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WoP #14: Great Scott: Mass of a DeLorean


SgtLongcoat

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Many have seen the Back to the Future trilogy, in which Marty McFly and Doc Brown use a modified DeLorean to travel through time. According to Doc Brown, the machine requires "1.21 Jigawatts" of power (confirmed by the directors to simply be a mispronunciation of Gigawatts) to power the flux capacitor, which enables time travel. This is achieved by bringing the DeLorean up to a speed of 88 mph, roughly 39.34 m/s. Using this information, I will do what any sane person would do: calculate the mass of the DeLorean.

Before I can calculate the mass, there are a few missing pieces I need to know or assume. First, the coefficient of friction between the tires and the road. Considering that roads at the time were mostly made of concrete, it's safe to use the coefficient of friction for rubber on concrete, which will be somewhere between 0.6 and 0.85. Being the car is in motion, and the wheels are rotating, the static coefficient of friction should be used, so I'll take the higher value of .85. Second, I'm going to assume that air resistance is negligible in this case, and that all work done on the DeLorean comes from the force of friction, which is used to accelerate the car forwards. Finally, I'm going to assume that the DeLorean moves with a constant acceleration, such that the average velocity of the car is equal to half the final velocity, or 19.17 m/s.

With that done, I can work backwards from the beginning to determine the DeLorean's mass. First of all, being power can be calculated using the equation P=F•v, and the net force on the car and velocity of the car are in the same direction, Net Force = P/v = 1.21 x 10W / 19.17 m/s = 6.31 x 107 N. Being friction is the only force acting to accelerate the car, this is also the force of friction. Now, being the force of friction = µ(Force normal) = µmg, the mass of the DeLorean = Ffriction / (µg) = 6.31 x 107 N / (0.85 x 9.81 m/s) = 7.57 x 10kg. Looking up the actual value for the mass (yes, you can find it), it's about 1230 kg, a large discrepancy. While the assumptions made above, especially concerning air resistance, don't help the numbers, the fact of the matter is that Doc Brown never fully explained how the DeLorean worked, so it's almost impossible to calculate a realistic number for its mass. Besides, would you really want him to? If so, be prepared to sit through a full movie dedicated simply to explaining the science behind it before even beginning the actual trilogy.

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