Physics behind roller coasters !

For many people, there is only one reason to go to an amusement park: the roller coaster. Some people call it the "scream machine," with good reason. The history of this ride reflects a constant search for greater and more death-defying thrills.

How does a roller coaster work?
What you may not realize as you're cruising down the track at 90 km/h is that the coaster has no engine. The car is pulled to the top of the first hill at the beginning of the ride, but after that the coaster must complete the ride on its own. You aren't being propelled around the track by a motor or pulled by a hitch. The conversion of potential energy to kinetic energy is what drives the roller coaster, and all of the kinetic energy you need for the ride is present once the coaster descends the first hill. Once you're underway, different types of wheels help keep the ride smooth. Running wheels guide the coaster on the track. Friction wheels control lateral motion (movement to either side of the track). A final set of wheels keeps the coaster on the track even if it's inverted. Compressed air brakes stop the car as the ride ends.

The types of roller coasters
Roller coasters can be wooden or steel, and can be looping or non-looping. You'll notice a big difference in the ride depending on the type of material used. In general, wooden coasters are non-looping. They're also not as tall and not as fast, and they don't feature very steep hills or as long a track as steel ones do. Wooden coasters do offer one advantage over steel coasters, assuming you're looking for palm-sweating thrills: they sway a lot more. Tubular steel coasters allow more looping, higher and steeper hills, greater drops and rolls, and faster speeds.

My favourite roller coaster
My favourite roller coaster has got to be Millenium Force at Cedar Point in Ohio, United States.When I visited this amusement park 2 years ago, I was thrilled to go on this ride. Although its height had been surpassed by Top Thrill Dragster, opened in 2003, I have never experienced the thrill I encountered on Millenium Force. This immense ride has a height of 94 metres a length of 2,010 metres with a maximum speed of 150 km/h.

RESOURCES
http://themeparks.about.com/gi/o.htm?zi=1/XJ&zTi=1&sdn=themeparks&cdn=travel&tm=108&gps=343_533_1345_600&f=20&su=p974.8.121.ip_p284.9.336.ip_p531.51.336.ip_&tt=2&bt=1&bts=1&zu=http%3A//cec.chebucto.org/Co-Phys.html

http://tlc.howstuffworks.com/family/roller-coaster3.htm

http://www.physicsclassroom.com/mmedia/circmot/rcd.cfm

How to add vectors

Vectors pointing in the same direction

These are the easiest kind of vectors to add. You can just pretend the directions aren't there and add the numbers. For example if you have to add 17m, East, and 13m East, just add the numbers and slap the direction on to the end. 30m, East is the correct answer. Another Example: 5m/s, 30° North of East + 2m/s, 30° North of East=7m/s, 30° North of East. It's pretty simple.

Vectors in the opposite direction

This one is a little trickier. What do you do when you have to add 10m, North and 30m, South? Step one: Find the larger number, in this case 30. Now subtract the smaller number from that. 30 - 10=20. Now just attach the direction from the larger number. 20m, South is the answer. It's just like adding negative numbers in math. Here is another example. 700N, 0° North of East + 300N, 0° North of West=400N, 0° North of East. As a side note, if you are asked to add many vectors, (I.e.: 1m, East + 2m, East + 3m, West + 4m, West) First add all the vectors pointing in the same direction (so you are left with 3m, East + 7m, West) then follow the steps above. (Final result equals 4m, West).

Adding perpendicular vectors

Now that we can add vectors on the same line, it's time to move onto the next section. Perpendicular Vectors. Your teacher asks you to add 300m, 0° North of East and 400m 90° North of East. Here's how you do it. Remember Geometry? Remember the Pythagorean theorem? (a² + b² =c²) We have to use that. Since the vectors are at right angles to each other, we can form a right triangle out of them. The resultant vector (the answer) will be the third side of the triangle. Use the vectors you have as the bases of the triangle and plug it into the equation.

a² + b² =c²
300m² + 400m²=c²
250000m²=c²
c=500m

We still need to find the exact angle that the vector points. To do that we need to sell our soul to the demon of trigonometry. If you remember Tan=Opposite side/adjacent side. So, Tan=400m/300m, Tan=1.3333, Inverse Tan=53°. So the final answer is 500m, 53° North of East.

