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Problem 2 A block of mass 1 kg is sitting on top of a compressed spring...

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Physics

Problem 2 A block of mass 1 kg is sitting on top of a compressedspring of spring constant k = 300 N/m and equilibrium length 20 cm.Initially the spring is compressed 10 cm, and the block is held inplace by someone pushing down on it with his hand. At t = 0, thehand is removed (this involves no work), the spring expands and theblock flies upwards.

(a)Draw a free-body diagram for the block while the hand isstill pressing down. Try to get the forces approximately to scale.The following question should help.

(b)What must be the force (magnitude and direction) exerted bythe hand on the block?

(c)How much elastic potential energy was stored in the springinitially?

(d)Taking the system formed by the block and the earth, how muchtotal work is done on it by the spring, as it expands to itsequilibrium length? (You do not need to do a new calculation here,just think of conservation of energy.)

(e)How high does the block rise above its initial position?

(f)Treating the block alone as the system, how much net work isdone on it by the two external forces (the spring and gravity) fromthe time just before it starts moving to the time it reaches itsmaximum height? (Again, no calculation is necessary if you canjustify your answer.)

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