CarTalk - Poor Score in Physics
31/05/08 08:14 Filed in: Physics
Tom, Ray, I still think you are Awesome
However, your physics seems to be incorrect.
In CarTalk episode #0821 the car talk guys take a caller with a physics question. "How does a car crashing into an immovable wall compare to a car crashing into another similar car going in the opposite direction?" This is the basic question. Tom and Ray claim that a car crashing into an immovable wall going 120 mph is equivalent to two cars going 60 mph crashing head on.
However, your physics seems to be incorrect.
In CarTalk episode #0821 the car talk guys take a caller with a physics question. "How does a car crashing into an immovable wall compare to a car crashing into another similar car going in the opposite direction?" This is the basic question. Tom and Ray claim that a car crashing into an immovable wall going 120 mph is equivalent to two cars going 60 mph crashing head on.
Before going into details about this question and Tom
and Ray's answer, I must say that this has most
certainly been discussed on the car talk forum.
Please forgive me if you have already stated this
somewhere else. So, instead of just focusing on the
correct explanation (which I will also do) I think
this is a good opportunity to look at common ideas
about force and motion.
First, the correct explanation:
Here is a diagram of a car crashing into an immovable wall.
First, the car going 60 mph crashing into an immovable wall. Here is a a diagram (drawn by myself)
What is important in this analysis? The key thing is that the car gets compressed as it crashes into the wall. Let me suppose it compresses an amount d. During this time, there is a force acting on the car from the wall pushing on it (there is also the ground and gravity acting on the car, but they are equal and opposite and thus cancel). So, let me assume the force the wall exerts on the car is Fwall. Whenever you have a force acting over a distance, the best way to analyze it is by using the Work-Energy principle. This basically says that (for this case):
Where v1 is
the initial velocity (in this case 60 mph). This
expression could be used to solve for the force
needed to be exerted on the car by the wall in
order to stop it in the given distance.
Now to look at two cars hitting head on:
I am showing the cars as being compressed the same amount as before. One way you could explain this is that they have to both stop in the middle (how could one car push more than the other if they are the same?) Also, imagine that the there is a thin sheet of paper at the location where they collide. If the paper didn't tear, it would look like this paper is an immovable wall. So, how does this work. Well, in order for the same car to stop in the same distance, it needs the same force. BUT WAIT! There are TWO cars now. That really doesn't matter. This goes back to Newton's third law with basically says:
For every force there is an equal and opposite force - or as I like to put it: "Forces have two ends" or "Forces are an interaction between TWO objects". Really you can think of it as the force between the two cars. The force between the two cars would be equal to Fwall. Thus the left car would exert a force of Fwall on the right car and the right car would exert a force of Fwall on the left car. This does not mean the force has to be twice as much since it is acting on two cars. Forces are ALWAYS an interaction between two objects.
Now what about the misconceptions?
Here are the key parts of the conversation (mostly paraphrased - I intentionally left out some stuff that was not related to the physics):
Tyler: Presents the question. My dad says that two cars colliding at 60 mph each is equivalent to one car going 120 mph colliding into a brick wall.
Ray: I believe this is correct.
Tom: Your dad is correct.
..
Ray: Give us your rationale, maybe you will sway us.
Tyler: The argument is that there is a certain amount of force, right? These two cars approach...these two cars approach each other, but that force is getting divided two objects, each car. If you are driving into a stationary wall, all of that force is going into one car. So if you are driving 120 mph into a brick wall, that is 120 mph worth of force. Whereas if you are driving into another car, and they are each going 60 mph, that is only 60 mph of force.
Tom: Yeah, the other car is sucking up some of the danger here.
..
Ray: my impression from high school physics is that it is equivalent to hitting the wall at 120 mph
What can be learned form this discussion? First, I believe that Tom, Ray and Tyler are all thinking of force as a property of an object. This is a common idea in normal discussions, and you can see this above with the following statements:
Why do people try to associate a force with a property of an object when it should be associated with an interaction BETWEEN two objects? I am not completely sure. I can say that ideas of force and motion are not as easy as one would think. Even Aristotle got these ideas wrong (though he did not explicitly talk about forces). It seems that people want to associate something with the object. I guess all people are object-oriented.
