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

  • #1
Iamconfused123
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9
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
pf3 (2).jpg

Thank you
 
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  • #2
1) Please indicate your stated positive convention.
2) Provide equations of motion for each mass given that convention.
 
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  • #3
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?
 
  • #4
Iamconfused123 said:
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...
 
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  • #5
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.
 
  • #6
Iamconfused123 said:
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.
 
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  • #7
erobz said:
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
 
  • #8
Iamconfused123 said:
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.
 
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  • #9
no? How? They are pulling pulley down and the tension force is holding him up
 
  • #10
Iamconfused123 said:
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... :bow:
 
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  • #11
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?
 

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  • #12
erobz said:
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... :bow:
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
 
  • #13
Iamconfused123 said:
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.
 
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  • #14
Iamconfused123 said:
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.
 
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  • #15
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.
 
  • #16
Iamconfused123 said:
But I really don't know what is 3rd force?
What is holding the pulley up?
 
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  • #17
erobz said:
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
 
  • #18
Iamconfused123 said:
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).
 
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  • #19
Iamconfused123 said:
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!
 
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  • #20
I finally figured it out. Thanks everyone.
 

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

There are several reasons why you may have obtained two different results for the mass m2. One possibility is that there was a measurement error in one of the experiments. Another reason could be that there was a systematic error in one of the instruments used to measure the mass. It is also possible that there was a random error present in one of the experiments, leading to a different result. It is important to carefully analyze the experimental procedures and data to determine the cause of the discrepancy.

2. How can I ensure consistent results for the mass m2?

To ensure consistent results for the mass m2, it is important to carefully calibrate all instruments used for measurement. Additionally, conducting multiple trials and averaging the results can help minimize random errors. It is also crucial to follow standardized procedures and protocols to reduce the likelihood of systematic errors. By paying attention to these factors and maintaining a high level of precision in your experiments, you can increase the reliability of your results for the mass m2.

3. Could environmental factors have influenced the different results for the mass m2?

Yes, environmental factors can certainly influence the results of an experiment, including measurements of mass. For example, changes in temperature, humidity, or air pressure can affect the behavior of materials being measured. It is important to control for these variables as much as possible during experimentation to minimize their impact on the results. Additionally, conducting experiments in a controlled environment, such as a laboratory with stable conditions, can help reduce the influence of external factors on the mass m2 measurements.

4. Is it possible that the mass m2 itself changed between experiments?

While it is unlikely that the mass m2 itself changed between experiments, there are certain factors that could lead to this perception. For instance, if the material being measured is volatile or subject to degradation, its mass could potentially change over time. It is important to ensure that the material remains stable and consistent throughout the experimental process. By carefully handling and storing the sample, you can minimize the risk of any changes in mass m2 affecting your results.

5. What steps can I take to troubleshoot the discrepancies in the results for the mass m2?

When faced with discrepancies in the results for the mass m2, it is important to conduct a thorough analysis of the experimental procedures and data. Start by reviewing the methods used for measurement and identifying any potential sources of error. Check for consistency in instrument calibration and ensure that all measurements were taken under similar conditions. Additionally, consider repeating the experiments to see if the same discrepancies arise. By systematically troubleshooting the issue and making adjustments as needed, you can improve the accuracy and reliability of your mass m2 measurements.

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