinking out loud", much less trying to fight people who are helping me. Sorry if it sounded like that

Well, when you say "No? How?" instead of "give me a minute to cook that up", it comes off as " I don't think you have any idea what you are talking about" whether or not you feel otherwise.

Back to the problem, I hinted that there should be three forces acting on the pulley ( ignoring its own weight). You draw a FBD of the pulley by "severing" the ropes holding the masses revealing the internal forces developed inside them.

 

[Iamconfused123]

I really don't know what is the third force. Though I did figure that 42N(tension on m1 and m2) × 2= 84N.
But I really don't know what is 3rd force? perhaps force in x direction to the right? caused by larger masses acceleration downwards.

You are right, I should have said give me a minute to cook it up.

 

[erobz]

But I really don't know what is 3rd force?

What is holding the pulley up?

 

[Iamconfused123]

What is holding the pulley up?

dynamometer, ohh is it hooke's law? elastic force? But I don't know the constant, nor do I know change in "distance" spring did

 

[erobz]

dynamometer, ohh is it hooke's law? elastic force?

Yeah, its a spring, but don't worry about how much its stretched. What is important for this problem is that whatever it is, it is a force ( call it $F_d$) keeping the pulley from accelerating (translational) while this is all happening. So after drawing a correct FBD of the pulley you write Newtons Second Law for it (the pulley).

 

[PeroK]

Homework Statement: Basically, as the sketch is drawn. I was given tension force and acceleration. T=42N, a=4m/s^2.
I need to find masses and force that dynamometer shows.
Relevant Equations: F=ma

I wonder why did I get two different answers for m2 using two different approaches? The correct answer is m1=3kg, m2=7kg.
So pleases if someone can take a look.

Also can someone suggest how am I supposed to find the force that dynamometer is showing?
I was thinking that it equals (m1+m2)*g, which would be 100N, but it's 84N, according to the solutions. I thought it's 100N, and as a reason for such thought would be that the rope is infinitely long and it's the same thing as having 10kg hanged on dynamometer therefore 100N

Thank you

For your second solution, you tried to transform the problem into one of linear motion. This is possible (and in fact it's a good idea), but you have to careful. The biggest problem is not that you went wrong, but when you saw it was wrong, you couldn't find the error. The answer is, of course, that you ignored the force on $m_1$.

The simple pulley system is equivalent (in a sense) to the following scenario on a frictionless surface:

$m_1g \ \leftarrow m_1 ----\leftarrow T \rightarrow ---- m_2 \rightarrow \ m_2g$

You can see that this system generates the same equations of motion as the simple pulley system.

For the pulley question, you allowed your intuition to overrule Newton's laws of motion. You presumed that the force on the pulley must be 100N. But, you didn't test that presumption by applying Newton's laws. You need to retrain your initution.

When an object or system is accelerating downwards, it is not pulling an object above it with its full weight. That's twice yesterday that you fell into the trap of assuming that it must. Once in this problem and once here:
https://www.physicsforums.com/threads/why-body-a-has-greater-acceleration.1058427/

You must really get into the habit of testing your assumptions against Newton's laws. And lose that the habit of letting your intuition overrule Newton!

 

[Iamconfused123]

I finally figured it out. Thanks everyone.