In this problem we have to account for both gravitational potential energy and elastic potential energy. In a "worst-case" design scenario, a 2000 kg elevator with broken cables is falling at 8.00 m/s when it first contacts a cushioning spring at the bottom of the shaft. The spring is supposed to stop the elevator, compressing 3 00 m as it does so (Figure 1). As an energy consultant, you are asked to determine what the force constant of the spring should be Ignore air resistance and friction in the elevator guides.
According to the conservation of energy, the total energy of a system remains constant. Energy cannot be created nor be destroyed, but can only be transferred from one form to another.
When an object is lifted to a height above the surface, energy is stored in the object. This is known as the gravitational potential energy. Similarly, when a spring is compressed, it stores energy. This is known as the elastic potential energy.
Energy is said to be stored in the previous two cases is because when an object is dropped from a height, it accelerates and falls to the ground and in the case of the spring, when released it gains velocity and stretches back to its relaxed equilibrium position. In both cases, the potential energy is converted into kinetic energy. Kinetic energy is energy of an object in motion and is dependent on both the mass and velocity of the object.
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