Riddle me this...

I'm currently reading George Gamow's classic stories about Mr. Tompkins. One chapter is a simplified physics lecture on relativity. At one point the professor says "In fact, if something is moving fast through space and you yourself move as if to meet it, the moving object will strike you with greater relative velocity, equal to the sum of velocity of the object and the observer." [emphasis added]

This is what I've always understood the situation to be. Yet some months ago I watched Mythbusters ep where they answer questions from the fans by conducting experiments, usually to prove or disprove a point. IN this case the point was that Jamie had claimed two objects (trucks, I think) travelling at 40 mph and crashing head on, would experience a collision speed of 80 mph. The fans claimed this was not so, that the impact speed would be 40 mph.

So they performed some experiments, consisting of crashing identical cars as follows: 1) against a wall at 40 mph, 2) against a wall at 80 mph, and 3) two cars head on at 40 mph.

Taking the first two tests as controls, you'd expect the last experiment to settle things. This is empirical data, if dramatically shown largely through wrecked cars. Well, the result was in the head on collision the cars experienced deceleration (measured in g) and damage similar to a 40 mph collision.

What gives??

Either the objects would strike, as Gamow says, adding their velocities or they would not. Who's right? I can't overlook the empirical data. facts are facts (and stubborn things, too). Yet a physicist of Gamow's caliber wouldn't make such and error in elementary mechanics.

This matters in practical matters beyond mere traffic accidents, too. Imagine an asteroid hitting the Earth, which one will eventually. While the mass of the thing is the most important factor, its speed matters, too. If crashing head on it should have a speed much different than if it were overtaking the Earth, or intersecting its orbit. If it's the size of a mountain, it doesn't matter, but for smaller objects it would matter enough to make a difference between a catastrophe and the collapse of civilization.

So which is it?

Quote: Nareed

So they performed some experiments, consisting of crashing identical cars as follows: 1) against a wall at 40 mph, 2) against a wall at 80 mph, and 3) two cars head on at 40 mph.

Taking the first two tests as controls, you'd expect the last experiment to settle things. This is empirical data, if dramatically shown largely through wrecked cars. Well, the result was in the head on collision the cars experienced deceleration (measured in g) and damage similar to a 40 mph collision.

What gives??

It probably has something to do with the fact that it involves two, presumably equal, cars, and each one is going to take half of the damage - something that isn't true when you run a car into a wall, or an asteroid into a planet.

My physics isn't as sharp as I like to think it is, but in a case where there's no loss of energy upon collision, if an object runs into a wall or if it runs into an identical object with equal velocity but in the opposite direction, wouldn't the result be the same - the object would now be going the same velocity, but in the opposite direction?

Of course, the deceleration is going to be 40 to 0 over the distance that the cars can crumple, in the time that that crumpling takes. That will also be true of one car hitting a (presumably more-or-less indestructible) wall.

It's also worth pointing out (although not really relevant here) that a car going 80mph has 4x the kinetic energy of the same car going 40mph, since energy is proportional to the square of velocity.

Quote: ThatDonGuy

It probably has something to do with the fact that it involves two, presumably equal, cars, and each one is going to take half of the damage - something that isn't true when you run a car into a wall, or an asteroid into a planet.

Half the damage, yes, I can see that. But why half the deceleration?

Quote:

My physics isn't as sharp as I like to think it is,

Neither is mine :)

Quote:

but in a case where there's no loss of energy upon collision, if an object runs into a wall or if it runs into an identical object with equal velocity but in the opposite direction, wouldn't the result be the same - the object would now be going the same velocity, but in the opposite direction?

The only way I can see three being no damage in a collision, is if either the striking or struck object are 100% elastic, or nearly so. So a rubber ball meeting the wall, or better yet the floor, head-on at any speed, will rebound in the opposite direction at nearly the same speed.

That, BTW, was what they were partly testing in the case of the frozen vs thawed chicken striking an aircraft windshield. I forget what the conclusion was, after revisiting a couple of times.

Forget complex physics. My intuition says this is a faulty experiment.

The variable is speed. Yet they add in a second variable which is wall v car. You can't have two variables, it makes the experiment void.

