Scaling Problem: How Much Would He Weigh?

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In summary: Thus, if we scale the height by a factor of ten, the weight will increase by a factor of 1000. If we scale the width by a factor of ten, the weight will increase by another factor of 1000. And the same for the depth. So in summary, if we were to make the 6ft tall, 190 lb man 60 feet tall with the same proportions, he would weigh 190,000 lbs. If we were to make him 50 feet tall, he would weigh 125,000 lbs. This is all assuming that the man's density remains constant as he is scaled up.
  • #1
kuartus4
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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?
 
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  • #2
"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.
 
  • #3
kuartus4 said:
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.
 
  • #4
economicsnerd said:
"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.
 
  • #5
kuartus4 said:
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 said:
"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.

kuartus4 said:
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?
 
  • #6
berkeman said:
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.
 
  • #7
kuartus4 said:
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?
 
  • #8
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.
 

1. How is the scaling problem related to weight?

The scaling problem is related to weight because it involves determining how much an object or person would weigh if they were a different size or scale. This can also refer to the difficulty of accurately measuring or predicting the weight of an object or person that is significantly different in size.

2. Why is it important to consider the scaling problem when weighing objects or people?

It is important to consider the scaling problem when weighing objects or people because weight is not solely determined by size or mass. Other factors such as density and composition can also affect weight, making it difficult to accurately estimate or calculate without taking scaling into account.

3. Can the scaling problem be solved using a simple mathematical equation?

No, the scaling problem cannot be solved using a simple mathematical equation because it involves multiple variables and factors that cannot be accurately represented by a single equation. It requires careful analysis and consideration of various factors to arrive at a reasonable estimate of weight.

4. How do scientists approach the scaling problem in their research?

Scientists approach the scaling problem by conducting experiments and collecting data to understand how weight is affected by size and other variables. They also use mathematical models and simulations to help predict and estimate weight in different scenarios. Additionally, they may also compare their findings to existing theories and principles in physics to gain a better understanding of the scaling problem.

5. How does the scaling problem impact real-life situations?

The scaling problem has a significant impact on real-life situations, especially in fields like engineering, medicine, and sports. In engineering, accurate weight measurements are crucial for designing and building structures that can withstand different loads. In medicine, understanding the scaling problem is essential for determining proper dosages of medication and designing medical devices. In sports, the scaling problem affects athletes' performance and training, as their weight can impact their speed, agility, and strength.

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