Would a pile of feathers weigh the same as a pile of gold at Earth's center?

[Goongyae]

What weighs more?

An ounce of feathers?
Or an ounce of gold?

 

[micromass]

Well, obviously, their mass is the same. But does that mean that they weigh thesame? I think not: an ounce of feathers will take up more place than an ounce of gold. Therefore, the feathers will be more prown to local fluctuations of g. In particular, the center of mass of the feathers will be at an higher altitude then with the gold. Thus g for the feathers will be a bit lower. This is why I think that the weight of the feathers is less then the weight of the gold!

 

[Goongyae]

Answer: the ounce of gold will be noticeably heavier than the ounce of feathers.

Spoiler

Because precious metals are conventionally measured in troy ounces, not in avoirdupois ounces.

 

[BobG]

Well, obviously, their mass is the same. But does that mean that they weigh thesame? I think not: an ounce of feathers will take up more place than an ounce of gold. Therefore, the feathers will be more prown to local fluctuations of g. In particular, the center of mass of the feathers will be at an higher altitude then with the gold. Thus g for the feathers will be a bit lower. This is why I think that the weight of the feathers is less then the weight of the gold!

Ounces are a measure of weight or a measure of volume. However, using your logic, they could have a slightly different mass - in this case, somewhere in the 1 millislug range ().

 

[Gokul43201]

Well, obviously, their mass is the same. But does that mean that they weigh thesame? I think not: an ounce of feathers will take up more place than an ounce of gold. Therefore, the feathers will be more prown to local fluctuations of g. In particular, the center of mass of the feathers will be at an higher altitude then with the gold. Thus g for the feathers will be a bit lower. This is why I think that the weight of the feathers is less then the weight of the gold!

[Ignoring the QI klaxons]

The correction in g goes like 2h/R (R is Earth's radius). So, for a pile of feathers that's a whopping 60 cm high, the relative difference of weight is about 60cm/6000km or about 1 in 10 million.

On the other hand, there is a much bigger effect, somewhere in the region of 1 in 1000, from the difference in buoyant force (I assumed that feathers have a density similar to most organic matter, somewhere in the range of 1g/cc).

 

[micromass]

Wow, I thought that nobody would take my answer seriously. But you guys even did the calculations I really love this forum :!)

 

[Goongyae]

BTW the ounce of gold will be about 10% heavier than the ounce of feathers.

 

[BobG]

Wow, I thought that nobody would take my answer seriously. But you guys even did the calculations I really love this forum :!)

Variations in the local g are very important to satellite attitude control.

In fact, this caused a problem with one of the shuttle experiments. The goal was to take measurements of the Earth's magnetic field. Unfortunately, electrical currents in the shuttle create their own magnetic field, so the magnetic sensor had to be located far enough away from the Shuttle that the sensor wouldn't detect the shuttle's magnetic field. Putting that sensor out on the end of a long boom put it into a slightly weaker gravity. Since it was obviously going the same speed as the shuttle, it meant the sensor at the end of the boom should pull further away from the Earth than the shuttle, creating a constant torque which would cost the shuttle fuel to counter with its thrusters, and thereby shorten the mission.

The 'solution' was a hose that went along the boom and let fuel leak out at the end of the boom. Even though it generated a tiny amount of 'thrust', the torque generated was equal to the thrust times the radius (the length of the boom). Unfortunately, the hose became clogged and they wound up having to shorten the mission anyway.

BTW the ounce of gold will be about 10% heavier than the ounce of feathers.

Are you trying to hijack this thread?

 

[D H]

BTW the ounce of gold will be about 10% heavier than the ounce of feathers.

On the other hand, a pound of gold is about 18% less massive than a pound of feathers.

Gotta love those English units!

 

[Fun Value]

[Ignoring the QI klaxons]

The correction in g goes like 2h/R (R is Earth's radius). So, for a pile of feathers that's a whopping 60 cm high, the relative difference of weight is about 60cm/6000km or about 1 in 10 million.

On the other hand, there is a much bigger effect, somewhere in the region of 1 in 1000, from the difference in buoyant force (I assumed that feathers have a density similar to most organic matter, somewhere in the range of 1g/cc).

Most of the gold is deep in the earth. If it was at Earth's center, would it weigh anything?
Most feathers might be closer to Earth's surface where g = 9.8m/s/s.