A spring of natural length 30 cm is attached to the floor directly below an identical spring that is attached to the ceiling. The ceiling is at a height of 3 m above the floor. A ball of mass 3 kg and radius 5 cm is projected vertically downwards with a speed of 10 m s-1from midway between the two springs. (a) If the lower spring is compressed to a length of 10 cm when the ball first comes to rest, calculate the spring constant of the springs. (b) After bouncing off the lower spring, the ball impacts the upper spring. Calculate the length of the upper spring when the ball comes to rest for the second time.

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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.