Explanation Given: The work done before break down of the pump is 4.7 × 10 5 J . The height of the tank is 3 m. Take the mass density of the water ρ w as 1000 kg/m 3 Write the expression to find the work done W to pump the water from a to b , when a force f ( x ) is applied on it. W = lim n → ∞ ∑ i = 1 n f ( x i ∗ ) Δ x = ∫ a b f ( x ) d x (1) Calculation: Assume the value of acceleration due to gravity g as 9.8 m/s 2 . Consider the point O at top of the tank as the origin, introduce a vertical coordinate line extending downwards as shown in Figure 1. Refer Figure 1. The water extends from 0 m to 3 m. Divide the interval [ 0 , 3 ] into n sub intervals with endpoints x 0 , x 1 , ... , x n . Choose x i ∗ in the i t h subinterval. The i t h layer is a rectangular slice with length l , width b and depth Δ x . Calculate the volume of the rectangular slice at i t h subinterval as shown below: V = l b h (2) Substitute 8 m for l , x m for b, and Δ x for h in Equation (2). V = 8 × x × Δ x = 8 x Δ x Calculate the weight of the water w in the rectangular slice. w = weight density of water×volume of rectangular slice = w w × V (3) Substitute 8 x Δ x m 3 for V and 9800 kg/m 3 for w w in Equation (3). w = 9800 N/m 3 × 8 x Δ x m 3 = 78400 x Δ x N Calculate the work done W i to pump the water from the rectangular slice using the relation. W i = Force×distance = F × d (4) The force required to lift the water from the rectangular slice is same as the weight of the water in the rectangular slice. Substitute w for F and x i ∗ for d in Equation (4). W i = w × x i ∗ (5) Substitute 78400 x Δ x N for w in Equation (5). The volume water in the x i ∗ region is to be pumped by a distance of ( 5 − x ) m

Bundle: Single Variable Calculus: Early Transcendentals, Loose-leaf Version, 8th + Webassign Printed Access Card For Calculus, Multi-term Courses, Life Of Edition

18th Edition

ISBN: 9780357008034

Author: Stewart

Publisher: CENGAGE L

See similar textbooks

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

Videos

Question

Chapter 6.4, Problem 27E

To determine

To calculate: The depth of the water remaining in the tank after the pump breaks down.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6.4, Problem 26E

Chapter 6.4, Problem 28E

Students have asked these similar questions

Let a = (-4, 5, 4) and 6 = (1,0, -1). Find the angle between the vector 1) The exact angle is cos 2) The approximation in radians is

Find the (exact) direction cosines and (rounded to 1 decimal place) direction angles of = (3,7,6)

Let a = (-1, -2, -3) and 6 = (-4, 0, 1). Find the component of b onto a.

Chapter 6 Solutions

Bundle: Single Variable Calculus: Early Transcendentals, Loose-leaf Version, 8th + Webassign Printed Access Card For Calculus, Multi-term Courses, Life Of Edition

Ch. 6.1 - Find the area of the shaded region.Ch. 6.1 - Find the area of the shaded region.Ch. 6.1 - Find the area of the shaded region.Ch. 6.1 - Find the area of the shaded region.Ch. 6.1 - Sketch the region enclosed by the given curves....Ch. 6.1 - Sketch the region enclosed by the given curves....Ch. 6.1 - Prob. 7E Ch. 6.1 - Sketch the region enclosed by the given curves....Ch. 6.1 - Prob. 9E Ch. 6.1 - Prob. 10E

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

The depth of the water remaining in the tank after the pump breaks down.

Solution Summary: The author calculates the depth of the water remaining in the tank after the pump breaks down.

Concept explainers

Videos

To calculate: The depth of the water remaining in the tank after the pump breaks down.

Want to see the full answer?

Chapter 6 Solutions