The Physics of Roller Coasters (Blog 13)

As someone who is clearly interested in roller coasters, it would be pretty embarrassing if I did not know how roller coasters worked. Using an example of a simple out-and-back coaster with no inversions, I will explain the physics of it.

Essentially, for a wooden or steel roller coaster that just has airtime hills, a train is carried up a lift chain and dropped down with gravity powering it. Two types of energy are significant in roller coasters - potential energy and kinetic energy. 

A roller coaster train has more potential energy as it goes higher above the ground. Basically, the higher the lift-hill, the more potential energy the roller coaster has. At the highest point of the coaster's lift, the maximum potential energy is reached. As the train drops from that height, gravity powers the train downward, gaining velocity. At this point, the potential energy is transferred into kinetic energy. Potential energy is regained on succeeding hills.


Kinetic energy is the energy of motion. On a roller coaster, it is determined by the train's motion and its mass. Gravity induces speed of the roller coaster train, thereby creating kinetic energy. Along with potential energy, kinetic energy is part of the total mechanical energy of the coaster. Potential energy transfers into kinetic energy, and that is the basis of what powers a roller coaster. 

Diamondback, a B&M hyper coaster, located at Kings' Island.

How to Add Vectors (Blog 12)

Steps on adding vectors:

1. Draw out the lines of direction.

2. Mark origin; draw "shortest distance" from origin to destination. (creating hypotenuse)

3. Define positive axes (N and E are positive, S and W are negative).

4. Group X and Y lines together; add X's together and Y's together.

5. Use Pythagorean theorem (c² = a² + b²) to determine the shortest distance's distance.

6. Use trigonometry to find the required angle.

Big Five Equations #4 (Blog 11)

How to derive equation number four from a graph.
Equation 4 is d = V2Δt - ½aΔt².

The area of the rectangle drawn on the graph is d = V2Δt.
The area of the triangle formed above the line V1 to V2 is d = ½ (V2 - V1) (Δt).
Therefore, the displacement equals the area of the rectangle minus the area of the triangle.
d = V2Δt - ½ (V2 - V1) (Δt).
From equation 1 (from the big five), V2 - V1 = aΔt.
Sub equation 1 into displacement equation:
d = V2Δt - ½ (aΔt) (Δt)
d = V2Δt - ½aΔt²

Big Five Equations #3 (Blog 10)

How to derive equation number three from a graph.
Equation 3 is d = V1Δt + ½aΔt².

The area of the (A) rectangle is d = V1Δt.
The area of the (B) triangle is d = ½ (V2 - V1) (Δt).

Therefore, the displacement is equal to the area of the area of the (A) rectangle plus the (B) triangle.
From the big five's equation 1, V2 - V1 = aΔt
Sub equation 1 into the displacement equation.
d = V1Δt + ½ (aΔt) (Δt)
d = V1Δt + ½aΔt

Walking the Graphs (Blog 9)

Last week we did an interesting lab. We had to actually exercise! ...although not much. Nevertheless, it was a great experience working on a lab which involved us trying to follow the lines on the graph by running, walking, and stopping.

1. Stay for a distance of 1m for 1 second.

2. Walk 1.5m in 2 seconds (0.75 m/s) away from the origin.

3. Stay at a distance of 2.5m for 3 seconds.

4. Walk 0.75m in 1.5 seconds (0.5 m/s) towards the origin.

5. Stay at a distance of 1.75m for 2.5 s.

1. Start at a distance of 3m from the origin. Walk back towards the origin 1.5m in 3 seconds (0.5 m/s).

2. Stay at a distance of 1.5m for 1 second.

3. Run towards the origin 1m in 1 second (1 m/s).

4. Stay at a distance of 0.5m for 2 seconds.

5. Run away from the origin 2.5m in 3 seconds (0.83 m/s).

1. Stay still for 2 seconds.

2. Walk away from the origin at 0.5 m/s for 3 seconds.

3. Stay still for 2 seconds.

4. Walk towards the origin at 0.5 m/s for 3 seconds.

1. Slowly accelerate away from the origin to 0.5 m/s in 4 seconds.

2. Continue walking away from the origin at 0.5 m/s for 2 seconds.

3. Turn around and walk towards the origin at 0.4 m/s for 3 seconds.

4. Stop and stay still for 1 second.

1. Start at a distance of 0.8m from the origin and walk away 1m in 3.5 seconds (0.29 m/s).

2. Stay at a distance of 1.8m for 3.25 seconds.

3. Continue walking away from the origin for 1.4m in 2.25 seconds (0.62 m/s).

1. Walk away from the origin at 0.35 m/s for 3 seconds.

2. Walk towards the origin at 0.35 m/s for 3.5 seconds.

3. Stand still at that position for 3.5 seconds.

Building a Motor (Blog 8)

Looking at those real-life engines of automobiles and technological devices and machines amazes me. One thing that runs them is the motor. Today we created this very motor - albeit a very amateur version of it. However it was still quite an experience.
The tools and materials we used for our endeavour:

• piece of wood
• wine bottle cork
• skewer
• Lego pieces (in replacement of paperclips)
• wires
• pop can
• nails
• tape, hammer, sandpaper, thumbtacks

Before the insertion of the cork.

The first thing we did was measure the distances between the four nails to make sure they were in the right position. After we hammered the nails into their positions and placed the makeshift paperclips (Lego pieces) in its proper positions. Getting the skewer to go through the cork proved to be a difficult task. We came up with the conclusion of hammering a nail inside the middle of the cork to make the hole more easily accessible. After some necessary force, we finally got the skewer in through the cork. It was pretty straightforward after this step. 

Before the insertion of the brushes.

We put the brushes (pieces out of a V8 can) into its positions and with a little bit of adjustments we were able to complete the project. The only thing left to do was test our "motor" to see if it worked. We went up to the front to get our motor tested.

As you can see from the video, our motor was successful - we were the fifth group to complete the task. Our final product looked like this:

In retrospect, it was a rather fun activity - it was both fun and educational at the same time. Those kinds of activities seldom come, so it will probably be one of the more memorable in-class school projects this year.

Right Hand Rules (Blog 7)

Today we learned about two important components of magnetism in class: right-hand rule #1 and right-hand rule #2.
Firstly, Oersted's Principle states that electric charge moving through a conductor creates a circular magnetic field around the object. Thus, right hand rules are used to determine the magnetic forces around an object.

Right-Hand Rule #1:
Grasp the object (conductor) and make sure your thumb is pointing in the direction of the current direction (conventional flow). Curve your fingers inwards and that will tell you the direction of the magnetic field.


Right-Hand Rule #2:
Grasp the object with curved fingers in the direction of the flow. The thumb represents the North direction.