Calculus based Physics

[burty1]

I am attending Cedar Point's Calculus/Physics day on May 15th. For those that don't know, Cedar Point is a world famous amusement park in Sandusky, Ohio.

Anyways, I have to come up with a handful of questions to answer for when I attend. They can be related to their roller coasters or fictitious roller coasters. I know relationships amongst the position funcion, v(t), and a(t). I can also come up with any kind of optimization problems. I'm trying to find/think of one that may somehow relate to the number of people in the park at any given time or the number of people riding the trains within the park, etc.

Anyone have any good examples or resources that you could direct me to?

Thanks,
burty1

[flipdeadshot22]

you really need to be more specific within the context of your question. Are you asking how to calculate the rate that new people enter the park, or perhaps how fast that rate increases? If those are your questions you'll need a well defined function of how many people are within the park at a given moment of time (x(t)) for example. This is a rather arbitrary question, so i cannot direct you to many resources, but would rather find your free time better spent finding what types of problems calculus is suited to dealing with, and then studying a little more. Good luck man!

[Duke]

1. Something involving a funnel cake. If it were made of water, somehow, you could talk about laminar flow.

2. Tension in a rubber band strung between the two trains on the Gemini as a function of time over the course of one sample race. Different races would have different values.

3. At what point on the track would Mike Tyson have to stand to punch the Magnum train and actually have it stop?

4. Calculate the force at impact between two demon drop cars traveling at each other. This looks like a U and the cars hit each other as soon as they're horizontal. Assume that they drop at the same time, and that they're the same weight. Your answer should be a function of their mass. State your other assumptions.

5. If the Rip Cord line snapped, at what angle would the passengers "fly" the farthest in terms of horizontal distance?

[burty1]

Thank you for the responses...let me be more specific...
I CAN do all of the calculations I need to do given a specific function.

It is my job to actually come up with specific equations/situations for others to solve. They can be optimization problems (people in the park, etc.), related rate type problems (water flow, etc.), or v(t)/a(t) problems (we have studied only linear motion..."an object is dropped" or "an object is shot straight up at an initial velocity of"...Any books/websites or other materials that have "premade" problems that I may be able to copy or tweak the numbers slightly to fit my situation?

Outstanding possibilities Duke, but they are not supposed to be any rubber band/collision kind of stuff...that is left specifically to the physics class...

As always, this is the smartest group of individuals I have seen on a forum. Thanks for the prompt responses!!!

[daryn]

how many g's on the turkish twist

[burty1]

Any suggestions at all?

[thylacine]

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Any suggestions at all?

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If you can use vectors then a roller-coaster-related topic one is to break down acceleration into two orthogonal components, one component in direction parallel to velocity, namely d(speed)/dt, and one component in direction perpendicular to velocity, namely (speed)^2/r where r is radius of curvature of the path. Here velocity and acceleration are vector valued functions of a real variable t (time). You can use interesting stuff such as product rule for dot product and cross product, combined with other vector concepts (e.g. components of a vector a, parallel to and perpendicular to a given vector v). Check out a calculus textbook, about second semester 1st year. I have no further details to offer. If you think it is a bit tough for your audience, just go for it anyway (as long as you thoroughly understand it yourself).