Question

Find the amount of work done by lifting 150 ft of wire that weighs 4 lbs/foot.

Answer 1

:|

Answer 2

i will watch. good morning sensei

Answer 3

Gmornin :)

Answer 4

im sure we are starting at one end and winding the whole thing up, at least that is what I pictured

Answer 5

honestly if i pretended to help i would be making things up. never had a physics class in my life.

Answer 6

(150-x) would be the length of each "portion" which then weighs 4 lb/ft
maybe:

\[\int_{0}^{150}(150-x)4\ dx\]

Answer 7

its very easy

Answer 8

im sure it is, but im wondering if I did the integral correctly ...

Answer 9

i will learn something...

Answer 10

i got another one about fluid density pressure after this :)

Answer 11

physics class?

Answer 12

The total weight of the cable is 600 lb. Find the vertical distance the center of mass moves in ft., then multiply that distance by 600, and you have the ansewr in ft. lb. The hard part is finding the vertical distance. The problem, as stated, does not provide enough information on that score.

Answer 13

calculus1

Answer 14

It assumes it moves vertically, just enough to leave the ground.

Answer 15

Then the vertical distance is 75 ft.

Answer 16

So W = (600lb)(75ft) = 45,000 ft. lb.

Answer 17

so the 75 comes from 150/2 right?

Answer 18

how would we set that up as an integral?

Answer 19

I picture one end being lifted up until the other end is just about to leave the ground. Is that the rright scenario?

Answer 20

Half the length. Yes, Amistre.

Answer 21

i dunno if thats the right scenario; i believe the question was asking, my interpretation is this, you have 150 feet of cable suspended by a winch; how much work is required to roll it all up onto the winch?

Answer 22

weight of cable being 4 lb/ft

Answer 23

If you want to set it up as an integral, you can start with\[\int\limits_{0}^{150}F(x) dx,\]where F(x) is the force needed to lift x feet of cable off the ground.

Answer 24

If the weight is 4 lb/ft, then x ft weighs (4x) lb, so 4x is the integrand.

Answer 25

The integral evaluatex to 2x^2, where x = 150. Works out to 2* 22500 =
45,000 ft. lb.

Answer 26

so if anything, I would have been off by makeing the force = length*weight?

[150ft - (x ft off the ground) ] * 4 lb/ft?

\[\int_{0}^{150}(150-x)4\ dx\]
\[\int_{0}^{150}(500-4x)\ dx\implies500x-2x^2|^{150}\]

Answer 27

:\[W = \int\limits_{0}^{150}4x dx = 45,000.\]The length is x ft, and the weight pre foot is 4 lb/ft.

Answer 28

thanx :)

Answer 29

Remember the definition of work?

Answer 30

:^)

Answer 31

Work = Force x Distance yes :)

Answer 32

That's the idea ; ^)