In a needle biopsy, a narrow strip of tissue is extracted from a patient with a

Question

In a needle biopsy, a narrow strip of tissue is extracted from a patient with a hollow needle. Rather than being pushed by hand, to ensure a clean cut the needle can be fired into the patient’s body by a spring. Assume the needle has mass 5.60 g, the light spring has force constant 375 N/ m, and the spring is originally compressed 8.10 cm to project the needle horizontally without friction. The tip of the needle then moves through 2.40 cm of skin and soft tissue, which exerts a resistive force of 7.60 N on it. Next, the needle cuts 3.50 cm into an organ, which exerts a backward force of 9.20 N on it. Find the maximum speed of the needle.

Explanation / Answer

work done by the net force is change in mechanical energy

(-7.6*0.024)-(9.2*0.035) = 0.5*m*Vmax^2 - 0.5*k*x^2

-0.5044 = 0.5*0.0056*Vmax^2 - 0.5*375*0.081*0.081

Vmax = sqrt(0.7257875/(0.5*0.0056)) = 16.1 m/s

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