Question

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. If the mass of the elevator (with four fewer passengers than before) is 1800 kg, what should the spring constant be for a maximum compression of 3.00 m?

          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.
If the mass of the elevator (with four fewer passengers than before) is 1800 kg, what should the spring constant be for a maximum compression of 3.00 m?

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