Consider the track shown in the figure below. Section AB is a quadrant of a circle of radius r = 2.00 m and is frictionless. From B to C is a horizontal section 3.0 m long with a coefficient of kinetic friction μk = 0.250. The section CD under the spring is frictionless. A block of mass m = 1.00 kg is released from rest at A. After sliding on the track, the block compresses 0.200 m the spring. Determine (using conservation of energy): (a) the speed of the block at point B. (b) the thermal energy (internal energy) produced when the block slips from B to C. (c) the velocity of the block at point C. (d) the stiffness constant k for the spring.

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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.