7) A mad scientist wants to design a mechanical spring that has the ability to l

Question

7) A mad scientist wants to design a mechanical spring that has the ability to launch a 2 metric ton payload into deep space. Assuming that the spring's maximum compression is 150 m, what would its stiffness have to be to successfully launch such a payload? [Note that the mass of the Earth is about 6×1024 6 × 10 24 kg and its radius is about 6.4×106 6.4 × 10 6 meters.] Answer: 8) If mad scientist invents a new material that is twice as stiff as the material in the previous problem, what speed will the payload have when it is very far away from the Earth, assuming a compression equal to the one in the previous problem? Answer:

Explanation / Answer

7. form the data in the question

m = 2 metric tonne = 2000 kg

xo = 150 m

k = ?

M = 6*10^24 kg

Re = 6.4*10^6 m

hence

PE stored in spring = PE of earth mass system ( For KE = 0 at infinity)

hence

0.5kxo^2 = GmM/Re

hence

k = 11116666.66 N/m

now, for k' = 2k

final speedin space = v

then

from conservation of energy

0.5k'xo^2 - 0.5kxo^2 = 0.5mv^2

v = 11183.13462317 m/s

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