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.