# Energy of a car

i got into a disagreement with someone about how much damage a car would do if it collided with a tree. the other person said that the faster you are going when you hit the tree the more dmage is done to the tree. i replied by saying that at a point the structure of the car yeilds and this is not true. my exact response was :

if you have x amount of energy when you hit a tree the energy has to go into somehting. it can crush the car, break the tree, be dissapated as heat etc... if you hit the tree at a velocity where the energy only involves the frame of the car and the tree then the tree will probably be damaged. however at a high enough velocity the momentum of the engine block will cause it to shear from the body (as it is designed to break off and drop down) and keep going. this will affect the mass of the car. if the frame of the car stays intact all of the energy is dissapated on the tree as the tree must exert that force back. however if you hit the tree with enough velocity that the body deforms and crushes it is a different problem. look at a beer can against your head. if you move the can at a smedium velocity it will hurt like **** and probably cut your head. however, if you provide enough energy into the system by giving the can a higher velocity, there will be enough energy for the structure to yield. when this happens not all of the energy is going into your forehead because some of it is required to cause the can to crush. you are ee, the physics you learned in high school can not explain the new problem of the yeilding object. please to not try to talk about that which you do not know
kthnx

could someone explain to me if her is right why it doesn't matter if the structure yeilds, or let me know that i am right
thanks
jguth

Homework Helper
Here is the part of your beer can analogy that is NOT like the car/tree. Your hand is pushing the beer can. If you ever found it to be true that moving the can fast does not hurt your head, while moving it medium/slow, then you probably "braked" the can with your hand before the bent pieces of metal entered your skin.

DO the following test: fire the beer can from a special sling shot at high and low speeds. Not at your head, of course, but maybe at a pice of styrofoam. You will see that the faster the can goes, the more damage to the can AND the styrofoam.

Regarding the car: if the engine sheers off, and does not hit the tree, then yes: less damage to the tree, because the tree had to supply less net impulse (force times time). If you hit the tree at a high speed, and the car crumples up, the tree still had to stop the momentum (despite what happens to the energy)and it will be damaged.

IF, at a high speed, the car does NOT crumple, then the car WILL rebound off the tree. (This because you have a super-elastic bumper and a new kind of chassis?) THis will increase the damage to the tree (that's counterintuitive, but it's true: this is why cars are designed to crumple).

If you hit the tree at a low speed where the car does NOT crumple, it's probably not much of an accident and the tree will be fine.

Mentor
Originally posted by Chi Meson
Here is the part of your beer can analogy that is NOT like the car/tree. Your hand is pushing the beer can. If you ever found it to be true that moving the can fast does not hurt your head, while moving it medium/slow, then you probably "braked" the can with your hand before the bent pieces of metal entered your skin.
Actually, you'd be surprised. Such a thing is possible. Its a question of force vs distance vs time. An acutal mechanics of materials test:

A "Charpy" tester takes a 50 lb axe shaped head on a 4 foot pendulum and hold it horizontal. At the bottom of the swing you place a sample of metal with a knotch in it. The other side of the apparatus from where the pendulum is held initially has a slider to mark how high the pendulum swings after breaking the sample. The height difference between the downswing and upswing tells you how much energy it took to break the sample.

Now consider two different samples: Iron and aluminum. What happens to each? The iron is many times stronger than the aluminum but its brittle - if you made a plate out of it and dropped it, it would break like glass. The charpy's pendulum cuts through it like its not even there: it takes an extremely small amount of energy to break because it is so brittle even though the force required is huge.

The aluminum is many times weaker than the iron, but it is ductile - instead of snapping so easily it bends before breaking. As often as not, the aluminum sample will STOP the pendulum, absorbing all of its kinetic energy. Even though the forces are smaller, the ductility allows it to take more TIME and DISTANCE to absorb the energy than the iron sample gets.

Theoretically, the beer can and car (and a karate kid breaking a board with his hand) should work the same way. In reality, only the karate board does. You can pick as strong of a board as you want as long as its very stiff and even grain (no knots) and it will act like the iron and snap.

