You are a Systems Engineer working for an architecture firm. You are asked to pr

Question

You are a Systems Engineer working for an architecture firm. You are asked to provide the design for a residential elevator. The house owners require that all three members of their family (husband, wife and 15-year old child) are able to get on and use the elevator at the same time (if necessary). The structure is a three-story building. The first two stories have 5m-high ceilings while the top floor has a 7m-high ceiling. The elevator is supposed to service all three floors and an elevator shaft is already created at the construction site with dimensions 2m width and 1.5m depth. The elevator movement is controlled by a pulley mechanism (image below) with size (from A to B) equal to 50cm. The pulley is designed to work with cable wire. You will be given all the parts'so don't worry about material and cost. You will also be given a crew to help you build your elevator and install it. However, the crew needs direction: specification and a design to build the elevator. You must state all of your assumptions clearly and show all of your work. (Tip: I expect relevant diagrams, calculations and assumptions.) Notes: Shaft is the structure of the building that houses the elevator. Pulley

Explanation / Answer

given

1. three members of the family hsould be able to climb the elevator

2. first 2 storeys have height 5 m each, the third one has 7 m height

3. depth of elevator floor = 1.5 m

4. pulley volume, V = 50 cm^3

so the elevator will first of all have a counter weight of the order of the mass of the elevator and mass of three family members

so mass of each member = m = 80 kg

mass of elevator = M

total mass = M + 3*80

factor of safety = 5

total mass that can be carried = M' = 5(M + 240) kg

lets say the counter weight is of the same weight

now, for usual elevators acceelration is about 1 m/s/s

so net tension in the cable including factor of safety is T1 on one side of pulley T2 on other side of the pulley

T1 - M'g = M'a

M'g - T2 = M'a

(T2 - T1)r + T = 0.5rho*50*a [ here rho is density of pulley material in kg/cm^3]

so for pulley thickness t, radius r in cm

pi*r^2*t = 50 cm^3

r = sqrt(50/pi*t)

(M'(10.81) - M'(8.81))sqrt(50/pi*t) + T = 0.5rho*50*a [ here T is torque being provided to the pulley by the motor]

hence T1 > T2

T1 = 10.81*M'

so, the rope thickness is t

its ultimate stress be E

then take another factor of safety of 3

then

4T1/pi*t^2 = 3E

t = 2*sqrt(T1/3E*pi)

T1 = 10.81*5(M + 240) kg

r = sqrt(50/pi*t)

hence by knowing mass of elevator at first M, we can know T1, t ( thickness of pulley) radius of pulley

we have top chose material that meet the requirements of ultimate strength of the rope

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