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Chris Peterson SM '13

Aug 26, 2011

My Life, As Physics Problem

Posted in: Miscellaneous

First off: 

The Tech ran an article about our site redesign / admissions wiki today. Amita Gupta, a freshman member of the inaugural Tech FPOP, interviewed Matt and I yesterday for it, and the article is pretty awesome, so go read it! 

Secondly: 

Some of you may have read my blog post about my bike accident

In it, I talked about how my internal dialogue immediately after my accident was all about trying to figure out the physics of my crash and how that might have affected the fact that I escaped mostly unharmed. 

The problem is I haven't taken physics in like six years, and besides F=MA and watching my teacher set his hair on fire I don't remember many of the specifics. So I emailed Yan '12, who is also President of MIT Undergraduate Women in Physics, and asked her to do some physics for me. 

Here's what she emailed back: 

So sometimes when I'm modeling the physics of real-life scenarios, it's useful to start with the absolute simplest scenario that may or may not answer all the interesting questions about what's going on. Let's call this "Level 0."

At Level 0, it's pretty easy to explain what happened. I'm going to assume that (1) only the component of the car's velocity along your line of travel (make this the y-axis) affects your probability of survival and (2) the relative y-velocity between you and the car is related to the force along y delivered to your bike in some simple way (for instance, linearly).

Say that the car is traveling at 35 MPH. Its y-velocity is then 35/sqrt(2) MPH, or around 25 MPH. If you're traveling at 20 MPH along y and collide with the car, the situation is the same as if you collided with a stationary car while biking at 5 MPH. As opposed to if the car had been traveling directly at you or from the side, in which case you would have collided with it at significantly higher velocities (55 MPH and 35 MPH, respectively).

Hope this helps!
Yan

 It does help, Yan. It does help. It helps me confirm what I had already thought to be true: that angular velocity saved my life. 

p.s. a blogging brownie to whomever in the comments can come up with the best illustrations for the various scenarios described by Yan above. I'll edit any into the body of the text. 

Comments (Closed after 30 days to reduce spam)

Hi Chris! Glad that you made it out of that circle in not-too-terrible shape! :D. Yay for vectors indeed~

But, so far as the life-or-death physics problem goes, I'd like to respectfully point out the fairly high importance (as my thoughts lead me to believe) of the car's x-velocity.

(Now, I do assume that the car was in front of you for all impact-relevant frames of time [as I understand it was]--correct me if i'm totally wrong.)

So, as I was quickly sketching this problem out, I realized that the presence of the car's x-component (also ~25 mph) presented the most significant danger to you. If we isolate the components,
(With Car @ 45 degree angle:)
Car's Y-Velocity=~25 mph
Chris' Y-Velocity=20mph
The car is travelling in front of you, so if you're standing still, it's relatively travelling 5mph faster than you. Not, perhaps, posing much danger to you (isolated situation). Either way, change in velocity would be small compared to:

Car's X-Velocity=~25mph
Chris' X-Velocity=0mph
I think that here, the car is imparting a much greater change to your system-the x-movement of the vehicle is much, much higher than your movement in the x-direction(0), which should end up impacting you much harder. There's a (conceptually) greater change in momentum here compared to the above Y-component situation (with all masses the same). The collision happens in the same amount of time, so the impulse would be greater here too.

In fact, if we gradually eliminate the car's x-component and move more of its velocity into the Y-direction, we find that possible damage to you is reduced because more of the car's velocity is travelling *away* from you (in the same direction as you, but the car is in front for relavant collision times).
Conceptually then, if one totally eliminates the x-component of the car, you'd be totally fine (as you're behind the car during the frame of impact, the car is travelling away from you).

As soon as we start introducing a slight x-component (making the angle from vertical larger) danger to you increases.
As Yan said, the danger to you would be considerably *higher* if the car was coming at you from the side---at which point the car would have 0% Y-velocity and 100% (35mph) x-velocity. This hurts mostly because you're not moving in the x-direction compared to the car. None of the car's energy is in the Y direction, so :(. X-velocity bad.

So basically, I think that it is the x-velocity of the car that's really posing the danger to you. As you said in your previous post, your Y velocity "bled" into the car's Y velocity, which helped save you! Y-Velocity (only because the car is in front of you for the impact moments) is good! More of your velocity bleeds into the car's velocity. I say that the higher percentage of the car's velocity that falls in the Y-component, the less danger to you (life probability higher)! The more in the X-component, the worse off for you. I think the x is most significant as far as danger goes.

As you said, luckily the car was at an angle, and not perpendicular to your motion (with velocity only in the X-direction if you're moving the the Y-direction).

Because of that, you seem to be okay :D. And for that, i'm glad.

If you've read this whole thing, then wow! Thanks for your time!
I end up modeling real-life though physics quite a bit as well!

Thanks again,
-Suyash :D


Posted by: Suyash on August 27, 2011

Ah and forgive me, Yan put it nicely (yay Level 0)~ I just thought through it differently and figured the importance of the x-component into it^ [so randomly chimed in].
Glad that you're ok Chris! MIT, Chris, and MIT admissions blog ftw.
All very awesome. :D

Posted by: Suyash on August 27, 2011

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