A small cart of mass 9 kg slides down from the top of a curved track of unknown length. It first passes a small patch of rough surface, and then it hits a spring of rest length 1.61 m and stops. The spring is also located on a second patch of rough surface. If the spring constant of the spring was 18 N/m, it was compressed from 1.61 m to 0.79 m after the cart had finally stopped, and the velocity of the cart when it first entered the second rough patch was 9 m/s, what was the magnitude of negative work done by friction force from the second rough patch in joules? Use g = 9.8 m/s2 in your calculations and retain your answer to two decimal places.

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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.