Is 1kg of feathers heavier than 1kg of stones?

Answer 1

It's a trick question, but with a not-so-trick answer:

The expected "correct" answer, is that since both "weigh" 1kg, they both have the same weight, and so neither one is heavier.

The CORRECT answer actually depends on a few more details, which will be explained in steps as follows:

1) The kg is a unit of mass, whilst weight, in the correct meaning of the word, is a measurement of forcemeasured in Newtons.

2) Force = mass x acceleration

-> Weight = mass x acceleration-due-to-gravity (g = 9.81 m/s2)

So up until now, we could argue that the stones and the feathers each have a weight of approx. 9.81 Newtons. However, so far we've only calculated the downward force on the two objects due to gravity.

Assuming that we're measuring the weight of these two objects somewhere on Earth, we must also consider the effects of the Earth's atmosphere, specifically the upward force this causes. Since air is a fluid, we must consider the effects of upthrust on these two objects:

3) Upthrust = weight-of-displaced-fluid

Now this is where things start to get interesting! Since we can safely assume that stone is more dense than feathers, then for the two objects to have the same mass of 1kg, the volume of the feathers must be greater than the volume the stone. Therefore, they will displace more of the fluid (air):

4) Stone-upthrust < Feathers-upthrust

So, getting back to weight:

5) Weight = downforce-due-to-gravity - upthrust-from-fluid

So, since the downforce due to gravity is equal in both instances, BUT the feathers produce more upthrust, the weight of the stone is, in fact, greater than the weight of the feathers.

Therefore, if they are both measured at the same location on Earth, 1kg of stone will be heavier than 1kg of feathers.

(Just don't tell your school Physics teacher this, unless you want him to think you're a smart-ass :-)