A wall, if we're talking generally, doesn't have any give. A vehicle does. The rate of deceleration is going to be much more rapid against a solid object like a wall as opposed to a crumply vehicle.

Quote: Nareed

Half the damage, yes, I can see that. But why half the deceleration?

ThatDonGuy and AxiomofChoice both have it correct. From the perspective of one car in a head-on collision, it's pretty much the same thing as hitting a solid wall -- or perhaps two cars hitting opposite sides of the same solid wall at the same time.

Half the deceleration? Perhaps its terminology. Both cars decelerate from 40 to 0 in the same amount of time as they would when hitting the wall and receive the same damage (roughly). Now the deceleration of one car with respect to the (variable) position of the other is from 80 (relative) to zero in that amount of time. But I'm not sure what that has to do with anything, unless it's something associated with Nareed's initial comment about a simplified discussion of the theory of relativity. I guess I'm not sure just what the question is in that regard. Explain the question, and I'll take a stab at the answer.

They should have collided two cars together at 40mph each, and compared that to colliding a car going 80 with a stationary car.

Quote: Nareed

Imagine an asteroid hitting the Earth, which one will eventually.

An estimated 500 meteorites reach the surface of the earth each year. Just not really big ones.

Per:

http://en.wikipedia.org/wiki/Impact_event

Each of the 2 cars absorbed 1/2 the energy of the hit, so the damage WAS doubled, but assuming they used two identical cars, the force acted equally on them. The wall (presumably) didn't take any significant damage or absorb any of the energy; it reflected it back on the single car at both 40 and 80 mph. If you ran one of those cars head-on into a large Peterbilt, each going 40mph, I bet the car would exhibit considerably more damage than it did running into an identical car, and the Peterbilt would have maybe a couple scratches.

This is one of the reasons I buy large, heavy cars. If I ever DO get into a head-on, I'd prefer the odds were on the side of my winning.

Quote: Doc

But I'm not sure what that has to do with anything, unless it's something associated with Nareed's initial comment about a simplified discussion of the theory of relativity. I guess I'm not sure just what the question is in that regard. Explain the question, and I'll take a stab at the answer.

OK. Forget the Gamow book, it's just something I'm reading. Relativity has nothing to do with this.

I misstated Jamie's claim on Mythbusters. The claim was that two cars colliding head-on at 40 mph would experience the same force of impact as a car hitting a wall at 80 mph. Ergo the experiments with the identical cars colliding with a wall and each other.

My question is, if two objects moving on opposite trajectories collide head-on and their speeds are added, regardless of what their speeds are, then shouldn't two cars crashing head-on each travelling at 40 mph experience a collision speed of 80 mph? And shouldn't the damage be the same, as Jamie claimed, as that of hitting a stationary object at 80 mph?

Now, thinking about what actually happens, it seems to me that each car is moving at 40 mph and will slow down from that to zero, more or less, in a given amount of time. That determines, or rather is, the rate of deceleration measured in g (g=9.81 m/s^2). Whereas a single car striking a stationary object going at 80 mph will decelerate faster.

But what is the kinetic energy in each type of collision, and how does it spend itself in the body of the car?

And should I really be tackling such things so early in the morning?

Quote: Nareed

My question is, if two objects moving on opposite trajectories collide head-on and their speeds are added, regardless of what their speeds are, then shouldn't two cars crashing head-on each travelling at 40 mph experience a collision speed of 80 mph? And shouldn't the damage be the same, as Jamie claimed, as that of hitting a stationary object at 80 mph?

Now, thinking about what actually happens, it seems to me that each car is moving at 40 mph and will slow down from that to zero, more or less, in a given amount of time. That determines, or rather is, the rate of deceleration measured in g (g=9.81 m/s^2). Whereas a single car striking a stationary object going at 80 mph will decelerate faster.

But what is the kinetic energy in each type of collision, and how does it spend itself in the body of the car?

And should I really be tackling such things so early in the morning?

I think Babs nailed what I was trying to say.

