Weighing Long Things

[Chesterton]

If you lay a 2x4 of wood on something like a normal bathroom scale, and the wood is say, 20 feet long, will you get an accurate measure of its weight? I'm imagining so much of the mass will be being pulled toward the center of the Earth away from the scale, that some of it doesn't get measured? Or no?

FYI, I'm wanting to weigh my guitars because I want to buy a lighter one. I realize I can weigh myself with and without the guitar and subtract the difference, but I think it might be slightly more accurate if I can just lay it on a scale. Anyway I'm still interested in the physics question though.

 

[Michael]

If you lay a 2x4 of wood on something like a normal bathroom scale, and the wood is say, 20 feet long, will you get an accurate measure of its weight? I'm imagining so much of the mass will be being pulled toward the center of the Earth away from the scale, that some of it doesn't get measured? Or no?

FYI, I'm wanting to weigh my guitars because I want to buy a lighter one. I realize I can weigh myself with and without the guitar and subtract the difference, but I think it might be slightly more accurate if I can just lay it on a scale. Anyway I'm still interested in the physics question though.

As long as you have a decent scale, it shouldn't matter if the object hangs off the edge of the scale, as long as the object is reasonably balanced on the scale, and it's not touching the ground anywhere. You'll get an accurate measure of it's weight.

 

[Ophiolite]

If you lay a 2x4 of wood on something like a normal bathroom scale, and the wood is say, 20 feet long, will you get an accurate measure of its weight? I'm imagining so much of the mass will be being pulled toward the center of the Earth away from the scale, that some of it doesn't get measured? Or no?

And what do you imagine is supporting the wood that is "distant" from the scale? Nothing. The mass rests upon the scale. As long as no part of the wood is touching the ground, or other object, then the scale will give you the weight of the wood.

One caveat: There may be peculiarities of scale design and sensing mechanism that could introduce complications, but offhand I can't think of any that would be relevant in your instance.

As long as you can do subtraction, I don't see why you would think it is more accurate to take the measurement by itself, rather than via you with and without the guitar. I would repeat each reading three times to satisfy myself as to the precision of the scales. (More if the three readings show significant differences.)

 

[Dave-W]

I'm imagining so much of the mass will be being pulled toward the center of the Earth away from the scale, that some of it doesn't get measured?

The earth is approx 8000 miles in diameter. Your 2x4 length would have to be a significant portion of that number before any changes in gravity would be noticeable on your scale.

 

[JackRT]

All the mass of an object acts as if it resided entirely at its center of mass. If it is of uniform density the center of mass will be at the geometrical center. So if the 2X4 is balanced on the scale there is no problem. For very long objects two scales could be used.

 

[RaymondG]

If you lay a 2x4 of wood on something like a normal bathroom scale, and the wood is say, 20 feet long, will you get an accurate measure of its weight? I'm imagining so much of the mass will be being pulled toward the center of the Earth away from the scale, that some of it doesn't get measured? Or no?

FYI, I'm wanting to weigh my guitars because I want to buy a lighter one. I realize I can weigh myself with and without the guitar and subtract the difference, but I think it might be slightly more accurate if I can just lay it on a scale. Anyway I'm still interested in the physics question though.

You can get one of those luggage scales.......the ones you attach to your bag and hold up in your hand......to avoid extra luggage costs..

This way, you can also carry it to the store and get the weights of many guitars in no time.

 

[essentialsaltes]

All the mass of an object acts as if it resided entirely at its center of mass.

This is the critical and correct observation.

For objects that fit in the room, the difference in distance between the center of mass of a tall thing and a short thing is no more than the height of the room. 10 feet of extra radius on top of the 4000 miles to the center of the earth won't make any measurable difference.

 

[sesquiterpene]

If you lay a 2x4 of wood on something like a normal bathroom scale, and the wood is say, 20 feet long, will you get an accurate measure of its weight? I'm imagining so much of the mass will be being pulled toward the center of the Earth away from the scale, that some of it doesn't get measured? Or no?

