During a fierce battle with an alien ship all power has been cut toyour starship

Question

During a fierce battle with an alien ship all power has been cut toyour starship. Only life support systems are working! your captaincomes to you and asks you to design a spring launcher fixed to thestarship that will give a 12.5 kg quantum photonic hyperbolictorpedo a speed of 405 m/s. this is your one shot to take out yourenemy!!!!! you attach the torpedo to the spring and oscilate itback and forth and discover that the frequency of oscilation is4Hz. You can ignore the springs mass, the recoil kinetic energy ofthe spacecraft, and changes in gravitation potential energy. youare in deep space! a.) make an initial and final sketch of thesituation. b.) calculate the stiffness constant of the spring andthe distance by which the spring should be compressed.

Explanation / Answer

frequency(f)=/2 =2*4 =8 2=k/m k=(8)2*12.5 =8002 Potential energy of the spring when compressed a distance 'x' =1/2kx2So all this PE converts toKE(1/2mv2) after launch... 0.5*8002*x2=0.5*12.5*4052     642x2=4052 square-rooting both sides.. 8x=405 x=16.11m

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