You give a crate of mass m = 1.00 kg an initial speed of vi = 4.00 m/s up an incline of θ = 17°. The crate then slides along the incline, reaches a spring of spring constant k = 92 N/m , and compresses the spring by Δs = 15.0 cm before stopping. a) what is the distance d, in meters, along the incline that the crate slides, assuming there is no friction? b)What distance ds, in meters, along the incline had the crate moved when it just touched the spring? c)If there were friction between the crate and incline, what coefficient of kinetic friction would stop the crate after it travels ds (just before it compresses the spring)?

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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.