It’s getting to be that time of year. When students roll up their sleeves and take the Texas Assessment of Knowledge and Skills (TAKS). I’ll have a series of classic posts for helpful hints.
Full disclosure time:
- I haven’t seen a TAKS test in a while, but these hints should still be very useful for you.
- I now work for the company that makes the TAKS test. I DO NOT work on or with the TAKS. I do not see the TAKS test (because I have these hints). I have no knowledge about the test at all… other than from the perspective of a teacher and seeing where students need help.
With that, I give you TAKS hints – The Physics Units
First a quick math check:
5 divided by 5 = ?
1 – correct
248423/248423 = ?
1 – correct
meters / meters = ?
it equals 1. The units go away.
Remember this always.
Anything you do to numbers, you also do to units.
Units can be multiplied, divided, squared, etc. Everything!!! I cannot stress this enough.
First you need to know the basic units of the metric system. More here Actually, you only need to know 3 of them for physics and another for chemistry. A fourth is required, but only rarely. (Headings link to the wiki article, but don’t go there unless you really really want to… you’ve been warned… on the other hand, learning can be fun.)
The physics units you need:
Mass – kilogram
Length – meter
Time – second
That’s it. Now for the fun stuff. We combine them.
Velocity – Let’s say you go 5 meters in 1 second. That 5 meters per second or 5m/s. Velocity (well, speed, add a direction to be velocity). What if you go 5 meters in 2 seconds? Well, you put 5 meters over 2 seconds and simplify. 5 meters / 2 seconds = 2.5 m/s
Acceleration – Let’s say your velocity is changing. You hit the gas in the car. Your velocity increases by 2 meters per second (2m/s) every second. So at the end of the 1st second, you’re going 2m/s. At the end of the next second, you’re going 4m/s. Follow?
Basically, you’re changing the distance you go each second. You can find this by taking the final speed subtracting the initial speed and dividing by how long you accelerated. If you start at zero, things are easy. Let’s say you start from rest and take 6 seconds to accelerate to 24 m/s. So your formula is:
(24m/s – 0m/s) / 6 seconds = 4 m/s^2
In math, since you’re dividing by seconds twice, you square it. So you’re acceleration is 4 meters per second squared or 4 m/s^2
Still basic right… now things get fun
Let’s say that you have to accelerate a block that masses 2 kilograms to 15 m/s and you have 3 seconds to do so. You must apply a force to the object to make it change. How much force you ask? That’s a good question, let’s find out.
First, let’s find out how fast we must accelerate the object (see above). (15 m/s – 0m/s) / 3 seconds = 5m/s^2.
So we have to accelerate it by 5 meters per second squared for 3 seconds to get the object to 15m/s. Now, if we multiply the acceleration by the mass (trust me here). 5m/s^2 * 2kg = 10 kgm/s^2
What the heck is that you ask? kgm/s^2. That is one kilogram meter per second squared. It’s a measure of the force you apply to an object. A force of 1 kgm/s^2 will accelerate a 1 kilogram object to 1 m/s in 1 second. Still with me?
This unit has a special name since ‘kilogram meter per second squared’ is long. It’s called a Newton. 1N is 1kgm/s^2.
That’s what we mean when we say derive the unit. If you see Newton, you can replace it with kgm/s^2. That way, you can do math on Newtons.
Work is the amount of energy transferred by a force. Work is always energy. It can be mechanical (push, pull) or thermal (heat) or electricity. The actual derivation is a little beyond IPC, but we can say this:
Work is the amount of energy gained by an object as force is applied to the object over a distance. So if we apply the 10 Newton force (above) to the object over a distance of 10 meters… 2kgm/s^2 * 10m = 20 kgm^2/s^2. Wow? What does that mean?
First let’s simplify it a bit. Instead of kgm/s^2, let’s replace all that with N. So 20Nm. 20 Newton meters. This is a measure of the this distance an object moved by the force applied to it. Further on, you will learn that this changed the energy of the object. We added energy, so a Newton meter is a measure of energy.
Newton meter is still pretty long, so we call this a Joule. A joule is a Newton meter or a kilogram meter^2 per second ^2. See how all these begin to look familiar?
Next we have power. Power is how long it takes us to transfer a certain amount of energy. Let’s say the lead linebacker for the football team and the head of the chess club both have to lift 200 kilograms. Which one will lift it faster (you may be surprised)? The one that lifts faster has more power. Makes sense right?
Power is measured in Joules/second. That is energy delivered per second. This Joule per second has a special name too… you know this one. It’s called a Watt. Yep, like the light bulbs.
Consider if you have a short lunch break and need to heat your frozen dinner. Would you rather use a 200W microwave or a 1000W microwave. The 1000 Watt microwave has way more power, so use that one.
Potential and Kinetic Energy
Last, but not least… these are forms of energy, so what units do we use? Yes, Joules… or kgm^2/s^2.
Now, you know everything you need to know. Remember, if you can do it to numbers, then you can do it to units.
If you apply 15 Watts of power for 20 seconds, how much energy have you used?
15 W = 15 J/s
15 J/s * 20s = 300J
the seconds cancel out here because one is on top and one is on bottom.
OK, if you apply the 300 Joules to an object over a distance of 10 meters? Then how much force was applied?
300 J = 300 kgm^2/s^2
300 kgm^2/s^2 / 10m = 30 kgm/s^2 = 30N
The meters divide out here. How did I know to multiple in the first example and divide in this one? Because the units told me to. I was going from Joules to Newtons (energy to force). The only way to get there is to divide by a distance in meters. THIS IS THE TRICK. By knowing where the units are, you can get the right answer, even if you don’t know the formulas!!!!
You apply 30N of force to object that masses 2 kilos . What was the acceleration of the object?
30N = 30kgm/s^2
30kgm/s^2 / 2 kg = 15 m/s^2
Again, kilograms on top, so I had to divide by kilograms. kilos/kilos = 1
If you accelerate an object at 15m/s^2 for 10 seconds. What is the final speed?
15m/s^2 * 10s = 150m/s
I’ll stop there, you can figure out the rest.
I hope that helps.