Explanation Given information: The required force to maintain a spring stretched from its natural length of 12 cm to 20 cm is 30 N. Apply Hooke’s Law to find the spring constant: F ( x ) = k x (1) Here, F ( x ) is force, k is spring constant, and x is amount of extension. Calculation: Calculate the spring constant using Equation (1). Substitute 30 N for F and ( 15 cm − 12 cm ) for x in Equation (1). 30 N = ( 15 cm − 12 cm ) × k = ( 3 cm × 1 m 100 cm ) × k = 0.03 k k = 30 0.03 = 1 , 000 N/m Show the expression to find the work done to stretch the spring from 12 cm to 20 cm. W = ∫ a b k x d x (2) Here, a is the lower limit and b is the upper limit. Consider that the lower limit as 0 cm. Hence, a = 0 cm Calculate the upper limit as follows: b = Stretching length − Natural length = 20 cm − 12 cm = 8 cm × 1 m 100 cm = 0

8th Edition

ISBN: 9781285741550

Author: James Stewart

Publisher: Cengage Learning

See similar textbooks

Concept explainers

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the se…

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integratio…

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects th…

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.

Videos

Question

Chapter 6, Problem 27RE

To determine

To calculate: the work done in stretching the spring from 12 cm to 20 cm.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6, Problem 26RE

Chapter 6, Problem 28RE

Students have asked these similar questions

A 20 foot ladder rests on level ground; its head (top) is against a vertical wall. The bottom of the ladder begins by being 12 feet from the wall but begins moving away at the rate of 0.1 feet per second. At what rate is the top of the ladder slipping down the wall? You may use a calculator.

Explain the focus and reasons for establishment of 12.4.1(root test) and 12.4.2(ratio test)

use Integration by Parts to derive 12.6.1

Chapter 6 Solutions

Calculus: Early Transcendentals

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 - Sketch the region enclosed by the given curves....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 - Sketch the region enclosed by the given curves....

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 work done in stretching the spring from 12 cm to 20 cm .

Solution Summary: The author calculates the required force to maintain a spring stretched from its natural length of 12 cm to 20 cm using Hooke's Law.

Concept explainers

Videos

To calculate: the work done in stretching the spring from 12 cm to 20 cm.

Want to see the full answer?

Chapter 6 Solutions