00:01
Question 33 asks us to determine the forces that act on the brain as it moves inside the head.
00:06
So we've got our 3 .3 kilogram head that encases a 1 .5 kilogram brain.
00:11
Everything starts out at rest.
00:14
And then your head is subjected to a fairly large force, 28009 ,000, for a short amount of time, 0 .0065 seconds, which causes your skull or your cranium to accelerate, but not your brain since your brain is floating inside there.
00:28
That means the back of your head is going to collide with the back of your brain and cause it to accelerate as well and so we're supposed to figure out in question a what is the speed of your brain or sorry the speed of your cranium after this force acts and then in part b the back of the cranium collides with the back of your brain which is still at rest what's their final speed after they collide and then finally see the cranium hits an external object and suddenly comes to a rest the brain can take continues of course to move forward, that's inertia, and if the front of the brain interacts with the front of the cranium over a period of 15 milliseconds before coming to a rest, what average force is exerted on the brain by the cranium? so a whole bunch of beating your brain up here and purely physically instead of the typical mental gymnastics that physics has us do.
01:16
So let's start by finding a, the velocity of the cranium right after this force acts.
01:23
This is an impulse momentum thing, so remember the average force times the the time over which it acts is equal to the change in momentum of the object.
01:33
Well, its initial momentum was zero because it was initially at rest.
01:36
So this is going to be its final momentum, m times final velocity minus zero, its initial momentum.
01:43
And so i can just take this 2 ,800 newtons times, it told us 65 milliseconds, but millies times 10 to the negative third, so 0 .0065, and set that equal to the mass.
01:55
Now this is just accelerating the cranium 3 .3 kilograms times v.
02:00
And if we work this all out, we get a final velocity for part a.
02:05
Our velocity is 3 .5 .5 meters per second.
02:12
Now, the back of your brain is going to smash into the back of your, i guess the back of your cranium smashes into the back of your brain, causing everything to move together.
02:21
This is going to be a momentum conservation thing.
02:26
So this looks like we had initially 3 .3 kilograms of matter moving with the velocity of 5 .5 meters per second...