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Physics Help?
An elevator mass of 1000 kg falls from a height of 12 m after a sudden failure in the hoisting cable. The mass is stopped by a spring at the bottom of the shaft having a spring constant of 80 kN/m. Determine the spring's compression distance in m that brings the falling elevator momentarily to rest.
so the problem checker says the answer is 1.84, but I don't know how to find that.
1 Answer
- 5 years ago
We can solve this problem using conservation of energy: when the spring brings the falling elevator to a momentary rest, it will have absorbed all of its falling energy.
The energy of the elevator is equal to its potential energy before it started falling: E = m*g*h = 1000kg * 9.81m/s^2 * 12m = 117'720J.
So the energy stored in the spring will be 117'720J at the moment when it stops the elevator. Plugging this number into the spring energy equation allows us to find how much it compresses:
Spring Energy = 117'720J = 0.5 * Spring Constant * Compression = 0.5 * 80'000N/m * Compression.
Solving for compression gives us 2.943m.