How do you calculate a human volume from a given weight?

[5P@N]

Homework Statement

Hypothesize a human with a weight of: 61.14 kg (not an abnormal specimen in this wise).

density of a human body: 985 kg/m^3

Homework Equations

What is the volume in cubic meters of such a hypothetical person?

The Attempt at a Solution

The mass of this person is determined by dividing weight by the force of gravity on Earth (9.8 m/s^2), to arrive at this result: ~6.24 kg.

I know the formula: Volume = Mass/Density

HOWEVER! When I divide 6.24 by 985, I get a volume in m^3 which is: ~.0063 m^3

I have a sneaking feeling that this result just cannot be correct. Why? Because it means that, when you divide 1 by .0063, you get: ~158. Meaning: that if you were to (very hypothetically) get 158 of such humans and puree them, they would fill a volume of only 1 cubic meter. This cannot be right! It is way too low a result.

So my question is: what's wrong with my reasoning?

 

[Chestermiller]

61.14 kg is not the weight of a human body; it is the mass. When you came up with the value 6.24 kg, did it make sense to you to think that this could be the mass of a human body?

 

[Andrew Mason]

If the problem actually states that the person weighs 61.14 kg, the "kg" unit means kilogram force or 9.8 x 61.14 Newtons. This gets really confusing in Imperial units where "pounds" means pound weight and mass is measured in slugs (1 slug mass weighs 32 pounds). It is better to use Kg for mass and Newtons for weight.

AM

 

[Mister T]

If you are given a value of 61.14 kg it's the object's mass, regardless of the fact that in legal parlance it's called weight. The value of the local free fall acceleration is not relevant. The pound used in the United States for purposes of legal trade is, by definition 0.453 592 37 kg. Move it around the globe where the free fall acceleration varies from 9.78 m/s² to 9.83 m/s² and by law, it's a pound in both places.

I agree that the best way to clear up the confusion is use Newtons and kilograms. If something is measured in kilograms it's a mass. If something is measured in Newtons it's a force.

 

[Chestermiller]

The pound used in the United States for purposes of legal trade is, by definition 0.453 592 37 kg. Move it around the globe where the free fall acceleration varies from 9.78 m/s² to 9.83 m/s² and by law, it's a pound in both places.

As Andrew points out, in the US system, there are two units with the tag pounds. There are pounds mass, designated lb_m, and pounds force, designated lb_f. 1 lb_m is equal to 1/32.2 slug, and the standard weight of 1 lb_m is 1 lb_f. It can drive you crazy if you're not used to it. If you are used to it, no problem.

 

[Mister T]

As Andrew points out, in the US system, there are two units with the tag pounds. There are pounds mass, designated lb_m, and pounds force, designated lb_f. 1 lb_m is equal to 1/32.2 slug, and the standard weight of 1 lb_m is 1 lb_f. It can drive you crazy if you're not used to it. If you are used to it, no problem.

The pound is defined as a unit of mass, but it's also used as a unit of force. There is, however, no officially sanctioned definition of the pound force.

There was an officially sanctioned unit called the kilogram force, and that was defined as the force needed to make an object of mass one kilogram accelerate at 9.806 65 m/s². Unfortunately, no such a thing was ever done for the pound force.

The word "weight" means different things to different people. In commerce, medical fields, and others, it's the same thing that we define as mass. The kilogram-force was officially abandoned because of these types of confusion. In physics and other technical fields it's a force, but there is no agreement on how that force is defined.

The one thing that's simple for students to remember, and everyone agrees on: If you're measuring something in kilograms, it's a mass. If you're measuring something in Newtons it's a force.

That's particularly relevant in this case.

 

[5P@N]

Thanks everyone! I don't feel so dumb after all!

Here's my revised solution: 61.14 kg / (985 kg/m^3) = .062m^3

This means that if you were to puree ~16.1 people of this size, then they would fit into a 1 cubic meter vessel. Now that I've arrived at a more reasonable result, I don't feel like I want to puree myself!