Consider a simple elevator design in which a 15,000 kg car A is connected to a 1
ID: 1856996 • Letter: C
Question
Consider a simple elevator design in which a 15,000 kg car A is connected to a 12,000 kg counterweight B. Suppose that a failure of the drive system occurs(the failure does not affect the cable connecting A and B) when the car is at rest and 50 m above its buffer (i.e. car support at the bottom of the elevator shaft), causing the elevator car to fall. Determine the speed with which the elevator car impacts the buffer. Treat the elevator car and the counterweight as particles. Treat the cable as massless and inextensible. Model the action of the emergency brakes (acting vertically as to slow down the fall) using coulomb friction model with kinetic friction coefficient equal to 0.5 and a normal force (due to the elevators shaft's walls acting on the car) equal to 35% of the car's weight.
The problem is in the book, Engineering Mechanics Dynamics 1st edition By: Gary L Gray, Francesco Costanzo, Michael E Plesha
ISBN-13: 9780077275549
Chp: 4 problem 60
I am having a hard time working through the algebra to obtain the answer, if you could show me the steps through it so i can see where i messed up that would be great. Please show work thank you for your time and effort.
Explanation / Answer
generalised eqns
To determine Force of rope (Fr) using the elevator FBD:
Fnet = Fg + ( - Fr)
ma = mg + (-Fr)
ma - mg = -Fr
mg - ma = Fr
Fr = 2400 N
Using the counterweight FBD we have the equation:
Fnet = Fr + (-Fg)
ma = Fr + (-mg)
ma + mg = Fr
m (a+g) = Fr
m = Fr/(a+g)