Weight of 160lbs on Polystyrene Planet Same Size as Earth

[bozo the clown]

I wieigh 160 pounds on Earth.
How much would I weigh on a planet same size as Earth but completely made out of polystirine ?

 

[check]

I actually started to do this but I got lazy. Anyway, you don't weigh 160 pounds on earth. You have a mass of 160 lbs 72.5747792 kg to be more SCI correct.

Anyway, you're weight is your mass x the acceleration due to gravity of the planet/object you're standing on. So in your case, your weight is 72.57 kg x 9.81 m/s^2 = 711.9117 Newtons.

Just thought I'd clear that up.

 

[bozo the clown]

hey my brain is small let's keep it simple !

 

[Gza]

check, you just converted his weight, a measure of force from the English system, to the SI system, which doesn't really answer his question. Your weight would definitely change if the planet was made of a less dense material such as "polystirine"(not really sure what material you are referring to, but am assuming it to be less dense than rock.) The calculation of the force of gravity on you isn't at all difficult, just multiply the density of the material by the volume of the Earth, and use that in Newton's law of Gravitation.

 

[check]

Gza, I know I didn't answer the question. I clearly stated, "I actually started to do this but I got lazy". I just wanted to correct him on the difference between weight and mass.

As for his question itself, the density throughout the polystyrene planet would not be consistent.

EDIT: Ok, just to make sure I have this correct, are pounds a measure of weight, like Newtons, or mass like kilograms? I'm not that familiar with the english system so just to make sure.

 

[Integral]

Lbs are a measure weight, not mass. The official unit of mass in the english system is the Slug.

 

[check]

Ooooohhh. I see. Ok, nevermind about all that then.

Oh well, I think english units are silly anyway.

 

[BobG]

Your weight is the force with which gravity is pulling you towards the Earth's center.

$$F=\frac{GM_1m_2}{r^2}$$

The only difference between using the equation on Earth or on your polystyrene planet is the mass of the planet. So your weight is directly proportional to the mass of the planet.

The mass of a planet is equal to its density times its volume. The density of the Earth is about 5.52 g/cm^3.

The mass of your polystyrene planet is not so easy to figure out, since you weren't specific as to the type of polystyrene you were talking about (comes in high density, low density, etc). Since you weren't specific, I picked for myself - I picked low density polystyrene used for boat bouyancy (the things they stick in the bow and stern of rental canoes so the yahoos don't send their canoes to the bottom of the lake). It's density is .016 g/cm^3.

In other words, the mass of your polystyrene planet is going to be .016/5.52 times that of the Earth. That ratio holds regardlesss of the units used. That way you can avoid conversion of units, altogether.

Your weight on a polystyrene planet is equal to:

$$\frac{.016 g/cm^3}{5.52 g/cm^3}\ast160 lbs$$
(the g/cm^3 cancel out, so the sloppy mixing of units won't affect the result)

About 7 ounces.

 

[Nereid]

bozo said 'same size', BobG assumed this meant 'volume', which would be fine (it's important to be very clear about assumptions!).

Bigger problem: a big ball of plastic would likely not have sufficient mechanical strength to resist compression, so there'd be some crushing and so on. That could result in melting and chemical changes. Etc.

Net: a ball of 'polystirine' the 'same size' as the Earth wouldn't be polystyrene all the way down, and would very likely have an average density considerably higher than that of a 1 kg polystyrene lump on the surface.

Q: how to calculate the radial density and composition profile of a polystyrene planet (assume no relative vertical motion of material)?

 

[Math Is Hard]

What the heck is polystyrene anyway? Is that like Styrafoam?

 

[Artman]

What the heck is polystyrene anyway? Is that like Styrafoam?

Styrofoam (TM) is a polystyrene product. Polystyrene can be hard like a jewel case for CDs, computer cases, parts for home appliances, etc, can be rubbery, or when mixed with air or carbon dioxide can be more of a foam like material (only about 5% polystyrene the rest is air or carbon dioxide). The density would vary depending on which form we are talking about.

I think what Bozo is trying to get at is if the planet material was the density of foam polystyrene and could maintain this density through to it's center. Given this material is 95% air, we can assume that 95% would be the density of air (This also would vary toward the center with heat and pressure, but I think he wants us to ignore this.)

If we place the plastic on just the surface and all the air in the center we would have a balloon planet. Perhaps we could consider his question from this perspective? Basically, what would we weigh on a balloon the size of the Earth?

 

[Math Is Hard]

I just found it peculiar that the problem didn't contain a given for the density of polystyene - as if it was something everyone would just know off the top of their heads. But hey, what do I know. Maybe I was sleeping in class on polystyrene day. :zzz:

Hey, hey, Check - if I weigh 130 lbs on Earth, how much do I weigh in Canada? Jes' kiddin!

 

[Andre]

When I progressed grazing this tread I was thinking of compression/increased mass problems but I see that Nereid beat me on that one. Perhaps check this thread that elaborates on increasing density with depth. When we know the density-pressure characteristics for poly-whatevers, we can do the same numerical intergration.

 

[Artman]

When I progressed grazing this tread I was thinking of compression/increased mass problems but I see that Nereid beat me on that one. Perhaps check this thread that elaborates on increasing density with depth. When we know the density-pressure characteristics for poly-whatevers, we can do the same numerical intergration.

That was kind of my point. The density varies greatly with the material, depending on the form used. We would need to make some decisions on which of the varieties we are using to arrive at a density. In the foam version we're almost (approximately 95%) dealing with air.

 

[russ_watters]

I don't consider this much of an issue, but weight and mass are often used interchangeably when talking about people. A bathroom scale uses springs and therefore measures weight - but you can read it in pounds (weight) or kg (mass). A balance like the doctor weighs (yeah, weighs) you with actually measures mass but reads out in pounds, which is weight.