Pounds are a measurement of mass, not weight. Since lead is more dense, Assuming all things being equal and we weigh both as spherical objects with their base touching a scale at sea level, the lead will weight slightly more since it’s centre of mass is slightly closer to the centre of mass of the earth.
If we adjusted it so both COM were at sea level instead, then the feathers would weigh more since gravity works on an inverse scale so the bottom part of the feathers would weight more than the bottom part of the lead by more than top part of the feathers would weight less than the top part of lead.
Please correct me, but I thought that the definitions relevent were:
weight = force of gravity on an object (so same for objects of same mass in same place)
air resistance = force opposing motion (so same for objects with same velocity and same surface)
boyancy = force upwards due to being deplaced by air (same for objects with same volume at same height)
Are these correct?
If so then lead and feathers of the same mass (stationery in the same place) would have the same weight, but the lead would register more put on scales.
Which does ‘weigh more’ refer to?
(The way I imagined the difference is to compare a deflated balloon and a helium filled balloon. The second is more boyant despite having a greater weight.)
As an aside, there must also be a point at which both spheres have equal mass.
The radius of a slice of a sphere of radius r at distance x away from the centre is abs((r^2 - x^2)) using pythagoras. therefore the area is pi * (r^2 - x^2)^2 and, from this we can deduce the weight of a spherical object at distance n away from the centre of the earth will be <integral from - r to r of> G * m1 * m2 / (n + x)^2 * pi * (r^2 - x^2)^2 dx where G, m1, m2, r are known.
Comparing two objects, the G, m1, m2 and pi cancel leaving <integral from - r to r of> (r^2 - x^2)^2 / (n + x)^2 dx
The numerical solution to this problem is left as an exercise to the reader.
A pound is a unit of force (and is therefore a measure of weight, not mass). The English unit of mass is the slug. Broken down, a pound is a slug-foot per second squared (slug-ft/s[sup]2[/sup]).
Interesting answers all, but they’re not the ones I was looking for… Here’s what I had in mind:
If you look up “ounce” in a decent-sized dictionary, you’ll find that a second meaning is “a snow leopard”. Snow leopards, of course, weigh about 100 pounds.
Well, it’s an interesting range of responses. At least we seem to have established that lead is measured in avoirdupois, so that implies that the riddle is, in fact, intended as a simple trick question to fool six-year-olds.
All the futzing around with buoyancy and centers of gravity seem irrelevant to me. Since pounds measure weight*, if a bunch of feathers weighed less than a pound, then it wouldn’t be a pound of feathers. Similarly, a pound of feathers on the moon weighs the same as a pound of feathers on earth (although it’s a different number of feathers). Only if the pound units are different could a pound of something weigh more than a pound of something else.
I agree with Collibri. We should all just go metric.
Shalmanese was mistaken when he/she claimed that pounds measure mass.
Of course the original joke was just a simple misdirection and the “correct” answer was that they were the same, be we have had a lot of fun making it more interesting.
Also, I am amazed no fellow engineers have stopped by yet to note that a pound is BOTH a unit of mass and of weight. I believe one pound mass weighs about 0.0311 pounds force at sea level.
One of your fellow engineers did point out that slug was the unit of mass in the non-metric system. I’ve never heard of a mass pound, and if there were such a thing, I would guess it would be calibrated to earth’s gravity. That is a “mass” pound would weigh about an avordupois pound. Do you have any kind of cite, or are you just repeating something your big brother told you once?
Naw, it’s a two parter. I’ve had it pulled on me (got it right0 and pulled it on others.
The first part is “which weighs more- a # of lead or a pound of feathers?”. the answer is- of course- they weigh the same.
Then, if they get that right- you can ask- " Right…well then…which weighs more- a pound of Gold or a pound of lead?". Where the answer is Lead- due to the troy/ avoirdupois glitch.
