Question

Use Hooke's Law for springs, which states that the distance a spring is stretched (or compressed) varies directly as the force on the spring. A force of 220 newtons stretches a spring 0.12 meter. What force is required to stretch the spring 0.16 meter?

Name: Problem 46, Chapter 1: Precalculus: A Concise Course
Uploaded: 2021-07-07T00:21:49-08:00
Duration: 1 min 46 s
Channel: Erika Bustos
Description: Use Hooke's Law for springs, which states that the distance a spring is stretched (or compressed) varies directly as the force on the spring. A force of 220 newtons stretches a spring 0.12 meter. What force is required to stretch the spring 0.16 meter?

   Use Hooke's Law for springs, which states that the distance a spring is stretched (or compressed) varies directly as the force on the spring.
A force of 220 newtons stretches a spring 0.12 meter. What force is required to stretch the spring 0.16 meter?

Precalculus: A Concise Course

Ron Larson, David C.… 2nd Edition

Chapter 1, Problem 46

Instant Answer

Solved by Expert Erika Bustos

07/07/2021

Step 1

This can be represented by the equation $y = kx$, where $y$ is the distance the spring is stretched, $x$ is the force applied, and $k$ is the constant of variation. Show more…

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Use Hooke's Law for springs, which states that the distance a spring is stretched (or compressed) varies directly as the force on the spring. A force of 220 newtons stretches a spring 0.12 meter. What force is required to stretch the spring 0.16 meter?

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Key Concepts

Hooke's Law

Hooke's Law is a principle in physics that states that the force needed to extend or compress a spring by some distance is proportional to that distance. This relationship is often expressed as F = kx, where F is the force applied, x is the displacement from the equilibrium position, and k is the constant of proportionality known as the spring constant.

Direct Variation

Direct variation refers to a relationship between two variables in which an increase in one variable results in a proportional increase in the other. In the context of Hooke's Law, the extension of the spring is directly proportional to the applied force, meaning that if the force increases, the extension increases proportionally, assuming the spring’s elastic limit is not exceeded.

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