1. The problem statement, all variables and given/known data In a needle biopsy, a narrow strip of tissue is extracted from a patient using 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 that 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. After the needle leaves the spring, the tip of the needle moves through 2.40 cm of skin and soft tissue, which exerts on it a resistive force of 7.60 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) the speed at which the flange on the back end of the needle runs into a stop that is set to limit the penetration to 5.90 cm. 2. Relevant equations 3. The attempt at a solution I am having trouble understanding (b) My original attempt was : Find the work done by friction: (7.6)(0.024) + (9.2)(0.035) = 0.5044 J and then I used KE = 1/2mv^2 to find the velocity because I thought in order for the needle to stop exactly at 5.90 cm the initial KE should be the same as the work done by friction. So, why am I wrong? Is it because if KE = work done by friction then there will be no energy for the needle to move? Also, I want to ask if an object is already moving and then the KE is changed to a value that is the same as that of the work done by friction. Then, is the object moving at constant velocity? Thank you!