# Question about surface area/ volume

1. Sep 20, 2013

### DevPhysics

1. The problem statement, all variables and given/known data
We have two animals. One of them is as big as an elephant or it's an elephant and the other one is a small animal as a cat. When we drop them from a high place, the smaller animal hurts less compared to the bigger one. Why?

2. Relevant equations
Surface area / volume

3. The attempt at a solution

I am not really sure. But maybe it can be something about durability(Cross-sectional area/volume). Or the smaller one hurts less because he has a less surface area so when it hits the ground it recieves less force compared to other. I am not so sure that's why I'm asking

P.S. This is my first time on the forums and I am not a native speaker. So there can be some wrong usage of the words. But I hope you understand what I mean. In this unit we are learning how to calculate durability of the objects like cubes, spheres etc. Thank you for your understanding.

2. Sep 20, 2013

### haruspex

A crude analysis (and I suspect that is what is sought here) would say that the an animal's ability to cope with a force from the ground depends on surface area of the feet (and cross-sectional area of the leg bones), whereas the force to be borne varies according to the mass (and hence the volume).
However, this overlooks the fact that a larger animal would also have longer legs, and thus be able to spread the landing impact over a longer distance. So the energy it can absorb on landing should be in proportion to its mass, thereby allowing it land from the same height as a smaller animal without any greater harm.
The real answer must be more subtle. A large animal must be able to bear more weight even when standing still. This time the longer legs won't help, so the animal needs different body proportions. The legs need to be disproportionately stouter. If you took the body plan of a cat and magnified it to the size of an elephant its legs would be too thin to take its weight. Merely making the legs thicker would make them massive, and presumably too costly, so instead the leg ratios are adapted. An elephant has a much shorter lower leg section and much straighter legs, both of which reduce its ability to cope with a drop from a height.

3. Sep 21, 2013

### DevPhysics

Hi haruspex,

Thank you so much for you answer. I think this is what I was looking for. And also I want to know what happens when the animals don't hit the ground on foot.(instead, they hit the groun with their body) So in this case, is it something about the surface are of the animals?

Thank you!

4. Sep 21, 2013

### voko

I would think this has more to do with resistance due to air. It is proportional to the cross-section of the animal. while the force of gravity is proportional to them mass, which is roughly proportional to the volume.

5. Sep 21, 2013

### haruspex

Yes, I meant to cover that too, but forgot. And rereading the OP I see it says 'high place' so most likely it is intended as more to do with air resistance.

6. Sep 22, 2013

### DevPhysics

Hi,
First thank you for your answers. I know the question's answer depends on a lot of things. And I am so confused right now. To sum up In this unit we are learning durability of the objects and surface area/volüme ratios of the objects. So long story short the first one says, a larger animal needs shorter and thicker legs because it has to bear more weight. And this reduces its ability to cope with a drop from a height. I get it. But I am confused about the other answers. I would be grateful if you could make it clear.
My question on my notebook is "Small animals hurts less compared to larger animals when they hit the ground. Why?"
Thank you so much.

7. Sep 22, 2013

### haruspex

Air resistance ('wind resistance') depends on speed, shape, and cross-sectional area. Assuming the first two are the same for both animals, an animal of twice the linear dimension has four times the air resistance but eight times the gravitational force. That means its acceleration under gravity will be closer to the full value of g. From a sufficiently great height, an animal/object will reach 'terminal velocity', i.e. that speed at which its air resistance balances the gravitational force and it no longer accelerates downwards. The larger the animal the greater the terminal velocity. An ant falls quite slowly.

8. Sep 22, 2013

### DevPhysics

Thank you soo much! I think this's what I am looking for. Now everything is clear.
Thank you again and have a great day!