FINAL ROUND!

FIGHT!

Ok, don't. But finals are coming up. Wednesday for seniors, and monday of next week for underclassmen. So, get on it.

Bernoulli's principle

The fancy way:




For dummies: as the velocity of a fluid increases, the pressure exerted by that fluid decreases.


Even simpler: Velocity increases = pressure decreases



Its what make airplanes fly.

The air on the bottom maintains the same path and stays the same speed. The higher pressure on the bottom pushes the wing, and the plane, up.

Time to study water rockets

So go to aircommandrockets.com and do it. Ok? Good. Cause you can tottaly build this.

Charles Law and other Pressure Stuff

Kinetic Energy

Everything is made up of molecules. These molecules are never still. They are always wiggling around being pulled by different forces.



Look! Now you’re doing chemistry

Bonding

The molecules are all held together by bonds. These bonds are like holding hands with another person. You can hold on tight or you can hold on loosely. You can pull together or you can be stretched apart. You can be pulled apart with force or you can twirl around each other.



As the temperature increases, the molecules move faster. The faster they move, the more bonds they break. The molecules then spread out, bouncing all over everywhere. They are now a gas.

When the molecules are at room temperature they are wiggling a little with kinetic energy. In this state they are loosely bonded to the other molecules. They can hold on, there aren’t many forces pulling. This is why liquids flow.



Charles Law

When heat is added, the molecules begin to move faster and faster. This causes them to need more space and pressure to increase.



As temperature increases, pressure increases.

Why Should You Care?

If the molecules have room to defuse (spread out) all is good.

Inclined Planes

What it do

A simple machine consisting of
a flat surface which creates a slope from a horizontal plane and is used to reduce the force necessary to overcome gravity when elevating a heavy object

A ramp is an example of an inclined plane. By using a ramp less effort is needed than if you were to try and lift the object



A standard inclined plane does not move. It is merely a ramp. Objects move easier either up or down, but the plane is stationary. Examples include things such as bike jumps, trail switchbacks, and boat launches.

A screw is also an inclined plane twisted around a rod or shaft as to apply the force into another object.

A wedge, like an axe, or a sword, is a double inclined plane designed to be driven into another object using directional force.

And now onto the fun part....

Pythagorian Therum

a2+b2=c2 - write this down.

a is the opposite side and how high you are trying to lift the object.

b2 is the adjacent side and the horizontal distance the inclined plane covers.

c2 is the hypotenuse and the slope of the inclined plane. This is the distance the object actually travels across

Mechanical Advantage

Mechanical Advantage is the amount the machine multiplies the force put into it. This is the amount of advantage you receive from using the machine.

Force applied = Mechanical Advantage x Force Needed

MA= resistance height /effort length

Instead of lifting the heavy object straight up in the air, you space out the same force over a long distance. This way you are slowly fighting a small amount of gravity rather than trying to overcome the entire gravitational force all at once.

Bringing it all together

You decided to skip Mr. Evans’ physics class to play World of Warcraft……again. Sure it was fun, but there was one problem. He found out.

He called your parents and they dragged you back to school for detention.

Mr. Evans felt such a horrific crime needed manual labor to help build character. He said you had to load heavy crates full of bicycle magazines into the back of his pickup truck and you could only go home when the job was done.
What are you going to do?!?

So riddle me this-

How long is the board going to have to be for you to effectively use it?

How much force are you going to have to push with to move each crate?

How much nicer would it be to have gone to Mr. Evans’ class in the first place?

You begin reading notes from a previous class, determined to do something.

Some quick estimation and you decide each crate weighs 100 pounds.


Just then you notice a large, astonishingly indestructible, board from a local construction site. You place the board at the end of the truck’s tailgate creating…


Some quick phone calls and you decide none of your friends is willing to come help you.

Hint: The bed of the truck is 3 feet off the ground and the crates are 4 feet from the truck.
No, you can’t just lift them, you play too many video games and are out of shape. As always, there are multiple answers as long as you can explain them.

Trajectory

Definition

The path a projectile travels in motion.



Yes, that is really a person being shot out of a cannon.

A Few Comments Before We Start
There is going to be a lot of math in this section. Do not freak out. The math will not hurt you. Most of this is very much common sense oriented. Don’t think of it as math; think about how you threw things last week with Levers. The numbers just stand behind what you already know in your head.

CAN HAVE FUN WITH PROJECTILES!


How it works

As the projectile moves its velocities push it both up and across. It will always have both velocities for this reason.

When the projectile goes up, it fights the force of gravity until its vertical velocity is zero and it stops going up.

