BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 6, Problem 28RE
To determine

To calculate: the work done to raise the elevator from the basement to the third floor by 30ft height.

Expert Solution

Answer to Problem 28RE

The total work required to raise the elevator form basement to the third floor is 103,500ft-lb_.

Explanation of Solution

Given information:

The weight of elevator is 1,600 lb.

The weighs of cable is 10lb/ft.

Length of cable is 200 ft.

The height between basement and third floor is 30 ft.

Calculation:

Calculate the work done by the elevator w1 using the formula.

w1=Wd (1)

Here, W is weight of elevator and d is the distance from basement to third floor.

Substitute 1600 lb for W and 30 ft for d in Equation (1).

w1=1600×30=48,000ftlb

Determine the work needed to raise the bottom of the cable:

w2=dl×Wc×d

Here, dl is length of the cable above the third floor, Wc is weight of cable, and d is the distance from basement to third floor.

Substitute (200-30) ft for dl, 10lb/ft for Wc, and 30 ft for d.

w2=(20030)×10×30=170×10×30=51,000ft-lb

Expression to find the work required to raise the elevator by the cable at the third floor

(0 ft to 30 ft):

w3=abf(x)dx (2)

Here, f(x) is weight of cable.

Substitute 0 for a, 30 for b, and 10x for f(x) in Equation (2).

w3=03010xdx=[10x22]030=[5x2]030=[5(30)20]

=4500ft-lb

Find the total work required as shown below:

wtotal=w1+w2+w3 (3)

Substitute 48,000ft-lb for w1, 51,000ft-lb for w2, and 4500ft-lb for w3 in Equation (2).

wtotal=48,000+51,000+4,500=103,500ft-lb

Therefore, total work required to raise the elevator form basement to third floor is 103,500ft-lb_.

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