A fisherman is about to reel in a 9-lb fish located 15 ft directly below him. If

Question

A fisherman is about to reel in a 9-lb fish located 15 ft directly below him. If the fishing line weighs 1 oz per foot, how much work will it take to reel in the fish? Round your answer to the nearest tenth, if necessary. A vertical right circular cylindrical tank measures high and in diameter. It is full of oil weighing How much work does it take to pump the oil to a level above the top of the tank? Give your answer to the nearest ft %u2219 lb A force of 1000 lb compresses a spring from its natural length of 15 in. to a length of 12 in. How much work is done in further compressing it from 12 in. to 9 in.?

Explanation / Answer

1.) W=integral(F)dx
      15/16=0.9375
       F=9-0.9375x/15
      W=integral[9-0.9375x/15],-15 to 0
          = -(9x-0.9375x^2/30) =142.03ft-lbs

3.) I think the equation is (1/2)kx^2
      The other one you need to know is F=kx, since we don't know k, we can substitute F for kx.
      so.... Work = (1/2)(kx)x =(1/2)(F)(x)

      F=1000 lbs
      x=3 inches = (3/12) ft.

      so.... Work = (1/2)(1000)(3/12) = 125.00 ft lb

      We use this to solve for k, the spring constant...
      Work = (1/2)k(3/12)^2 =125.00
      so.... k= 4000

      Plug k into the formula now with the additional 5 inches of compression.
      Work = (1/2)k(x)^2
                = (1/2)(4000)(6/12)^2= 500 ft lb.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.