If a car hits a concrete wall at 80, assuming the wall is stout, almost no energy is absorbed and dissipated by the wall. Yeah, maybe the bonds between the silicates and limestone and asphalt compress the tiniest bit on the microscopic level, for for all intents and purposes the concrete absorbs nothing. All of that kinetic energy is absorbed by that one car. The plastic in the bumper cover deforms, stretches, cracks, the steel in the bumper itself deforms, stretches, cracks, the mounts what hold the bumper deforms, stretches, cracks, and on back we go to the frame, body panels, suspension, engine mounts, back and back through the car we go deforming, stretching and breaking, until all of the energy is used up.

Car on car though, it's totally different. I dunno what unit of energy is used (Newton meters?) but whatever it is will be halved because what you're crashing into is different. While the total amount of energy is the same, in the wall case it's all being absorbed by one car, in the head on case it's being absorbed by two cars. So a head on will have the same force as 80 into a wall, but only half will be absorbed by any one car.

In other words, same amount of energy, but different amounts absorbed.

Here's an easy visualization...

Next time you're home, go to your bathroom. Take a towel and fold it so it's 4 or 8 layers thick. Place it on your sink countertop and rap your knuckles on it sharply. Doesn't hurt, does it? Part of the energy is absorbed into your flesh, but part of it is absorbed in the soft, deforming towel. Now remove the towel. Rap your knuckles on the bare counter just as sharply. Hurts, doesn't it? The counter is absorbing nothing, leaving your flesh as the only absorber of the energy.

Same concept. The wall is the bare countertop, the towel is a car. Same total energy, but differing amounts absorbed.

Quote: Face

If a car hits a concrete wall at 80, assuming the wall is stout, almost no energy is absorbed and dissipated by the wall. Yeah, maybe the bonds between the silicates and limestone and asphalt compress the tiniest bit on the microscopic level, for for all intents and purposes the concrete absorbs nothing.

I'm sure if you poll the molecules and structures on the surface of the wall, they'd have something quite different to say :)

To me, the easiest visualization in making a comparison between one/two car collision and 40/80 mph is the one I suggested earlier: Consider two identical cars approaching each other with each going 40 mph. They could hit each other head-on and come to a stop very near the point of collision or, alternatively, they could simultaneously strike a rigid wall separating them and come to a stop.

I think it is reasonable to assume that the wall does not take on any significant amount of the energy or momentum from either vehicle. In that case, the two alternatives are very nearly equivalent. The head-on collision results in a similar amount of damage to each vehicle as if each had struck the rigid wall.

If you want to perform some sort of elementary mechanics analysis of these, then the momentum of each vehicle is mV in the direction of travel and the kinetic energy of each vehicle is 0.5*(mV^2) (no direction for energy). After the collision (wall or head-on) and coming to rest, the momentum of each vehicle is zero. The momentum is "destroyed" by the impulse (force times duration) experienced in the collision. The kinetic energy is probably converted to internal energy of the crumpled vehicles, likely evident in increased temperatures of the mangled parts until that energy is transferred to the surrounding air.

A single vehicle traveling instead at twice the velocity has twice the momentum and would exchange twice as much impulse with the wall it collides with. It would have four times as much kinetic energy to dissipate during and following the collision.

As a bit of a side issue, note that two cars colliding at 40 mph have only half the total kinetic energy together of one car striking the wall at 80 mph, i.e., 0.5*(2m)*40^2 vs. 0.5*m*(2x40)^2. Thus, in the one 80-mph vehicle collision, there is twice as much energy to be dissipated by crumpling and only half as much mass available to be crumpled.

Quote: Doc

If you want to perform some sort of elementary mechanics analysis of these, then the momentum of each vehicle is mV in the direction of travel and the kinetic energy of each vehicle is 0.5*(mV^2) (no direction for energy).

Thank you.

I think we can safely resume this thread with the following: I do not understand what adding speeds implies.

Or I didn't. I think I do now.

Quote:

The momentum is "destroyed" by the impulse (force times duration) experienced in the collision.

And I'm sorry but I'm going to have to report you "destroyed" something covered by a law of conservation ;)

Quote: Nareed

And I'm sorry but I'm going to have to report you "destroyed" something covered by a law of conservation ;)

Yes, I saw the smiley, but from a serious perspective, some people interpret "conservation" laws to mean that the total value cannot be changed. If you neglect E=mc^2 and the conversion of mass to energy, then conservation of mass and conservation of energy do perform that way -- the mass can be converted to another form and the energy can be converted to another form, but the total amount of mass and the total amount of energy are conserved.

