An elevator mass of 8100 kg falls from a height of 41 m after a sudden failure i

Question

An elevator mass of 8100 kg falls from a height of 41 m after a sudden failure in the hoisting cable. The mass is stopped by a spring at the bettom of the shaft having a spring constant of 125 kN/m. Determine the spring's compression distance in m that brings the falling elevator momentarilv to rest. An elevator mass of 8100 kg falls from a height of 41 m after a sudden failure in the hoisting cable. The mass is stopped by a spring at the bettom of the shaft having a spring constant of 125 kN/m. Determine the acceleration in m/s/s that the elevator undergoes when brought to rest by the spring. An elevator mass of 8100 kg falls from a height of 41 m after a sudden failure in the hoisting cable. The mass is stopped by a spring at the bettom of the shaft. Determine the spring constant in kN/m that will bring the elevator and occupants to rest at an acceleration of 7 g.

Explanation / Answer

acceleration = 7g

so the force acting should be m*a = 8100*7*g

spring force = kx

and gravity force = mg

so net force = kx - mg =ma

     ==> kx = ma+mg = 7mg+mg = 8mg

kx = 8mg

also initial energy = m*g*H = m*g*41

this is finally absorbed by spring= 1/2*k*x^2

so 1/2*k*x^2 = 41mg

1/2*kx *x = 41 mg

1/2*8mg *x = 41mg

x = 10.25 m

so kx = 8mg

so k = 8mg/x = 8*8100*9.8/10.25 = 61955.123 N/m

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