Another interesting aspect is the idea of doubling. Why is one car going at 120 mph colliding into a wall the same as two objects colliding into each other? I think the reason this is stated is by using ideas of relative velocity. If you are in a car traveling 60 mph towards a car that is going 60 mph, it looks like that car is going 120 mph towards you. Using this reason, Tom and Ray would be correct, but they forgot one important aspect. We are assuming the wall does not compress, but the other car does. This means that for two cars colliding, they BOTH are compressed and absorb energy. If the wall does not compress (even though it really would a little), it would not absorb any energy.
First, the correct explanation:
Here is a diagram of a car crashing into an immovable wall.
First, the car going 60 mph crashing into an immovable wall. Here is a a diagram (drawn by myself)
What is important in this analysis? The key thing is that the car gets compressed as it crashes into the wall. Let me suppose it compresses an amount d. During this time, there is a force acting on the car from the wall pushing on it (there is also the ground and gravity acting on the car, but they are equal and opposite and thus cancel). So, let me assume the force the wall exerts on the car is Fwall. Whenever you have a force acting over a distance, the best way to analyze it is by using the Work-Energy principle. This basically says that (for this case):
Where v1 is
the initial velocity (in this case 60 mph). This
expression could be used to solve for the force
needed to be exerted on the car by the wall in
order to stop it in the given distance.
Now to look at two cars hitting head on:
I am showing the cars as being compressed the same amount as before. One way you could explain this is that they have to both stop in the middle (how could one car push more than the other if they are the same?) Also, imagine that the there is a thin sheet of paper at the location where they collide. If the paper didn't tear, it would look like this paper is an immovable wall. So, how does this work. Well, in order for the same car to stop in the same distance, it needs the same force. BUT WAIT! There are TWO cars now. That really doesn't matter. This goes back to Newton's third law with basically says:
For every force there is an equal and opposite force - or as I like to put it: "Forces have two ends" or "Forces are an interaction between TWO objects". Really you can think of it as the force between the two cars. The force between the two cars would be equal to Fwall. Thus the left car would exert a force of Fwall on the right car and the right car would exert a force of Fwall on the left car. This does not mean the force has to be twice as much since it is acting on two cars. Forces are ALWAYS an interaction between two objects.
Now what about the misconceptions?
Here are the key parts of the conversation (mostly paraphrased - I intentionally left out some stuff that was not related to the physics):
Tyler: Presents the question. My dad says that two cars colliding at 60 mph each is equivalent to one car going 120 mph colliding into a brick wall.
Ray: I believe this is correct.
Tom: Your dad is correct.
..
Ray: Give us your rationale, maybe you will sway us.
Tyler: The argument is that there is a certain amount of force, right? These two cars approach...these two cars approach each other, but that force is getting divided two objects, each car. If you are driving into a stationary wall, all of that force is going into one car. So if you are driving 120 mph into a brick wall, that is 120 mph worth of force. Whereas if you are driving into another car, and they are each going 60 mph, that is only 60 mph of force.
Tom: Yeah, the other car is sucking up some of the danger here.
..
Ray: my impression from high school physics is that it is equivalent to hitting the wall at 120 mph
What can be learned form this discussion? First, I believe that Tom, Ray and Tyler are all thinking of force as a property of an object. This is a common idea in normal discussions, and you can see this above with the following statements:
- "60 mph of force"
- "that force is getting divided between two objects"
Why do people try to associate a force with a property of an object when it should be associated with an interaction BETWEEN two objects? I am not completely sure. I can say that ideas of force and motion are not as easy as one would think. Even Aristotle got these ideas wrong (though he did not explicitly talk about forces). It seems that people want to associate something with the object. I guess all people are object-oriented.
Another interesting aspect is the idea of doubling. Why is one car going at 120 mph colliding into a wall the same as two objects colliding into each other? I think the reason this is stated is by using ideas of relative velocity. If you are in a car traveling 60 mph towards a car that is going 60 mph, it looks like that car is going 120 mph towards you. Using this reason, Tom and Ray would be correct, but they forgot one important aspect. We are assuming the wall does not compress, but the other car does. This means that for two cars colliding, they BOTH are compressed and absorb energy. If the wall does not compress (even though it really would a little), it would not absorb any energy.
