# the work done to raise the elevator from the basement to the third floor by 30ft height.

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

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_.

### Have a homework question?

Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!