Understanding Multiple Scale Setup: M1 Hanging from Two Identical Scales

[Westside47]

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?

 

[tiny-tim]

Welcome to PF!

Hodwy Westside47! Welcome to PF!

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 F_total = 0 for each of the scales.

 

[hl_world]

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.

 

[berkeman]

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?

 

[Westside47]

Thanks so much for the timely responses. Now that i think of it like that, I think i have found the answer :) thanks!