Weight = 6 Ду. %3D Suppose it is at a vertical distance y from the winding engine, then Distance moved = A 15 - y) ft. Step 4 Now, the work done, W2, in winding up 15 ft of cable is 6(15 - у) dy %3D [15y- Y %3D ft-lb. %3D

Calculus: Early Transcendentals
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Author:James Stewart
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Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Consider a denolition crane with a 35-pound ball suspended from a 40-foot cable that weighs 6 pounds per foot.
Exercise (a)
Find the work required to wind up 15 feet of the apparatus.
Step 1
Note that in the current situation, as the cable is pulled, the following things happen.
1. The ball gets lifted with a constant
constant force.
2. The cable that is wound up gets lifted with a variable variable force.
3. The cable that doesn't get wound up is lifted with a constant
constant force.
Step 2
Calculate the work done, W,, in pulling up the ball while winding up 15 ft of the apparatus.
W, = force x distance = 35 x 15 = 525
525 ft-lb
Step 3
Consider an elemental length Ay, of the cable that gets wound up. As the cable weighs 6 pounds per feet:
Weight = 6
Ay.
Suppose it is at a vertical distance y from the winding engine, then
Distance moved = (6
15 -) ft.
a
e Type here to search
Transcribed Image Text:Consider a denolition crane with a 35-pound ball suspended from a 40-foot cable that weighs 6 pounds per foot. Exercise (a) Find the work required to wind up 15 feet of the apparatus. Step 1 Note that in the current situation, as the cable is pulled, the following things happen. 1. The ball gets lifted with a constant constant force. 2. The cable that is wound up gets lifted with a variable variable force. 3. The cable that doesn't get wound up is lifted with a constant constant force. Step 2 Calculate the work done, W,, in pulling up the ball while winding up 15 ft of the apparatus. W, = force x distance = 35 x 15 = 525 525 ft-lb Step 3 Consider an elemental length Ay, of the cable that gets wound up. As the cable weighs 6 pounds per feet: Weight = 6 Ay. Suppose it is at a vertical distance y from the winding engine, then Distance moved = (6 15 -) ft. a e Type here to search
weighs 6 pounds per feet:
Weight =
6 Ду.
Suppose it is at a vertical distance y from the winding engine, then
Distance moved =
A 15 - y) ft.
Step 4
Now, the work done, W,, in winding up 15 ft of cable is
W2 =
6(15 - y) dy
[15y-
6.
ft-lb.
Submit
Skip (you cannot come back)
Exercise (b)
Find the work required to wind up all 40 feet of the apparatus.
Click here to begin!
Transcribed Image Text:weighs 6 pounds per feet: Weight = 6 Ду. Suppose it is at a vertical distance y from the winding engine, then Distance moved = A 15 - y) ft. Step 4 Now, the work done, W,, in winding up 15 ft of cable is W2 = 6(15 - y) dy [15y- 6. ft-lb. Submit Skip (you cannot come back) Exercise (b) Find the work required to wind up all 40 feet of the apparatus. Click here to begin!
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