Mr. Montgomery approaches you and wants you to invest in a new scheme that would

Question

Mr. Montgomery approaches you and wants you to invest in a new scheme that
would launch the space shuttles into space by using a big spring. The space
shuttle would be placed on the spring and pulled down by some displacement
and then let go and soar into space.

What would the specification of the spring and launch system look like
(approximate values) give the assumptions below? Do you think this sounds
feasible and would you invest*?

Assume:
? Final velocity of the shuttle coming off the spring must be about 8,000 m/s
? Mass of the shuttle is about 80,000 kg
? Max. Acceleration shuttle can have is 80 m/s
2
(about 8 g’s), don’t want
passed out astronauts in space.

Explanation / Answer

The final velcoity vf = 8000 m/s the mass of the shuttle M = 80 000 kg The max acceleration a = 80m/s^2 From kinematic equations      vf = at then time t = vf/a = 8000/80 = 100sec and from equation          vf^2 = vi^2 + 2ax then displacement        x = vf^2/2a           = (8000m/s)^2 / 2(80)           = 4.0*10^5 m Now from law of conervation of energy         1/2mv^2 = 1/kx^2 therefore the spring constant         k = mv^2/x^2            = (80000)(8000)^2 / (400000)^2            = 32 N/m

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