You are hired to design a safety system for an elevator that needs to have a max
ID: 1644124 • Letter: Y
Question
You are hired to design a safety system for an elevator that needs to have a maximum weight capacity of 2000kg (the mass of the elevator is 200kg) and that can fall from a height of 20 meters. The maximum acceleration that a human can take safely is 9 g's. A) What spring constant is required and what clearance from the bottom of the elevator shaft is needed to ensure that it is safe with loads less than or equal to its maximum capacity? B) What would you list as the maximum number of people that the elevator could carry? C) Now what if 10 people got into the elevator and sadly, it dropped from its maximum height. Show that the people inside would be safe by calculating the maximum g force exerted.Explanation / Answer
From the given question,
A)maximum weight capacity of elevator(m1)= 2000 kg
weight of elevator(m2)=200 kg
height(h)=20m
maximum acceleration(a)=9g
Tension in the spring (T) =m(g+a)
=2000(10+90)
=200000 N
Potential energy(E)= mgh
=2000*10*20
=400000 J
let the spring constant=k
extension= x
T=kx
E=(1/2)kx2
E/T=x/2
400000/20000=x/2
x=4m
F=kx
200000=k(4)
k=50000 N/m
spring constant=50000 N/m and minimum clearance is 4m
B)Total weight of all people= (2000-200)
=1800kg
assuming average weight of a person = 70 kg
total number of people= 1800/70
=25.7
Maximum number of people the elevator could carry is 25.
C)Assuming average weight of a person =75 kg
Weight of 10 people=75*10=750 kg
Total weight capacity of elevator= 200+750
=950 kg
Potential energy(E)= mgh
E=950*10*20
=190 000 J
E=(1/2)kx2
x=2.76
T=kx
=50000*2.76
=138 000 N
T=m(g+a)
maximum tension= 950(10+90)
=95000
As 95000<138000, people inside are safe.
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