[10] (5) In a "worst-case" design scenario, a 2000 kg elevator with broken cables is freely fall

Step 1: Calculate the maximum compression of the spring when the elevator is at height H = 3.2 m

Question

[10] (5) In a "worst-case" design scenario, a 2000 kg elevator with broken cables is freely falling from height H when it first contacts a cushioning spring at the bottom of the shaft. The spring is supposed to stop the elevator, compressing d meters as it does so (Figure). [4] A. In testing the spring a mass of 1000 kg dropped from height H = 1.6 m compresses it by d = 1.5 m. What is the force constant of the spring? [6] B. If the cables break when the elevator is at height H = 3.2 m above the spring, what would be the maximum compression of the spring? (Ignore air resistance and friction in the elevator guides.) Elevator H d a) m = 1000 kg F = -kx h = 1.6 m ma = -kx x = 1.5 m 1000 (9.8) = -k (1.5) a = 9.8 m k = -6.53 x 10^3 N 6)

          [10] (5) In a "worst-case" design scenario, a 2000 kg elevator with broken cables is freely falling from height H when it first contacts a cushioning spring at the bottom of the shaft. The spring is supposed to stop the elevator, compressing d meters as it does so (Figure).
[4] A. In testing the spring a mass of 1000 kg dropped from height H = 1.6 m compresses it by d = 1.5 m. What is the force constant of the spring?
[6] B. If the cables break when the elevator is at height H = 3.2 m above the spring, what would be the maximum compression of the spring? (Ignore air resistance and friction in the elevator guides.)
Elevator
H
d
a) m = 1000 kg F = -kx
h = 1.6 m ma = -kx
x = 1.5 m 1000 (9.8) = -k (1.5)
a = 9.8 m k = -6.53 x 10^3 N
6)

[10] (5) In a "worst-case" design scenario, a 2000 kg elevator with broken cables is freely falling from height H when it first contacts a cushioning spring at the bottom of the shaft. The spring is supposed to stop the elevator, compressing d meters as it does so (Figure).
[4] A. In testing the spring a mass of 1000 kg dropped from height H = 1.6 m compresses it by d = 1.5 m. What is the force constant of the spring?
[6] B. If the cables break when the elevator is at height H = 3.2 m above the spring, what would be the maximum compression of the spring? (Ignore air resistance and friction in the elevator guides.)
Elevator
H
d
a) m = 1000 kg F = -kx
h = 1.6 m ma = -kx
x = 1.5 m 1000 (9.8) = -k (1.5)
a = 9.8 m k = -6.53 x 10^3 N
6)

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