FYI, I'm wanting to weigh my guitars because I want to buy a lighter one. I realize I can weigh myself with and without the guitar and subtract the difference, but I think it might be slightly more accurate if I can just lay it on a scale. Anyway I'm still interested in the physics question though.

As for the physics question, as others have pointed out, there should be no effects due to gravitational differences. As for the scale's design, it might have an effect.

For laboratory microbalances (weighing out to a microgram), it is recommended to place the sample in the exact middle of the pan, although each sample can be calibrated to minimize any effect.

For my two kitchen scales, the smaller one (to 10 mg)had <0.01% difference when I placed samples in the corners instead of the center. The kilogram scale had about 1% difference - but only in one of the corners, the others were fine.

So be a good scientist and measure the precision of your own scale in regards to sample placement/center of gravity. It only took me a couple minutes. Have fun!

 

[Tanj]

This morning my scales told me I put on half a kilogram.

The correct conclusion from this is that all scales are rubbish and should be banned.

 

[JackRT]

This morning my scales told me I put on half a kilogram.

The correct conclusion from this is that all scales are rubbish and should be banned.

The diet industry is obviously in secret collusion with the scale lobby.

 

[Ophiolite]

Since no one else is going to do it, I guess the responsibility falls on me.

In engineering companies, factories and the like it used to be commonplace to send apprentices to the stores, ostensibly, for a long weight, when the storesman would be well briefed to give him a long wait.

 

[JackRT]

When a friend joined the air force he was sent to the stores for a bottle of prop wash.

 

[Bungle_Bear]

The longest guitar I am aware of is a little under 5 feet. If you're worried about something 20 feet long, I want to see a picture of your guitar!

 

[Chesterton]

And what do you imagine is supporting the wood that is "distant" from the scale? Nothing. The mass rests upon the scale. As long as no part of the wood is touching the ground, or other object, then the scale will give you the weight of the wood.

I know, I just have this mental image of all that mass being pulled downward all along its length, and wondering how all that pull is detected in the relatively small area of the scale.

 

[Chesterton]

The earth is approx 8000 miles in diameter. Your 2x4 length would have to be a significant portion of that number before any changes in gravity would be noticeable on your scale.

So if it extended outside Earth's atmosphere, only the section of the wood subject to Earth's gravity would be weighed accurately?

 

[Chesterton]

All the mass of an object acts as if it resided entirely at its center of mass.

Why is that?

 

[Chesterton]

The longest guitar I am aware of is a little under 5 feet. If you're worried about something 20 feet long, I want to see a picture of your guitar!

Yes, there's an old song by The Clash which complains of "five guitar players, one guitar". I built a 20 foot guitar to solve that.

 

[Bungle_Bear]

Yes, there's an old song by The Clash which complains of "five guitar players, one guitar". I built a 20 foot guitar to solve that.

Got a solution for the 22 singers and only one microphone?

 

[jayem]

Why is that?

Weight is a measurement of the pull of gravity. Though a mass may be 20 feet long, the pull of gravity is the same anywhere along its length. As long as the object is resting on the scale, and no part of its mass is being supported elsewhere, the weight will be accurate--at least for practical purposes.

 

[essentialsaltes]

So if it extended outside Earth's atmosphere, only the section of the wood subject to Earth's gravity would be weighed accurately?

The atmosphere is not some magic barrier to gravity.

Anyway, because technically correct is the best kind of correct, assuming the scale is accurate, then it would always measure the weight accurately. The weight is defined as the force of gravity on an object, which will vary depending on the orientation and elevation and location of the object. The mass of the object, which is an intrinsic property that doesn't change with location, is a different thing entirely. Though in many circumstances, we commonly treat them equivalently, because under most circumstances the difference between mass and weight is a proportional factor that doesn't vary much, the distinction is an important one. American physicists have tried to popularize the slug, but we haven't gotten anywhere.