How do you derive equations 3 and 4 using a graph?

Equation 3 is d = v1Δt + ½aΔt²

To help us understand better, let's picture a trapezoid on a graph paper. The equation will be obtained once we find the area of that trapezoid. An important information that we know is that the area of the whole trapezoid will eventually end up to be the total displacement represented on the d-t graph that is correlated with the v-t graph that we are using. In order to obtain the area of the trapezoid, we can calculate the areas of the triangle and of the rectangle separately and later add them. Knowing that the equation used to calculate the area of a triangle is [A = bh/2], we can conclude that on the graph the equation would look like [d = ½(v2 - v1)Δt]. However, to make this equation much simpler, we can replace [v2 - v1] with [aΔt]. Such substitution is able to take place because from the equation used to obtain the slope of a graph [a = (v2 - v1) / Δt], we can further isolate and find [aΔt = v2 - v1]. Similarly, we use our knowledge of the area of a rectangle, which is (A = lw), to calculate the area of the rectangle on the graph, which turns out to be (d = v1Δt). Now that we have the equations to calculate both the areas, we can add them.

Final product - d = area of the rectangle + area of the triangle     
                            = v1Δt + ½(at)Δt                 
                            = v1Δt + ½aΔt²

Equation 4 is d = v2Δt - ½aΔt²

Unlike the method used for the derivation of the previous equation, we obtain the area of a large rectangle that is extended from the existing trapezoid; then we must subtract the area of a triangle from that area. Again, we use our knowledge of how to obtain area of certain polygons, in this case that of a triangle and a rectangle. Knowing that the area of a rectangle is equal to the product of the length and the width, we can say that the area of the large rectangle is [d = v2Δt]. The area of a triangle would be [A = bh/2], which on the graph would be equal to [d = ½(at)Δt].

Final product - d = area of the large rectangle - area of the triangle

                            = v2Δt  - ½(at)Δt

                            = v2Δt - ½aΔt²

Translating the motion graphs

A. Stand 1m away from the origin, and stay for 1 second.

B. Walk 1.5m away from the origin for 2 seconds.

C. Stand 2.5m away from the origin, and stay for 3 seconds.
D. Walk 0.75m toward the origin for 1.5 seconds.
E. Stand 1.75m away from the origin, and stay for 2.5 seconds.

 A. Stand 3m away from the origin, and walk 1.5m toward the origin for 3 seconds.

 B. Stand 1.5m away from the origin, and stay for 1 second.

 C. Walk 1m toward the origin for 1 second.
 D. Stand 0.5m away from the origin, and stay for 2 seconds.
 E. Walk 2m away from the origin for 3 seconds.

A. Stand approximately about 0.8m away from the origin, and walk 1m away from the origin for 3.5 seconds.
B. Stand 1.8m away from the origin, and stay for 3 seconds.

C. Walk 1.3m away from the origin for 3 seconds.

A. Speed up for 4 seconds.

B. Walk at a velocity of 0.5m/s away from the origin for 2 seconds.

C. Walk at a velocity of 0.4m/s toward the origin for 3 seconds.

D. Stay for 1 second.

[v --> a]
A. The acceleration is 0.1m/s^2, and the line is on the positive side.
B. There is no acceleration.
C. There is no acceleration.
D. There is no acceleration.

A. Stay for 2 seconds.

B. Walk at a velocity of 0.5m/s away from the origin for 3 seconds.

C. Stay for 2 seconds.

D. Walk at a velocity of 0.5m/s toward the origin for 3 seconds.

[v --> a]
A. There is no acceleration.
B. There is no acceleration.
C. There is no acceleration.
D. There is no acceleration.

A. Walk at a velocity of 0.35m/s away from the origin for 3 seconds.

B. Speed up, still away from the origin, for 0.25 second.
C. Slow down, now toward the origin, for 0.25 second.

D. Walk at a velocity of 0.35m/s toward the origin for 3 seconds.

E. Slow down, toward the origin, for 0.25 second.
F. Stay for 3 seconds.

[v --> a]
A. There is no acceleration.
B. The line is on the negative side.
C. The line is on the negative side.
D. There is no acceleration.
E. The line is on the positive side.
F. There is no acceleration.