0:06 in today's video we're going to look at
0:09 momentum which is a property that all
0:15 the main thing to know is that momentum
0:18 is equal to the mass of an object
0:21 multiplied by its velocity
0:24 so if we saw a four and a half thousand
0:26 kilo dinosaur
0:29 charging at 12 meters per second
0:30 then its momentum
0:33 would be 4 500
0:35 times 12.
0:40 so 54 000 kilogram meters per second
0:44 whereas if we had a 1200 kilo car
0:47 traveling at 25 meters per second
0:51 then its momentum would be 1200 times 25
0:59 an important thing to remember though is
1:02 that momentum is a vector quantity
1:05 so it has both a magnitude and a direction
1:07 direction
1:09 so here if we consider the forward
1:12 direction to be to the right then the
1:16 dinosaur will have a positive momentum
1:18 but the car must have a negative momentum
1:24 the next thing to know is the
1:27 conservation of momentum principle
1:29 which is the idea that in a closed system
1:30 system
1:33 the total momentum before an event like
1:34 a collision
1:36 is exactly the same as the total
1:38 momentum after the
1:41 event to see how this works let's
1:44 imagine our dinosaur and our car as two
1:47 particles which are traveling towards
1:50 each other and are going to collide
1:52 after which they'll both continue moving
1:55 together at the same speed
1:57 how would we find their velocity after
1:59 the collision
2:01 well the first thing we need to do is
2:03 find their total momentum before the collision
2:05 collision
2:07 which we can do by adding together the
2:11 dinosaurs and the car's momentums
2:13 so 54 000 plus
2:14 plus
2:16 negative 30 000
2:20 which gives us positive 24 000 kilograms
2:23 meters per second
2:24 then because of our conservation of
2:26 momentum principle
2:29 we know that once they've collided
2:30 their total momentum
2:34 must still be positive 24 000
2:36 and remember that in this scenario a
2:38 positive number means that it's going to
2:41 the right
2:43 so after our particles collide together
2:46 they'll both get carried to the right
2:50 because the purple one had more momentum
2:52 and because they're both moving together
2:54 we can now treat them as a single large particle
2:57 particle
2:59 so to work out their shared velocity
3:02 all we have to do is rearrange our
3:05 momentum equation to show that velocity
3:08 equals momentum divided by mass
3:10 and then plug in the values for this
3:12 combined particle
3:15 so 24 000
3:17 divided by their combined masses from before
3:18 before
3:20 which would be four thousand five
3:21 hundred for the dinosaur
3:24 plus twelve hundred for the car
3:28 so five thousand seven hundred kilos
3:30 which gives us a velocity of four point
3:38 so basically after the dinosaur and the
3:39 car collide
3:42 that both continue moving to the right
3:51 now in some circumstances
3:54 the momentum before an event might be zero
3:55 zero
3:58 like it is for stationary objects
4:00 which don't have any momentum because
4:02 they're not moving
4:05 and so in these cases the total momentum
4:06 after the event
4:13 for example if we imagine a gun before
4:15 it's fired
4:17 then its initial momentum would be zero
4:20 because its velocity is zero
4:23 however once the gun fires the bullet
4:25 that flies out will have a momentum in
4:28 the forward direction
4:30 and so to compensate for this
4:33 the gun has to recoil backwards with an
4:34 equal momentum
4:37 so that together the total momentum is
4:44 so if we knew that this gun had a mass
4:45 of 2 kilos
4:48 and that a 5 gram bullet was fired out
4:52 at a velocity of 120 meters per second
4:54 we should be able to work out the
4:57 velocity of the gun's recoil
4:59 the key to this is remembering that the
5:01 gun's momentum
5:03 plus the bullet's momentum
5:05 must equal zero
5:07 because it started off at zero before
5:10 the gun fired
5:12 the first thing we want to do is find
5:13 the bullet's momentum
5:16 using this bottom equation
5:17 so we do 0.005
5:19 0.005
5:22 which is its mass in kilos
5:25 times its velocity of 120
5:28 which will give us a momentum of 0.6
5:34 next we want to try and find the gun's momentum
5:35 momentum
5:39 so again we just do the mass of two
5:41 times the velocity
5:42 but because we don't know what the
5:44 velocity is yet
5:47 we can just write v for velocity
5:50 so the momentum will be two v
5:53 where two is the mass in kilos
5:56 and v stands for the gun's velocity
5:59 which we're about to find out
6:02 finally we can use these momentum values
6:05 for the gun and the bullet to rewrite
6:06 our equation
6:08 as 2v
6:10 plus 0.6
6:12 equals 0
6:13 and then we can just rearrange this
6:16 equation to find out the missing value
6:18 of v
6:22 so first we subtract 0.6 from both sides
6:26 giving us 2v equals negative 0.6
6:30 and then we divide both sides by 2
6:33 leaving us with v equals negative 0.3
6:35 meters per second
6:39 which is the gun's recoil velocity
6:42 and remember the fact that it's negative
6:43 means that it's effectively going backwards
6:45 backwards
6:47 or in other words it's going in the
6:55 the one thing we haven't mentioned yet
6:57 is that you need to know that the letter
7:01 symbol for momentum is row which looks
7:02 like a p
7:04 so the momentum equation can also be
7:06 written as p
7:14 that's everything for this video though
7:17 so i hope you enjoyed it if you did then
7:19 give us a like and subscribe
