I already mentioned the MythBusters’ crashing two cars episode where they correctly doubled the speed of a pendulum type object. Overall, this was a very visual (although expensive) demo. There was one part that left a sour taste in my mouth – the final explanation from the narrator. First, they showed this.
And then they had an explanation that went something very similar to to this (after restating what the sign above said)
“Although the two-car crash doubles the speed, the energy the crash is transferred to twice the mass resulting in a crash that looks like just one car hitting a wall at 50 mph.”
Here is the graphic that went with that.
I had to re-listen to this narration a couple of times because something seemed not quite right. First, let me comment on the last diagram. Really, maybe it would have been better to leave this off. It doesn’t really add any useful explanation other than to point out that the kinetic energy is dependent on the square of the velocity. And what about the narrative? I think what bothered me is that they said the two-car crash doubles the speed, but what they probably should have said is “the two car crash doubles the kinetic energy and this energy is spread out over 2 cars.” Using their statement, you would say “oh, double speed means 4 times as much energy.”
Here is the real question: what concept are you trying to get across? Newton’s third law? The idea of kinetic energy? Conservation of momentum? I would just pick one and stick with it. Otherwise, you are kinda implying that “action and reaction” have something to do with kinetic energy. Oh, have I ever mentioned how much I hate “action and reaction” explanation of Newton’s 3rd law? Action? Reaction? How about this for Newton’s third law:
Forces are an interaction between two objects. Forces come in pairs. Or, if you must: For every force there is an equal and opposite force.
Oh sure – you can make the action reaction thing work, but it can also cause problems. Either way, I would suggest sticking with the energy explanation. Here, I want to help. I am going to give an energy explanation that the MythBusters could use and a force explanation for the two-car collision.
Two-car crash, energy explanation
Why are two cars crashing into each other not the same as one car going into a wall at twice the speed?
Explanation: In terms of energy, the energy of motion is called kinetic energy. Kinetic energy depends on the square of the velocity. This means a car moving at twice the speed with have 4 times the kinetic energy.
So 10 + 10 is not the same as 40.
Two-car crash, force explanation
This is a little more complex, but I will try to make it simple. First, two key points:
- Forces are an interaction between two objects. Object 1 pushes on object 2 the same as object 2 pushes on object 1 (same interaction).
- A force on an object changes the object’s momentum where momentum is mass times velocity.
Suppose a car crashes into a wall with a velocity v. While it is interacting with the wall, the wall exerts a force (F) on the car and the car exert a force F on the wall.
Where the force the wall exerts on the car and the car on the wall have the same magnitude. Now, what if I replace the wall with another identical car traveling at the same speed?
Since the initial momentums are the same and the forces are same, the effects are the same on the two cars. So, two cars are the same as one car into a wall. If I now double the speed, I will have different initial momentum, so it will not be the same.
I actually forgot that I have talked about the MythBusters colliding two cars before. I wrote this post the first time they did this myth. That is a little more detail than I have here. Also, a similar thing came up when the MythBusters tried to pull two phone books apart. Here is my discussion of forces in that situation.
One more thing. I would like to emphasize how awesome this demonstration was. You hear people discussing things just like this all the time, but no one actually does it. For many physicists, the actual experiment doesn’t mean much. However, to many people this experiment is important. They just need to fix their final explanation (call me next time and I will be glad to help).