In the last episode of MythBusters, they tried to reproduce the following experiment. Suppose you are driving in a car at 60 mph and you shoot a ball backwards at 60 mph (with respect to the car). Will the ball just drop (with respect to the ground)? Actually, it is a cool demo - I saw some Japanese show did this a while ago.
So, what is the problem? The problem is with the MythBusters' use of their terms to explain this thing. Let me look at a couple of the things they said to explain this (surprisingly, they described it several different ways). This first one is my favorite.
Bad physics 1
"it makes sense that an object subjected to equal and opposite forces would drop like a rock."
Where to begin? First, I am not sure where they get these equal and opposite forces. I would love for the science diagram to include a free body diagram for the ball after it is shot out of the truck. It would probably look something like this:
Oh, I know. Neither of those are real forces - but that must be what they are thinking. Now for the next problem with that statement. Here is a correct force diagram for an air plane flying with a constant velocity.
I am not going to talk about planes - this was just the first example I came up with. In this case the force pushing forward DOES equal the force pushing back. Does the plane drop like a rock? The idea that a net force of zero (vector) means no motion is what Aristotle would say.
Bad Physics 2
Here is another quote regarding the ball:
"Does the forward momentum and the backward momentum cancel out?"
I think the main error here is that they are using the term "momentum" to either mean velocity or force - not sure which. Also, if they are talking about momentum, the momentum of what? The truck and the ball?
Bad Physics 3
"...see if the energies cancel out"
Can you get energies to cancel? Well, you could get the potential plus kinetic to be zero joules, but would that count as canceling? You can never get two kinetic energies to add up to zero because 1) it isn't a vector and 2) it is always positive.
I usually don't attack the MythBusters, but I couldn't help it in this case. Dear MythBusters, if you want to explain some stuff in the future give me a call. I will gladly look over your stuff for you.
I saw only the final 1/3 of the episode, so didn't see what they claimed was the source of the "myth" (I did think their video was pretty cool).
I first heard this "myth" as it concerned the old B-58 Hustler bomber - capable of speeds up to mach 2.
The original design had a 20-mm gun in the tail, and the stories were that when the gun was fired during high-speed flight "the bullets simply left the barrels and fell to the ground". It was a cool visual for a kid - I have no idea whether it actually happened.
Since the bullets are shot at something that's presumably following the bomber at Mach 2, the impact is the same for the target even if the bullet doesn't move relative to the ground. But to open the big can of worms, what if you're leading the target by shooting slightly above it to make up for the bullet drop? If you're watching from the stationary observer point, do you see the bullet go up in a straight vertical line, followed by a reversal of directions (assuming the horizontal velocity vectors still cancel out)?
I think my problem was the approach as a whole - this is one of those problems that is better handled (mathematically) using frame of reference transformations rather than traditional Newtonian mechanics methods. In fact, in modern physics (for the undergraduate) this type of scenario is one of the first examples we're taught before going on to Einstein's Relativity and how light handles reference frames differently.
The first statement is clearly erroneous. It massacres both the first and third laws. The second statement is fine as all you have to do is multiply the velocity addition formula by mass to obtain a "momentum addition" formula:
m*v_ball_ground = m*v_ball_car + m*v_car_ground
The forward momentum of the car and the backwards momentum of the ball "cancel". The third statement could refer to work-energy for the ball:
K_final = K_initial + W
The work on the ball is negative and "cancels" the initial kinetic energy. I agree with the woman in the picture. Go pick on ESPN's "Sports Science" again because they clearly just make stuff up.
Yikes - Sounds like this could be a good exercise for high school physics students. "Find all of the mistakes Jamie & Adam make". This might also help the "everything that comes from the TV or teacher is right" syndrome.
I don't know if that is a guy or girl. But you are right, ESPN just makes up crap and I still love the MythBusters.
@Erik + Rhett,
That is a boy in drag. A loony one at that. The MythBusters are great, we've just got to remember that they are special-effects guys and not practicing physicists! Perhaps they could use your help after all Rhett...
Adam Savage and Jamie Hyneman are actually speaking at my campus tonight. Unfortunately I didn't get tickets or else I could explain to them what Newton's 3rd law means.
I saw those issues in this episode and assumed you'd quickly blog about them, so I didn't. But I'm beginning to tire of Mythbusters, they're running woefully short of "myths" and are reaching.
The ball out of the truck was a great idea, it was a shame they did the force/energy/momentum talk. Then they say things like "science in progress." Well heck, science is always in progress. But they mean they're "doing science," why can't they take the time to learn the actual terminology?
The mythbusters are awesome at building stuff. Science, not so much. It used to be ok because they didn't try to explain science. In this case, I would have been ok if it had just been Tory and Grant talking - but when they put in the narrator, then it becomes official science explanation and at a different level.
The work on the ball is negative and "cancels" the initial kinetic energy. I agree with the woman in the picture. Go pick on ESPN's "Sports Science" again because they clearly just make stuff up. thank you good informayin good post
Actually this thread gives me an idea for a lesson. Teach students about airplanes and how they fly. (Any good ground school textbook will cover it nicely, let alone the classic stick and rudder). You can show how if you have more lift that gravity forces you climb, and the converse if you have less lift (which is why you throttle back to descend, and throttle up to ascend) You could also cover centripital forces with turning planes and how if you try to maintain level flight while turning depending on the angle you hold the wings at you will feel a g force. (Actually maybe get a hold of a flight simulator and demo it (except for the g forces, but when I took a few lessons it feeling the g forces pushed the concept home to me).
One small (but important point) - if the lift is greater than gravity, you would _accelerate_ upwards. This could be still moving down though - think about doing a loop the loop - on the way down the plane is moving down but the acceleration is partly upward.
I do like the idea of the simulator though.
If you're watching from the stationary observer point, do you see the bullet go up in a straight vertical line, followed by a reversal of directions (assuming the horizontal velocity vectors still cancel out)?
But to open the big can of worms, what if you're leading the target by shooting slightly above it to make up for the bullet drop? If you're watching from the stationary observer point, do you see the bullet go up in a straight vertical line, followed by a reversal of directions (assuming the horizontal velocity vectors still cancel out)?