Answer:
Explanation:
The question states that the chairs are spaced 20 m apart through a length of 1 km, or say, 1000 m.
It also does say that each chair weighs 250 kg, and as such the load is
M = 50 * 250
M = 12500.
Taking into consideration, the initial and final heights, we have
h1 = 0, h2 = 200 m
The work needed to raise the chairs,
W = mgh, where h = h2 - h1
W = 12500 * 9.81 * (200 - 0)
W = 2.54*10^7 J
The work is done at a rate of 10 km/h, and at a distance of 1 km, time taken would be
t = 1/10 = 0.1 h or say, 360 s
The power needed thus, is
P = W/t
P = 2.54*10^7 / 360
P = 68125 W, or 68 kW
Initial velocity, u = 0 m/s
Final velocity, v = 10 km/h = 2.78 m/s
Startup time, t is 17 s
Acceleration during the startup then is
a = (v - u)/t
a = 2.78/17
a = 0.163 m/s²
The power needed for the acceleration is
P = ½m [(v² - u²)/t]
P = ½ * 12500 * [2.78²/17]
P = 6250 * 0.455
P = 2844 W
