It is required that an elevator and its contents having a ma

It is required that an elevator and its contents, having a maximum weight of 2.5 kN, be lifted by 10m, starting from rest and then stoping after 6 seconds. A single motor and a cable winding drum can be mounted anywhere and used for the operation. During any lift or descent, the acceleration should not exceed 5 m/s^2. Design a cable and pulley system for the elevator and your design should include sketch/drawings of your system and plots of the power output required for the motor versus the height y travelled.

Solution

weight = 2500 N
Lets assume max acc of 5 m/s/s

so, 2500 + 2500*5/9.8 = T [ maximum tension in the rope] = 3775.51 N

Now, for first t seconds the mass accelerates to velocity v
v = 5t ... (1)
and in the last t seconds is decelerates with the same equation
and in the meantime ios travels some distance
so we know trhat
10 = 5*t^2 + v(6 - 2t) = 5*t^2 + 5t(6 - 2t) = 5*t^2 + 30t - 10t^2 = -5t^2 + 30t
5t^2 - 30t + 10 = 0
t^2 - 6t + 2 = 0
t = 0.3542 s
v = 1.771 m/s
power output = F*v
now, for first 0.3542s
P = 3775.51*5t = 18877.55 W

for next 5.2916 s
F = 2500 N
P = 12500 W

for next 0.3542 s,
P = 1224.489*5t = 6122.4489 t W