In old science fiction movies, writers attempted to come up withnovel ways of la

Question

In old science fiction movies, writers attempted to come up withnovel ways of launching spacecraft toward the moon. In onehypothetical case, a screenwriter envisioned launching a moon probefrom a deep, smooth tunnel, inclined at 65.0° above thehorizontal. At the bottom of the tunnel a very stiff springdesigned to launch the craft was anchored. The top of the spring,when the spring is unstressed, is 30.0 m from the upper end of thetunnel. The screenwriter knew from his research that to reach themoon, the 318-kg probe should have a speed of at least 11.2 km/swhen it exits the tunnel. If the spring is compressed by 95.0 mjust before launch, what is the minimum value for its forceconstant to achieve a successful launch? Neglect friction with thetunnel walls and floor.
? kN/m

Explanation / Answer

energy stored in the spring = 0.5*k*x^2 = 0.5*k*95^2=4512.5*k energy of the probe relative to the compressed spring at theend of tunnel = m*g*h + 0.5*m*v^2 where m= 318 , g=9.8, h=30+95 =125 m, v=11200 m/s so E=1.994*1010 this energy should be same as the energy stored in thespring so: 1.994*1010= 4512.5*k therefore k=4420022 N/m yes it is really stiffff........ enjoy it this energy should be same as the energy stored in thespring so: 1.994*1010= 4512.5*k therefore k=4420022 N/m yes it is really stiffff........ enjoy it

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