The vertical velocity is zero only for a second when it reaches the maximum height. Then the projectile is falling and accelerating with gravity.

The entire time the vertical velocity of the projectile is changing, the horizontal velocity is staying the same. The projectile is always moving horizontally. For this reason it always has the same horizontal velocity. At every moment the projectile is moving, both velocities are always acting upon it. Whether it goes up and across or down and across it is doing two things at once, meaning two velocities. Even when one velocity is zero it is acting upon it, because the projectile isn’t moving!

The Velocities

Since the horizontal and vertical velocities control the path of the projectile they are what you need to figure out for trajectory. If we know how the projectile is being pushed, we know where it is going to go.


The velocities of a projectile are a bit trickier. Since the projectile is symmetrical, we only have to deal with half of it to find both velocities. The horizontal velocity is always the same and the vertical velocity is effected by gravity (which we know) after the half way point.

Getting Crazy!


THE GREAT SOH CAH TOA

Write this down! It is UBER important!

.....

No really. Write it down.

Copy this on a piece of paper.

Soh- sin = opposite over hypotenuse.

Cah- Cos = Adjacent over total velocity

Toa- Tan = opposite over adjacent.

Your opposite and adjacent sides, as well as your hypotenuse could also be called vertical velocity, horizontal velocity, and total velocity.

For more information on this assingment, see Mr. Evans.


How much time?

To figure out how much time the projectile will take to reach its maximum height use this formula:

(Final velocity - vertical velocity)/acceleration


Don’t freak out. This is NOT as hardcore as it looks. You already know all the numbers.

Acceleration means a CHANGE IN velocity. When the projectile is going up, it is slowing down. It is changing its velocity due to gravity pulling on it. It is slowing down at the acceleration of gravity.

You know the acceleration of gravity = 9.8 meters/per second2
Remember, you are slowing down so the value of acceleration is NEGATIVE.

To figure out how high the projectile will go to reach its maximum height use this formula:

(Vertical velocity x time) + (.5 x acceleration x time2 )

Again. Don’t freak out. This is NOT as hardcore as it looks. You already know all the numbers.

Let’s Just Think About It….

8.34 - 4.17 = 4.17

You know the vertical velocity. You already figured it out with SOH, CAH, TOA. Remember, we fired the projectile at 65 degrees. Just fill the number in.


Time refers to the specific moment in air you want to find the height of. You just figured that out. At what time is the projectile at its maximum height?

.92 seconds

How Far Will It Go?

To figure out the distance the projectile will travel use the formula:

Distance = Horizontal velocity x time

By now, this one should look easy.


Let’s Just Think About It…

Distance = 7.76 meters
For time, you need to figure out what you want to know.
You already know the horizontal velocity. You figured it out earlier with SOH, CAH, TOA. The projectile was fired at a 65 degree angle so the horizontal velocity is 4.22 meters per second.


How much distance does the projectile travel before it hits the ground?
The trajectory is symmetrical. If it reaches its maximum height half way through the total flight, multiply the max. height time by 2 and you get the total flight time.
92 x 2 = 1.84

The “Evolution” of the Catapult

The Ballista

First invented in 400 B.C. in Greece
Dionysus of Syracuse
Used torsion tension with 2 flexible LEVERS!
At first, not very powerful.
Launched darts





The Greek and Roman Battlefield


The Good & Bad

The Pros
Allowed targeting of individual soldiers – accurate
Universal Joint – fast trajectory changes
VERY advanced for time
Used both for support and siege tactics.
Mobile

The Cons
Complicated and required maintenance
Not very powerful at first.
Compromise between bolt weight and velocity
Required technology and resources

Random pictures!






The Gastraphetes

The original, primitive crossbow
Handheld Ballista
Called the “Belly Bow”





The End of the Ballista
Rome conquers Greece…make improvements and use the Ballista throughout kingdom
Rome falls…and the resources and skills required to build the Ballista goes with it.

Bye, Bye Ballista!

The Magonel

Background of Mangonel

THE CATAPULT – modern image
Alexander the Great – 400 B.C.
More basic than the ballista
Used torsion tension from rope BUT eliminated the flexible levers
“Savage” compared to ballista

The Good & Bad
The Pros
Cheap & easy to build
Powerful
Able to throw heavy, large objects far distances.
Excellent as a siege weapon against fortifications
Ammunition was available






The Cons

Low accuracy
Cumbersome
Unwieldy and hard to manage on the battlefield
You had better understand trajectory!


The Ammunition


And other stuff like this.

Up next:
The Trebuchet