The one about the hyperloop The Hyperloop is a proposed form of high-speed trans

Question

The one about the hyperloop 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. 1. What is the force necessary to accelerate a full pod on a horizontal track with an acceleration of 0.5 g? 2. How long would the linear induction motor need to be to bring the fully loaded pod to cruising speed with this force?

Explanation / Answer

From the given question,

1.mass of empty pod(M)=3100kg

mass of total passengers(m)=28*65=1820 kg

total mass(M+m)= 4920 kg

acceleration(a)=0.5g=0.5*9.8=4.9 m/s2

Force= (M+m)a=4920*4.9=24108 N

2.v=u+at

v=760 mph=760*0.447=340 m/s

340=0+4.9*t

t=69.4 sec

3.work done = change in kinetic energy

=(1/2)(4920)(3402-02)

=2.84*108 J

4.Since the pod, starts from rest, the final kinetic energy is equal to work done.

Hence the ratio is 1:1

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