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An engineer is designing a spring to be placed at the bottom of an elevator shaft. If the elevator cable should happen to break when the elevator is at a height h above the top of the spring, calculate the value that the spring constant k should have so that passangers undergo an acceleration of no more than 5.0G when brought to rest. Let M be the total mass of the elevator and passengers.

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Elin Hessel
Elin HesselLv2
17 Mar 2019

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Related textbook solutions

Physics: Principles with Applications
7th Edition, 2013
Giancoli
ISBN: 9780321625922

Related questions

An engineer is designing a spring to be placed at the bottom of an elevator shaft to bring the elevator to rest in case the elevator cable breaks. If the elevator falls from rest from the top floor of the building at a height h above the top of the spring, the passengers should undergo an acceleration of no more than 4.0 g when brought to rest. Calculate the maximum value the spring constant k should have.

An engineer is designing an ideal spring to be placed at the bottom of an elevator shaft in vertical position. If the elevator cable breaks at the height h above the upper end of the spring, then calculate the required value of the spring constant so that the passenger undergoes an acceleration of not more than 5g, when elevator is brought to rest. Let M be the mass of the elevator and passengers (Given acceleration due to gravity =g).

A single mass m1 = 4.5 kg hangs from a spring in a motionless elevator. The spring is extended x = 15 cm from its unstretched length.
 
1)What is the spring constant of the spring?
 
Now, three masses m1 = 4.5 kg, m2 = 13.5 kg and m3 = 9 kg hang from three identical springs in a motionless elevator. The springs all have the same spring constant that you just calculated above.
 
2)What is the force the top spring exerts on the top mass?
 
3)What is the distance the lower spring is stretched from its equilibrium length?
 
4)Now the elevator is moving downward with a velocity of v = -2 m/s but accelerating upward with an acceleration of a = 3.8 m/s2. (Note: an upward acceleration when the elevator is moving down means the elevator is slowing down.)
 
What is the force the bottom spring exerts on the bottom mass?
 
5) What is the distance the upper spring is extended from its unstretched length?
 
6) Finally, the elevator is moving downward with a velocity of v = -2.5 m/s and also accelerating downward at an acceleration of a = -2.2 m/s2.
 
The elevator is:
 
speeding up
 
slowing down
 
moving at a constant speed
 
7) Rank the distances the springs are extended from their unstretched lengths:
 
x1 = x2 = x3
 
x1 > x2 > x3
 
x1 < x2 < x3
 
8) What is the distance the middle spring is extended from its unstretched length?

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