61. A child's pogo stick (Fig. P8.61) stores energy in a spring with a force constant of 2.50 X B) 10 N/m. At position (x -0.100 m), the spring com- pression is a maximum and the child is momentarily at rest. At position ® (x = 0), the spring is relaxed and the child is mov- %3D ing upward. At position ©, the child is again momentarily at rest at the top of the jump. The combined mass of child and Figure P8.61 pogo stick is 25.0 kg. Although the boy must lean forward to remain balanced, the angle is small, so let's assume the pogo stick is vertical. Also assume the boy does not bend his legs during the motion. (a) Calculate the total energy of the child-stick-Earth system, taking both gravitational and elastic potential energies as zero for x = 0. (b) Determine xe. (c) Calculate the speed of the child at x = 0. (d) Determine the value of x for which. the kinetic energy of the system is a maximum. (e) Cal- culate the child's maximum upward speed.

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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.