An object of mass M= 6.0 kg, initially at rest, is pressed against a spring with spring constant k =12,000 N/m, compressed a distance d = 0.12m from equilibrium. The mass and the spring are located at the top of a hill of height, h = 2.0 m. The mass is released and as the spring decompresses the mass slides down the frictionless hill and then encounters a horizontal patch of ground with unknown coefficient of kinetic friction μk. a. What is the speed of the mass just before it encounters the rough patch of ground? b. The mass comes to rest a distance L = 8 m after encountering the patch of ground. What is the coefficient of frictio

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A: Given information: The symbols have the same meaning as defined in the question.

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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.