00:01
Well, this set of problems is, like it says, intended to impart a sense of what the units of momentum mean.
00:13
In other words, how much momentum is a big momentum, how much momentum is a small momentum.
00:17
The format we're going to use for all three problems is momentum, which is abbreviated with letter p.
00:24
It comes from the latin word progressum, i believe, is equal to the mass of the object.
00:31
Times its velocity.
00:33
Momentum is a vector because velocity is a vector.
00:37
Whenever you multiply a vector times a scalar, you get another vector back.
00:41
But in this problem, they're just asking about the magnitude of the momentum in each problem.
00:47
The first one is pretty straightforward.
00:51
We are given that we have an object that has a mass of 58 kilograms.
00:59
So that's 58 kilograms.
01:03
And we're supposed to multiply that times the speed of five meters per second and we can get that easily enough multiplying by five or just using your calculator you get that it's equal to two hundred and ninety and there's no special unit for momentum it's just kilograms times meter per second so they say it kilogram meters per second and they gave us two significant digits in this one well actually they gave us only one significant digit for five meters per second, but we can presume that they want us to give at least two in the answer, i would suspect.
01:48
Now, the second part is involving a conversion first from miles to meters.
01:59
Well, i just looked up really quick on the internet, and i saw that 1 .609344 .4.
02:13
Kilometers is equal to one mile.
02:18
Now, to get that exactly, you'd have to start with the relationship between inches and centimeters because that is the official definition of the inch is that is 2 .54 centimeters.
02:30
And working from there, you could work your way to finding out how many kilometers are in a mile.
02:36
But we're going to do this conversion using that.
02:38
I'm not going to use all the digits because the numbers they gave us only have two significant digits so we write the number down we should probably write it down to two significant figures but i'm going to keep more digits than they give us so i don't over around so we're going to start out we want to talk about 67 miles per hour that's the unit we have to convert first now to do unit conversions what you have to do is you multiply your quantity by things that are representing one and as you know anytime you have an equal thing divided by an equal thing, that's equal to one.
03:16
Like, four divided by two times two.
03:20
Well, that's equal to one.
03:22
So what we're going to do is we're going to write factors of one here, but the factors are one are going to be equal things divided by equal things.
03:30
For example, i can say that 1 .609 kilometers is equal to one mile.
03:42
So therefore, when i multiply by that factor, i'm not actually changing the quantity, but changing the labels of its units.
03:51
Now, you'll notice what this gives me is i have a mile in the numerator over here and a mile in the denominator over here, so i can divide out by that.
04:00
I'm left with kilometers.
04:01
Now, we don't want it in kilometers per second...