The Hyperloop is a proposed form of high-speed transportation that accelerates c

Question

The Hyperloop is a proposed form of high-speed transportation that accelerates cylindrical pods that can carry up to 28 passengers in a low pressure tube at speeds of 760 mph. In a whitepaper published by Elon Musk (http://www.spacex.com/sites/spacex/files/ hyperloop_alpha.pdf), a 380 mile route between L.A. and San Francisco is discussed, and the following constraints are introduced: The route should follow existing freeways (i.e. I-5) as closely as possible, the maximum acceleration should be limited to 0.5 g for rider comfort. the maximum speed should be limited to 760 mph to avoid sonic booms. By levitating the pods using either air pressure or magnetism and evacuating most of the air from the tube, the pods can be made virtually frictionless. The pods would be accelerated up to cruising speed using linear induction motors (a line of electromagnets built into the track that act on the pod going over them).

For this assignment assume an empty pod has a mass of 3100 kg, and that each rider has an average mass of 65.0 kg.

So far we have completely neglected air resistance, but even in the low pressure of the tube, there is expected to be about 320 N of drag. Linear motors would be placed along the track to periodically boost the speed of the capsule to compensate for the loss of speed due to drag.

6. How much energy is lost due to drag when traveling between L.A. and San Francisco?

Explanation / Answer

given constant drag of F = 320 N
distance between L.A> and san Francisco , d = 380 miles = 611551 m

now for friction antiparallel to displacement
work done by friction = F.d = -Fd
and given that all the work is done just to overcome this friction
work done = Fd = 611551*320 = 195696320 J = 195.69632 Mega J
hence energy lost due to drag fromLA to san francisco = 195.69632 MJ

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