## amistre64 Group Title Find the amount of work done by lifting 150 ft of wire that weighs 4 lbs/foot. 3 years ago 3 years ago

1. elecengineer Group Title

:|

2. satellite73 Group Title

i will watch. good morning sensei

3. amistre64 Group Title

Gmornin :)

4. amistre64 Group Title

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

5. satellite73 Group Title

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

6. amistre64 Group Title

(150-x) would be the length of each "portion" which then weighs 4 lb/ft maybe: $\int_{0}^{150}(150-x)4\ dx$

7. elecengineer Group Title

its very easy

8. amistre64 Group Title

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

9. satellite73 Group Title

i will learn something...

10. amistre64 Group Title

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

11. satellite73 Group Title

physics class?

12. abtrehearn Group Title

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.

13. amistre64 Group Title

calculus1

14. elecengineer Group Title

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

15. abtrehearn Group Title

Then the vertical distance is 75 ft.

16. abtrehearn Group Title

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

17. amistre64 Group Title

so the 75 comes from 150/2 right?

18. amistre64 Group Title

how would we set that up as an integral?

19. abtrehearn Group Title

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

20. abtrehearn Group Title

Half the length. Yes, Amistre.

21. amistre64 Group Title

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?

22. amistre64 Group Title

weight of cable being 4 lb/ft

23. abtrehearn Group Title

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.

24. abtrehearn Group Title

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

25. abtrehearn Group Title

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

26. amistre64 Group Title

so if anything, I would have been off by makeing the force = length*weight? [150ft - (x ft off the ground) ] * 4 lb/ft? $\int_{0}^{150}(150-x)4\ dx$ $\int_{0}^{150}(500-4x)\ dx\implies500x-2x^2|^{150}$

27. abtrehearn Group Title

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

28. amistre64 Group Title

thanx :)

29. abtrehearn Group Title

Remember the definition of work?

30. abtrehearn Group Title

:^)

31. amistre64 Group Title

Work = Force x Distance yes :)

32. abtrehearn Group Title

That's the idea ; ^)