Physics behind roller coasters

Kinematics plays a huge factors in how roller coasters work. As roller coaster gain speed, the velocity increases therefore there is also an increase in kinetic energy. The faster a roller coaster is moving, the more kinetic energy it has. Due to this, kinetic energy is highest when the roller coaster is at the bottom of the track, while the kinetic energy decreases once the roller coaster starts to slow down.

Gravity is the acceleration that pushes the roller coaster down when it is descending. When the roller coaster is moving downwards, its acceleration increases because gravity is pulling the roller coaster down. When the roller coaster moves upwards, its acceleration decreases because gravity is working as an opposing factor.

I don't usually ride roller coasters. Actually I am not a fan of roller coaster, therefore there isn't one that I'm particularly fond of, so I don't have a favourite one.

How to add vectors

Fomulas:
Pythagorean: a² + b² = c²

Trigonometry:

Adding or subtacting vectors by scale diagram:

1. Head to Tail

2. Resultant is always origin to destination

3. subtracting vecotrs means adding a vector in the opposite direction

4. use protractor to mreasure the angle accordance to N or S

Adding or subracting vectors by Components:

1. Set your positive axes (N and E)

2. Break all vectors down into two components (x and y)

3. Solve for x and y

4. Use pythagorean to add the two sums of components (x and y)

5. Use trigonometry to solve for angle

Graphing Equation 3 and 4

Equation 3: d = v1 (t) + 1/2 (a) (t)2

The equation for triangle B is: (v2 - v1)(t) / 2
The equation for rectangle C is:  (v1) (t)
When you combine it together, it is: BC = ((v2-v1)(t)/2)+(v1)t
a = (v2-v1)/t
BC = [(v2-v1)/t](t2)/2 + (v1)t
BC = 1/2(a)(t)2 + (v1)t
Therefore BC is equal to equation 3


Equation 4: d = v2(t) - 1/2 (a)(t)2

The equation for triangle A is: (v2-v1)(t)/2
The equation for the entire rectangle is: (v2)t
When you subtract the triangle A from the total area, the equation is: (v2)t - (v2-v1)(t)/2
a = (v2-v1)/t
BC = (v2)t - [(v2-v1)/t] (t2)/2
BC = (v2)t - 1/2(a)(t2)
Therefore BC is also equal to equation 4

Motion Graphs

Starting position: 3m away, facing the origin
start walking forward for 3s
stay at 1.5m for 1s
start walking forward for 1m for 1s
stay at 0.5m for 3s
walk backwards for 2.5m for 3s

Starting position: around 1m away, facing the origin
walk backwards for around 1m for 3.5s
pause at 1.8m for 2.5s
walk backwards for 1.6m for 3.5s

Starting position: 1m away, facing origin
walk backwards for 1.4m for 2s
stay at 2.4m for 3s
walk forward for 0.6m for 1.5s
stay at 1.8m for 2.5s

Starting position: at 0m/s, facing origin
stay for 2s at 0m/s
walk backwards for 3s
stay for 2s
walk forward for 3s

Starting position: 0m/s, facing the origin
speed up backwards for 4s
walk backwards for 2s
walk forward for 3s
rest for 1s

Starting position: around 0.4m/s, facing the origin
walk backwards for 3s
walk forwards for 4s
rest for 3s

Picture of Motor

Here is the picture of the motor me and Florina built.

Building an Electric Motor

On Thursday, the whole Physics class got to partner up and built a motor. Even though my fingers were sore afterwards, it was still a great experience. The materials we used to build this motor were a piece of wood, nails, a cork, a pop can, a kabob stick and a long piece of wire. First we had to hammer the nails into the wood. It was particularly hard since the nails kept on becoming loose and end up falling out even though we got no idea why. So we had to put a lot of elbow grease into it. J Next, my partner, Florina, cuts the pop can into two rectangular pieces and we rubbed it with sandpaper. Another challenge was when we had to twist the kabob stick into the cork, but after A LOT of twisting and turning, we managed to get it through. Coiling the wire onto the cork was confusing since the wire should be coiled perpendicular to the nails, but we got it right the first time, so we did not have to redo it again. When everything was in its places, we realized how fragile it was. Every now and then, something falls out and the strips from the can were not touching the nails. Florina and I sort of panicked when the class was over but luckily, we got another 15 minutes today to fix things up a bit and test it out. Unfortunately, our first test did not go so well, and the second test did not go so well too. Even though we did not see our motor actually spinning, we did see some sparks flying, which was pretty cool, I guess.