The beer can is tough because people cheat. Its an unstable situation and the slightest perturbation from a perfect cylinder will reduce the force required to crush it by an order of magnitude. So when crushing it, hold it firmly and let your fingertips dig into it and it is significantly easier to crush.

The car is tough because its a complex object. I guess what you are asking is is it possible for the car to not break the tree even at high speed, while breaking it at low speed? If you take the engine out of the picture, maybe. But the engine is hard and heavy so it is what will do in the tree. The safest speed (if it exists) would be one so high it shears off the tree without damaging the car. Thats what planes do when they crash into the woods - cut off the trees while remaining intact (until they hit the ground).

Homework Helper
I conceed to each and every point. I was already coming up with other possibilities regarding the beer can/styrofoam scenario:

There would be a certain speed at which the beer can does not crush, but bounces off the styrofoam (go ahead and use your head if you want, it's still a free country). This would be the maximum speed for the elasticity of the can. At a slightly higher speed, the can would crush, and not bounce. The inelastic collision would cause less damage to the styrofoam than the elastic collision at a slightly slower speed.

Back to the car: Cars are designed to have minimally elastic collisions, so this scenario would not apply. I still am convinced that as the speed of the car increases, the amount of damage to both the car and the tree increases.

rdecker
energy transfer

Well yes the faster the car the greater the kinetic energy. In fact it is proportional to the square of the velocity so increasing velocity has more of an effect than increasing mass. When the car hits anything that energy will be transferred. How, though is a matter for automotive engineers to ponder. I am sure they would like the crumple zones to absorb as much as possible. The details of such a collision with a tree have many variables. The angle of collision, the density of the tree, the depth of the root ball etc.

You talk about the car hitting the tree at a fast enough speed so that the engine rips from the mountings. Think about this: By the time the engine rips from the mountings, the tree would have had to absorb more energy than a slower collision since it takes energy to remove the engine from it's mountings. You can't start midway into the collision and start throwing numbers around. Exchange of energy has already ocurred and you hadn't accounted for it.

Let me ask you one last question:

I have suspended from a bar a piece of string. At the end of this string is tied a weight. Tied to this weight is another piece of string hanging straight down. I will pull on the lower string until one of the strings break. Which one breaks first? Both strings are made of the same material.

This DOES relate to your question and I will ellaborate after I get a couple of answers.

rdecker
piece of string

the piece of string which is attached to the bar.

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More replies please. I want more input...

string on top, unless you pulled it really fast.

Ok, I guess those are the only replies I will get. No big deal. Both answers are correct, the second one more correct. I can make either string break by pulling on the lower string either fast or slow. The whole point of this is that it illustrates WHAT PART of the tree may suffer damage when it is hit by an object slowly or quickly. While it's not likely any cars will be hitting trees in the upper half, suppose one did. Think of the root system as the upper string, the lower half of the tree could be considered the weight, and the upper half of the tree could be considered the lower string. From experience I can tell you that it IS possible to pull certain types of pine trees out by the roots, but I don't know about various others. Of course it also depends on the type of soil. Now that I think about it, suppose you have a tree with a somewhat flexible top-section and hit the top of the tree quickly. The inertia in the bottom of the tree would keep the shock out of the root system and the top of the tree would just bend over and let the car sail by. But suppose you hit it at a slower speed. Would the inertia in the main trunk be overcome and rip the roots out? Maybe such trees don't occur in nature, but I'll bet a structure could be designed to behave this way. Any thoughts?

Originally posted by Chi Meson
You will see that the faster the can goes, the more damage to the can AND the styrofoam.

Got to thinking about this one too. Suppose you cut off the bottom of the beer can and fire it at the styrofoam until it busts through. Yeah, it's going to have to be mov'n if you only fire the bottom at it! So now we have this velocity dialed in, fire the whole can bottom first through the styrofoam. Why should the can crush? Isn't there enough mass in JUST the bottom to get through the styrofoam? Just like if I stood on someones shoulders and we jumped of a ten foot step through some plywood. I would feel it in my ankles. BUT, if we both jumped off of a 100 foot step, the bottom person would probably not need my help in sailing through that plywood. Although sometime I'm going to feel it because eventually we have to stop. I remember taking this stuff in high school physics, but nothing as in depth as this.