A 3kg mass slides down a smooth ramp from a height of 4m and begins sliding across the floor. The floor is smooth except for a 2m long section that applies a constant 15N force of friction against the mass while it passes over. The mass then bumps into a spring and compress it by 80cm. What is the spring constant of the spring? If the mass now slides back the way it came (crossing the floor and the rough patch once again, what maximum height it now attain when it slides back up the ramp?

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A: Answer is explained below

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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.