# Amusement Park Measurements II

Coaster

I’ve been thinking about the challenge of making measurements at the amusement park. Specifically, many of the assigned problems require an application of kinetic energy (KE = 1/2 mv^{2}), gravitational potential energy (GPE = mgh) and work (W = Fd). The interchange between the three is easy to grasp and the students have practiced this many time in this course. Train at the top of the hill loses GPE and acquires KE, with the exception of the work done by friction.

But how do I measure speed, necessary to calculate KE? Well, there is an easy trick that helps with this and the measurements are very easy to make. Think about distance: how do I access this? Well, think about how easy it is to measure the length of the train. Each is composed of multiple cars that come to a stop while loading and unloading. If I make a quick measurement of the length of a section of the train and then count the number of cars I can find the total length of the train, probably to within 10% of the true length.

In order to find velocity (or speed), what remains is time and every student carries a timer built into a phone device. If I wish to know the velocity at the top of the hill then all I need is to time how long it take for the car to pass a certain point at the top. If I wish to find the speed at the bottom then I choose another location and do the same. Repeating the measurement increases the chances that the measurement will be valid.

Now, what about other distances? If I know the length of a train and I examine (from afar) what percentage of a length of track (or loop) the train occupies then I can reasonably estimate the distance of something that I could never reach.

One final word about mass. What should I do if I get stuck on the mass of a car or train? The easiest was is to assume 1 kg (yes, just 1 kg!) for the problem. Therefore any answer you get would be per kilogram by default. That way any futre research would just multiply the factor found.

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