Vectors

ARRRRRRRRRRRRRRG HAPPY HALLOWEEN EVERYONE I TOTALLY DIDN'T FORGET TO BLOG BECAUSE MY MIND WAS OCCUPIED WITH HOLIDAY SPIRIT.
VECTORS. RIGHT.

SO. What happens with vectors is that we want to ADD THEM. Why? Because they're silly little things that tells you the direction by being SEPERATE so they can annoy you until you start pulling your hair out and head desk yourself.

OK not really they're basically lengths of directions, which can go North, South, East, West. They can also be known as North and negative North, East and negative East and vice versa, whatever is easier for you.

So when you get seperate vectors, you'll want to add them in order to see the sum of the vectors. If you don't get why, imagine you're trying to find a way to get to a destination the quickest. So for example, if you were given two vectors like 3 to North and 5 to South, the quickest way to get to the final point would be 2 to South. This is the sum of our vectors.

What if we get more then one dimention? Like 2 to the North and 5 to th East? Then we're going to have to use the Pythagorian Theorum. Oh yeah, more math, who's excited? I sure am not. If you try sketching the vectors, you might notice something.

That's right, the right angle triangle. So you can find out the total vector by adding the squares of the lines, then square rooting it. So it would be 2² + 5² = R², R = 5.39.

We can also find the angle of the vector so we know the exact direction. We do this by using trigonometry. Oh HEY there, SOH CAH TOA, long time no see. Here's a diagram of how we're going to use this:

The guy with the Zs and the angles are here too, joy. We want to use TOA, so it would be tan(data) = opp/adj = 2/5, (data) = tan^-1 (2/5), (data) = 21.8.
Finally, we would display the answer like this: 5.39 units [N 21.8^o E]. Well that's all folks, have a happy halloween that's over in half an hour. Good night.

kinematics equations

Oh god oh god I almost forgot about this sdkfjlsdkjfs
God I've been so absent minded recently this isn't good at all.
This week, we were learning about the Big 5 equations of kinematics that we use to find the displacement, time, velocity, etc. I'll be explaining two of those that we can get from the graph.

The third equation we learned was displacement = V₁t + ½ at²
The fourth equation was displacement = V₂t - ½ at²

If we take a look at a velocity/time graph while trying to find the displacement, it might be confusing. We can add math into this and make it much simpler then it could be.

A normal velocity/time graph looks like this:

To find the displacement, we must find the area of the triangle created by the line, the dotted line, and a line not yet on the graph that will go horizontal from V1, since v = dt.
If we try to find the area by dividing the graph into a triangle and a rectangle, it would look like this:

To find the area of the triangle, you must use the equation a = 1/2bh. Since in here a=d, b=t and h= v2-v1, the equation will turn out:
d = 1/2 t(v2-v1)
And we learned that a = (v2-v1)/t, so v1 = at-v2
Therefore
d = 1/2t(v2-(at-v2))
d = 1/2t(v2-at+v2)
d = 1/2t(2v2-at)
d = v2t - 1/2at²
Which is the fourth equation. We can get the third equation by doing the exact same thing, except instead of isolating v1, we isolate v2.

Distance, Velocity, Acceleration: Graphs

We had an activity again, this time having to walk a graph. No I'm not speaking in horrible grammer, we walked a graph.

Using a motion detector connected to the computer with a program called Logger Pro, we could graph our movements front of the motion detector. We were given 6 graphs already drawn, and had to move in certain ways to try matching the lines created by our movements to the predrawn graph. This would help us understand what the graphs show.
Unfortunately, our group was only able to finish two. Here they are:

Yeahhh we were focusing too hard on matching the graphs. The thing was lagging and skipping too, it totally wasn't because Jess is an OCD leader shut up so I say we were excused. We were about to finish one with velocity, but we didn't finish in time. I couldn't screenshot it.
NO STOP SHUNNING ME WITH YOUR IN YOUR MIND. I KNOW YOU ARE.

<Edit>
We're supposed to blog about the hypothesis of velocity and acceleration graphs for the ones we finished.
The first graph's velocity and acceleration would look something like this:

It's a basic sketch, so the numbers aren't correct. Acceleration is right though, it'll always be zero. For velocity, it'll first be zero, then rise to 1.5m/2s = 0.75 m/s, drop back to zero, then 0.7m/1.5s = 0.47m/s in negative, then back to zero again.

For the second graph it'll be like this:

Acceleration will be zero again, as there is no speeding up in these graphs. There probably were some graphs given that had some accerelation, but y'know, I didn't get to them.
Velocity will be at 1.5s/3m = 0.5 m/s at first, then zero, 1m/1s = 1 m/s, then zero, 2.5m/3s = 0.83 m/s at the end.

Motors

Oh my dear god I made something move without touching it and it made sparks.
I'M SO HAPPY.
I'd post the picture and the video of it working right here, but seems like my partner is having technicall difficulties. Sob.

Here have a picture of a sexier and shinier picture of a better motor for now:

I'LL BUILD THIS SOMEDAY, YOU'LL SEE.

And here's a diagram of what it was supposed to look like:

BE SATISFIED.

See we were given one day to find the materials, and one period to make this motor. The main problem of the whole thing was that I couldn't find a 4 inch nail. The best I had was a three inch and it was SO thick, it was like thicker then my pinky. No way I'm gonna be able to hammer that in the wood.
I had to ask my friends for some nails, desperately messaging to people on msn if they had nails. Luckily someone seemed to have them, after buying some for his own motor it seems.
Then he came to school pretty late. Oh sweet Jesus.

We were still one of the first people to finish, yayyyy.

So what happens is that current flows through the wires and creates a circular magnetic force. If we place those between north and south magnets, the forces would cause one to push itself up and the other to push itself down. Then we use conducting brushes to switch the currents whenever it gets to its limit in pushing itself up or down, so it continues to go around as it pushes itself the other way. This creates a motor, and DAMN did I learn to make one. I also learned I hate paper clips. A lot. Stupid things won't bend and won't stay in the wood.

They are always in my way.