Understanding Multiple Scale Setup: M1 Hanging from Two Identical Scales

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Discussion Overview

The discussion revolves around the readings of two identical hanging scales when a block of mass M1 is suspended from them. Participants explore the implications of the setup, considering various interpretations of how the scales would measure the weight of the block. The discussion includes conceptual reasoning and hypothetical scenarios to clarify the mechanics involved.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant initially suggests that both scales would read 1/2 M1, but later considers that they might both read M1.
  • Another participant argues that since the first scale and its load are supported only by the second scale, both scales should read M1, unless they were directly attached to the wall sharing the load.
  • A participant proposes a thought experiment involving traditional spring scales to illustrate how the readings might change based on the setup, questioning whether the top scale's reading would change when the lower scale is hung from it.

Areas of Agreement / Disagreement

Participants express differing views on the readings of the scales, with no consensus reached. Some believe both scales read M1, while others consider the possibility of each reading 1/2 M1 under different conditions.

Contextual Notes

The discussion includes assumptions about the mass of the scales and the nature of the forces acting on them, which may affect the interpretations of the readings. The implications of the setup are not fully resolved, leaving room for further exploration.

Who May Find This Useful

This discussion may be of interest to those studying mechanics, physics students grappling with concepts of tension and weight distribution, or anyone curious about the behavior of forces in a multi-scale system.

Westside47
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Howdy! I saw this question posted on someones blog the other day and just could not for the life of me reason out an answer that i could 100% agree with.

Say a block of mass, M1, hangs from a hypothetical hanging scale of 0 mass, which in turn hangs from a second identical scale, which in turn hangs from a nail in the wall. What would the scales read? both M1? 1/2 M1?

Originally i figured they would both read 1/2 M1, but the more i think about, i think i may have convinced myself that they would both read M1.

Here is a diagram if the wording was hard to understand.

. o nail
. |
. (o) hanging scale
. |
. (o) hanging scale
. |
. |M1| block of mass
Your thoughts?
 
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Welcome to PF!

Hodwy Westside47! Welcome to PF! :smile:
Westside47 said:
Howdy! I saw this question posted on someones blog the other day and just could not for the life of me reason out an answer that i could 100% agree with.

For cast-iron reasoning, call the tensions in the string T1 T2 and T3, and do Ftotal = 0 for each of the scales. :wink:
 
Since the 1st scale and its load are supported only by the 2nd scale, both scales should read M1. It would be 1/2 M1 for each if both scales were hanging directly on the wall sharing the load.

Unless I misread.
 
Westside47 said:
Howdy! I saw this question posted on someones blog the other day and just could not for the life of me reason out an answer that i could 100% agree with.

Say a block of mass, M1, hangs from a hypothetical hanging scale of 0 mass, which in turn hangs from a second identical scale, which in turn hangs from a nail in the wall. What would the scales read? both M1? 1/2 M1?

Originally i figured they would both read 1/2 M1, but the more i think about, i think i may have convinced myself that they would both read M1.

Here is a diagram if the wording was hard to understand.




. o nail
. |
. (o) hanging scale
. |
. (o) hanging scale
. |
. |M1| block of mass



Your thoughts?

Another way for you to think about it...

Picture the scales as traditional spring scales. The mass reading goes up as the spring extends, right?

Say you have one scale hanging from the wall nail, and are holding the other scale plus mass M1 with your hand. What do the two scales read? The scale in your hand has its spring extended the correct amount for it to read M1, right? What about the scale on the wall?

Now carefully hang the scale in your hand from the scale on the wall. Does the spring in the scale that you were holding change length? How would it know it was hung from your hand versus hung from another scale? What does the top scale read now?
 
Thanks so much for the timely responses. Now that i think of it like that, I think i have found the answer :) thanks!
 

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