A post from my defunct Marvel blog reprinting a strange letter that we’d received in the mail.
The week has taken an ugly term in terms of workload, which is why this blog entry is a bit late–hopefully, I’ll manage to get another one up before the end of the day, and maintain a “one-a-day” output, even if they all tend to jam up at the end of the week.
Every day, we get a lot of e-mail from fans and readers about our books. And it’s all greatly appreciated–regardless of the content, the fact that somebody is affected enough by the stuff we’re producing to take five minutes and send us off a note. Some of it is praise, some of it is anger–and then, there are other communications that defy easy classification, where the letter-writer has a point that’s of specific interest to them. These letters aren’t bad–they’re just kinda strange.
So here’s today’s Strange Letter From The Mailbag:
I’m sorry, but Carol would only need to exert a force similar to benching
12.7 tons to have stopped the car. You failed to do proper dimensional analysis when doing your calculations, mainly be completely ignoring units and what they even mean. Your first mistake was taking kilograms and multiplying that by miles per hour. If you’re going to do the problem in metric, do it in all metric units. The units in momentum would be kg*m/s which makes perfect sense. By the equation printed. You have a mass times a velocity. Mass is kilograms and velocity should be meters per second.
This is dimensional analysis. I’m going to solve the same problem two different ways now. The way I would solve it and your way with correct units.
The acceleration is 90mph in .5 seconds. 90mph is approximately 40m/s.
Force=mass*acceleration. The acceleration is (40m/s)/.5 = 80m/s. So F=1550kg*80m/s. This equals 124,000 Newtons (I’m ignoring significant figures for simplicity). Just for reference a Newton is kg*m/s^2. You used it as if it was kg*miles/(hour*seconds) which is not correct. So for Carol to have to deal with 124000 Newtons it would be similiar to her benching
12.7 tons. This is found with Force=mass*acceleration, only modifed with mass=Force/acceleration. In this case the acceleration is 9.8m/s as that is what she would have to cope with when bench pressing. So 124,000 N/9.8m/s=12,700kg. And since 1kg=.001 ton then it is 12.7 tons.
Your way, only with correct units:
momentum = mass * velocity. p=1550kg*40m/s. p=62000kg*m/s. Also note that p = momentum. Yes it doesn’t seem to make sense but this isn’t a physics history lesson. So then we take 62000kg*m/s and divide that by .5s to get the impulse which = 124,000 N. From there you should be able to understand how to convert it to 12.7 tons by the previous example.
Carol would only have to withstand a force similar to 12.7 tons and for a person than can bench 50 tons, 12.7 is nothing. By comparison. If you could only bench 150lbs it would be like having to bench 38lbs. Which would not be hard at all. A more direct comparison would be trying to catch something that weighs 4.68lbs going 90mph. This would hurt, a lot. It may injure you. To give you credit, this comparison would show that Carol was probably trying to avoid a little pain trying to catch the car, especially with it moving so fast. To explain catching the armored truck with ease in issue #1. It was only falling with gravity. It did not have very much horizontal velocity. It had some, but most of it’s force was in the vertical plane.
Well, this is probably too long to print, but butcher it however you want or don’t print it at all. Sometimes you need a little bit more than google.