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

9th Edition

ISBN: 9780357305041

Author: Stewart

Publisher: CENGAGE L

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 29E

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 28E

Chapter 6, Problem 30E

Students have asked these similar questions

Early Monday morning, the temperature in the lecture hall has fallen to 40°F, the same as the temperature outside. At 7:00 A.M., the janitor turns on the furnace with the thermostat set at 72°F. The time constant for the building is = 3 hr and that for the building along with its heating system is 1 K A.M.? When will the temperature inside the hall reach 71°F? 1 = 1 hr. Assuming that the outside temperature remains constant, what will be the temperature inside the lecture hall at 8:30 2 At 8:30 A.M., the temperature inside the lecture hall will be about (Round to the nearest tenth as needed.) 1°F.

Find the maximum volume of a rectangular box whose surface area is 1500 cm² and whose total edge length is 200 cm. cm³

Find the minimum cost of a rectangular box of volume 120 cm³ whose top and bottom cost 6 cents per cm² and whose sides cost 5 cents per cm². Round your answer to nearest whole number cents. Cost = cents.

Chapter 6 Solutions

CALCULUS, EARLY TRANSITIONS (LL)

Ch. 6.1 - (a) Set up an integral for the area of the shaded...Ch. 6.1 - (a) Set up an integral for the area of the shaded...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. 5.Ch. 6.1 - Find the area of the shaded region. 6.Ch. 6.1 - Set up, but do not evaluate, an integral...Ch. 6.1 - Prob. 8E Ch. 6.1 - Set up, but do not evaluate, an integral...Ch. 6.1 - Set up, but do not evaluate, an integral...

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