Physics Behind Roller Coaster

Gravity is the driving force of a roller coaster. The train is pulled to the top by gaining potential, or stored energy. As the train is pulled to the top, the train is released from the top of the lift hill; it is the acceleration due to gravity that brings it back to the beginning, its velocity increases. This causes the train to gain kinetic energy, which is the energy of motion. The faster the train moves, the more kinetic energy the train gains. The train begins to climb the next hill and the speed start to decreases.

                                                
                                        The initial hill is the steepest in the entire ride.

Behemoth is my favorite roller coaster, it clear shows the gravity and potential energy and also velocity and kinetic energy.

Vector Addition

Two or more vector can be added together to determine the result, there is no minus sign in those in vector addition, if the vector going to the opposite direction, for example, North and South, we use North + South instead of North + (-North).

We use Pythagorean Theorem and head to tail method to determining the magnitude and direction of adding two or more vectors.

 

 

We use trigonometry to determine a vector's direction

                                                                   1 km [N 45°E]         

                                                         One kilometer 45°east of north

Derive of Equation #4

Derive of Equation #3

Hypothesis of the six Graphs

Divided each graph into different sections whenever it breaks.

Graph 1

Velocity: A horizontal line on the x-axis, constant velocity in the positive direction,
A horizontal line on the x-axis; a horizontal line goes to the negative direction below the x-axis and a horizontal line on the x-axis.

Acceleration: No acceleration, a horizontal line on the x-axis.



Graph 2:

Velocity: Constant velocity in the negative direction, rest, constant velocity in the negative direction, rest and constant velocity in the positive direction.

Acceleration: No acceleration, a horizontal line on the x-axis.



Graph 3:

Distance: A horizontal line on the x-axis, increasing velocity in the positive direction, moving in the positive direction at a constant velocity, slowing down in the negative direction and then rest, slowing down in the negative direction and constant velocity in the negative direction.

Acceleration: no acceleration, velocity relative to the positive direction is increasing, no acceleration, velocity relative to the negative direction is decreasing, no acceleration, velocity relative to the negative direction is decreasing and no acceleration.



Graph 4:

Distance: Increasing velocity in the positive direction, moving to the positive direction at a constant velocity, decreasing velocity in the negative direction and moving to the negative direction at a constant velocity.

Acceleration: Velocity relative to the positive direction is increasing, no acceleration, velocity relative to the negative direction is decreasing and no acceleration.



Graph 5:

Velocity: Constant velocity in the positive direction, a horizontal line on the x-axis, and constant velocity in the positive direction.

Acceleration: No acceleration, a horizontal line on the x-axis.



Graph 6:

Distance: Moving to the positive direction at a constant velocity, decreasing velocity in the positive direction, moving to the negative direction at a constant velocity, increasing velocity in the positive direction and a horizontal line on the x-axis.

Acceleration: no acceleration, a horizontal line on the x-axis, velocity relative to the negative direction is decreasing, no acceleration, a horizontal line on the x-axis, speeding up in the positive direction and no acceleration, a horizontal line on the x-axis.

6 walking Graphs

Graph 1

The motion started at 1 meter from the origin to the positive direction rested for 1 second, walked positive direction constant speed for 2 seconds, stopped for 3 seconds, walked toward the origin constant speed for 1and half seconds and then stopped.

Graph 2:

The motion started at 3 meters away from the origin, from the positive direction walked toward the origin at constant speed 0.5m per second, rested for 1 second, run toward the origin at constant speed 1 meter per second, rested for 2 seconds, and walked fast to the positive direction at constant speed.

Graph 3:

The object rested for 2s speed up for 0.1 second walked away from the origin, for 2.8 seconds at 0.5 meter per second, speed up toward the origin for 0.1 second then rested for 1.8 second, speed up 0.1 second walked away from the origin at 0.5 meter per second and kept the same speed.

Graph 4:

The motion became faster and faster away form the origin for four seconds and kept the same speed 0.5 meter per second for 2 seconds; speed up for 0.1 second walked away from the origin, at 0.4 meter per second and kept the same speed for 2.8 seconds, then speed up 0.1 second toward the origin and stop.

Graph 5:

The motion started at 0.85 meter away from the origin, walked away from the origin at constant speed 1.15 meter for 3 and half seconds, keep the same speed at 1 second per 1.9 meters 3 seconds and then speed up away form the origin at constant speed.

Graph 6:

The motion started at 0.35 meter per second away form the origin, walked at the constant speed for 3seconds, slow down, speed up and 0.1 second walked toward the origin, kept the same speed for 4 seconds, slow down, speed up and 0.1 second walked toward the origin and stopped.