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 440 N/m, and the spring is originally compressed 8.10 cm to project the needle horizontally without friction. (The spring is fully uncompressed before the needle contacts the skin.) The tip of the needle then moves through 2.40 cm of skin and soft tissue, which exerts a resistive force of 7.50 N on it. Next, the needle cuts 3.50 cm into an organ, which exerts a backward force of 9.70 N on it. (a) Find the maximum speed of the needle.  m/s (b) Find the speed at which a flange on the back end of the needle runs into a stop, set to limit the penetration to 5.90 cm.  m/s

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Spring Potential Energy

The potential energy is the energy possessed by a body by virtue of its position or the energy held by the object due to its position relative to other objects, its force like stresses, charge, and other factors affecting the particles of the body. The potential energy is the measure of the net work done by or on the body. The spring potential energy is the potential energy stored due to the deformation of an elastic spring and this elasticity is due to the stretched spring. The elasticity is the ability of a solid-state matter to come back to its equilibrium position or original position after any kind of external force is acted on it. It is also known as Elastic potential energy. The potential energy here is caused due to the displacement of the spring from its equilibrium position to another position and this potential energy is equal to the net work done due to the stretching of the spring. It also resembles the same mechanics of the oscillation of a simple pendulum, where due to the external force, the object moves from its equilibrium position to its maximum ends and the periodic motion continues till it comes back to the equilibrium position to rest.