Scaling Problem: How Much Would He Weigh?

[kuartus4]

Let's say that we have a guy who is 6 feet tall and weighs 190 lb. If we were to make him 60 feet tall with the same proportions as before, how much would the man weigh? How much would he weigh if we make him 50 feet tall?

 

[economicsnerd]

"Same proportions"...
- So he scales the same amount in all 3 dimensions?
- So he weighs the same per cubic centimeter as he did before?

That might be a good start.

 

[pasmith]

Let's say that we have a guy who is 6 feet tall and weighs 190 lb. If we were to make him 60 feet tall with the same proportions as before, how much would the man weigh? How much would he weigh if we make him 50 feet tall?

You can approximate him as a 6ft x 1ft x 1ft block and then calculate his density. When you scale his height to 60 ft he will become a 60ft x 10ft x 10ft block.

 

[kuartus4]

"Same proportions"...
- So he scales the same amount in all 3 dimensions?
- So he weighs the same per cubic centimeter as he did before?

That might be a good start.

Both.

 

[berkeman]

Let's say that we have a guy who is 6 feet tall and weighs 190 lb. If we were to make him 60 feet tall with the same proportions as before, how much would the man weigh? How much would he weigh if we make him 50 feet tall?

"Same proportions"...
- So he scales the same amount in all 3 dimensions?
- So he weighs the same per cubic centimeter as he did before?

That might be a good start.

Both.

Please show some effort on your part in answering this question. You have been given good hints -- you should be able to solve the question fairly easily now. Please show some work.

And is this question for your schoolwork?

 

[kuartus4]

Please show some effort on your part in answering this question. You have been given good hints -- you should be able to solve the question fairly easily now. Please show some work.

And is this question for your schoolwork?

Nope. Not schoolwork. I'm not in school. I'm just a guy who was curious about this particular question after reading some comics with giant super heroes. Immature I know. But I guess I'll try answering the question.

The guys initial volume is 6 cubic feet?
His mass is 86 kg.
So his density is mass/volume.

8600g/169,901cm cubed.

So .5g/1 cm cubed.


.5=x/6000

So the sixty foot giant weighs 6,613.8 lbs.

 

[jbriggs444]

The guys initial volume is 6 cubic feet?

Yes.

His mass is 86 kg.

Yes. Though it is also 190 pounds. There is no need to change units.

So his density is mass/volume.

8600g/169,901cm cubed.

You typoed the 86,000g. There is also no need to change units again.

So .5g/1 cm cubed.

Yes. Note that you've rounded and this density has only one significant figure.

.5=x/6000

Where x is the mass in grams of a man/block whose volume is 6000 cubic centimeters?

So the sixty foot giant weighs 6,613.8 lbs.

It appears that you solved for x, obtained 3000 grams, interpreted that as kilograms, converted to pounds and added four unwarranted significant figures. You are making things way too complicated.

An alternate approach is to take it one step at a time. You scale the block up by increasing its height by a factor of ten and leaving its width and depth the same. What happens to its weight? Then scale it up by making it ten times larger front to back. What happens to its weight? Then scale it up by making it ten times larger side to site. What happens to its weight?

 

[HallsofIvy]

Weight and mass of an object with uniform density are proportional to the volume of the object and so scale as the cube of lengths.