In contrast, "laws" such as conservation of momentum just mean that the quantity does not change unless something acts to change it. In the case of momentum, it is an outside impulse that causes the change. If a stationary object (zero momentum) always had to conserve momentum, it could never be moved.

Conservation of momentum is a useful concept when considering a collection of bodies. In the case of two cars colliding with each other, their total momentum doesn't change in the collision, unless there is some force from an external source. In the case of the impending head-on collision, each car has momentum mV but in opposite directions. The total momentum of the two cars is zero even before the collision and remains zero after both have come to a stop. Momentum conservation principles are useful in problems such as one where you know the masses of the objects and their pre-collision speeds, but when they collide they do not stop. Instead they careen off at angles. If you know the direction and speed of one of them post-collision, you can calculate the direction and speed of the other. If the collision were totally elastic (not going to happen with cars) then the kinetic energy would be conserved, but in reality much or all of it is converted to another form of energy.

Quote: Doc

In contrast, "laws" such as conservation of momentum just mean that the quantity does not change unless something acts to change it. In the case of momentum, it is an outside impulse that causes the change. If a stationary object (zero momentum) always had to conserve momentum, it could never be moved.

I've been listening to several books (3) that make a point about how fast one is moving at all times, taking into account the Earth's motions, the Sun's motion and the Galaxy's motion. Perhaps I've taken that to heart and know there is always some kind of momentum everywhere ,) (That's a half-smiley).

Then, too, there's Asimov's novel "The Gods Themselves," recently brought up on DT, where the Law of Conservation of Momentum plays a crucial yet minor role near the end (I claim this spoils nothing; it's not like people reading it are used to thinking in terms of physics).

Speaking of speeds and Gamow's Mr. Tompkins' stories, I reverted to type, my type, and began to see some of the stories as stories rather than illustrations of physics. They're ok for what they are, as stories, but I couldn't help but notice a few flaws, or omissions, given the basic premise.

The premise is this: what if the speed of light were 10 miles per hour?

Gamow doesn't actually say this, nor does he quote the actual speed, but when you get relativistic effects from riding a bicycle on a city street, the guess of 10 mph isn't far off.

Now, imagine how life would be like fi that were the case. Nothing could travel or move faster than that. Let's ignore how long the day would be if Earth rotated at a fraction of the revised speed of light, but let's not ignore that if you sent a message through an optic fiber network, it would take one hour to travel ten miles. This means if you called someone a mile away, your message would take six minutes to arrive. Ergo the telephone would be impractical. Television would work, but you'd see a show hours after it was transmitted, or maybe even days after.

Gamow does a good job describing how things look from a bike rider's perspective, and from a moving train, but he ignores most other implications. For example, time would move more slowly for you than it does to others who are not moving relative to you. What does this mean when a non-moving, or even a slowly-moving object or person interacts with the bicycle rider going near the speed of light?

Let's suppose someone tries to cross the street at a corner right when the biker is about to reach the corner. In ordinary circumstances, that is where the speed of light is 186k miles per second, with the bike going 9.99 mph there would be options for both parties as they'd experience time at the same rate.

But under the revised speed of light, the bike rider would see the pedestrian very differently. What would happen? I think I have a clue, but I'm not sure about it.

Quote: Face

I dunno what unit of energy is used

I think its the Splat.

Quote: Face

Forget complex physics. My intuition says this is a faulty experiment.

The variable is speed. Yet they add in a second variable which is wall v car. You can't have two variables, it makes the experiment void.

A wall, if we're talking generally, doesn't have any give. A vehicle does. The rate of deceleration is going to be much more rapid against a solid object like a wall as opposed to a crumply vehicle.

Not faulty, what you're missing is the impact VECTORS. Crashing into a stationary wall has ONE net vector, the moving object. When TWO moving objects collide head-on there are TWO VECTORS; one is considered +, its opponent is -. What is true is that the CLOSING VELOCITY of the two vehicles is 80mph, but they are moving in opposite directions, and thus have opposing vectors of + and -.