# Volumes and areas

1. Oct 17, 2005

### net_nubie

People, suppose a man can lift a weight equal to his own weight 2 mtrs. off the ground with very little effort. If his dimensions (i.e. LENGTH, BREDTH, HEIGHT) are increased 10 times, keeping his average density constant, will it be easier for him to lift his new weight 2 mtrs. off the ground? Why?
P.S. The hint is in the title of the question.

2. Oct 17, 2005

### CRGreathouse

Could the man still stand, let alone lift the weight? I doubt it.

3. Oct 20, 2005

### Robokapp

Weight equals on earth 9.8 times the mass...so i'll use the word mass instead of weight since they are one and the same for man and box.

density = mass/volume.

density stays, volume increases. mass must increase as well. however, you used his instead of its twice. this means, the man will be 1000 times heavier becasue he is 1000 times more voluminous. SO...it would be like an elefant picking up an ant vs the orriginal where a turtle picked up an ant. YES, it will be much much much easier.

4. Oct 21, 2005

### HallsofIvy

Staff Emeritus
And exactly why would you think being heavier makes it easier to do things? Is it your experience that heavier people are necessarily stronger? That certainly isn't my experience.

"strength" depends on the cross-section area of the muscles. If a man were suddenly 10 times as large in each dimension, he would be 1000 times more "voluminous" and so weigh 1000 times as much. He would, however, be only 100 times as strong. As CRGreathouse said, it's unlikely that he would be able to stand!

You do have a good point that it is ambiguous whether lifting his "own weight" refers to the weight before or after enlarging. But even if it were he were trying to lift the same weight as he was lifting before enlarging, the problem would be to lift his own hands!

5. Oct 21, 2005

### Robokapp

well, japonese Sumo wrestlers are very very fat and also very very strong. Imagine a normal 150 pounds human colliding with a Sumo wrestler...you'd have to scrape him off floor. It takes bigger effort to move a bigger body, so a fat person is in fact stronger. It has less strength for display because he wastes it all on movement, it it is stronger...unless he gets 1000 times the weight instantly which would be unconceivable...

but why do i have the feeling i'm making this harder than it is?

6. Oct 22, 2005

### HallsofIvy

Staff Emeritus
How, exactly would getting 1000 times the weight be conceivable?
No, a "fat" person is not stronger! Certainly not just by virtue of being fat. Sumo wrestlers not only put on weight by eating an enormous amount, they also spend a lot of time exercising so that much of the weight put on IS muscle.
Now, why don't you go back and read the mathematics in my answer?

7. Oct 22, 2005

### renatzu

What you're thinking of is momentum. A Sumo wrestler has so much mass (easily 4 times an average person) running at half the speed they would exert twice the force, and the other person would get knocked back. However, this does not mean they can pick up large things. Many of them can, but that is because they exercise as well. If they were all fat and no muscle, they wouldn't be able to exert the torque on their arms necessary to lift something heavy. The strength your bicep muscle exerts on your lower arm has nothing to do with how heavy the rest of your body is. Increasing the size of your arm just means your muscle has to do more work, since it is pulling on a heavier object. The muscle would need to increase at the same rate.

8. Oct 28, 2005

### net_nubie

Hallsofivy got it right. When I said "lift his own weight" I meant lifting his new weight after the change in size.