a 1600 lb elevator is suspended by a 200-ft cable that weights 10 lb/ft.?

Question

how much work is required to raise the elevator from the basement to the third floor, a distance of 30 ft?

thanx everyone!!

Answer 1

Work = Weight times Distance

Work = ((200*10) +1600) * 30 ft

Work = 3600 lbs * 30 ft

= 108,000 joules of work

Answer 2

Work done to Raise an object to a height
= m*g*h
m is the mass of the body
g is the accleration due to gravity
h signifies the height to which the body is raised.

Thus;
m*g signifies the weight of the body
h signifies the height to which the body is raised.

Total weight = Weight of Elevator + Weight of Cable = m*g
= 1600 + 200 * 10
= 1600 + 2000
=3600 lb

h = 30 ft

Work done = 3600 * 30 = 108000 lb-ft

Unit of WORK DONE IN THIS CASE IS lb-ft NOT JOULES

Answer 3

im not sure why u need the wt and length of cable.i think the work done=mgh=1600 multiplied by 9.8 multiplied by 30

Answer 4

As the elevator is raised, the cable is shortened.
F(s) = 1600 + 2000 - 10s = 3,600 - 10s
..... .. 30..... .. 30..... ..... ..... ..... .... ..... ..... .... 30
W = ∫F•ds = ∫(3,600 - 10s)ds = [3,600s - 5s^2] | =
..... . 0..... ... 0..... ..... ..... ..... ..... ..... ..... ..... . 0
W = 3,600*30 - 5*30^2
W = 108,000 - 4,500 ft•lb
W = 103,500 ft•lb