In a needle biopsy, a narrow strip of tissue is extractedfrom a patient using a hollow

Chapter 8, Problem 78

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In a needle biopsy, a narrow strip of tissue is extractedfrom a patient using a hollow needle. Rather thanbeing pushed by hand, to ensure a clean cut the needlecan be fired into the patients body by a spring. Assumethat the needle has mass 5.60 g, the light spring has force constant 375 N/m, and the spring is originallycompressed 8.10 cm to project the needle horizontallywithout friction. After the needle leaves the spring,the tip of the needle moves through 2.40 cm of skinand soft tissue, which exerts on it a resistive force of7.60 N. Next, the needle cuts 3.50 cm into an organ,which exerts on it a backward force of 9.20 N. Find(a) the maximum speed of the needle and (b) thespeed at which the flange on the back end of the needleruns into a stop that is set to limit the penetrationto 5.90 cm.