Use Hooke's Law for springs, which states that the distance...

Name: Problem 45, Chapter 1: Precalculus: A Concise Course
Uploaded: 2021-07-05T22:09:48-08:00
Duration: 2 min 29 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 265 newtons stretches a spring 0.15 meter (see figure). (a) How far will a force of 90 newtons stretch the spring? (b) What force is required to stretch the spring 0.1 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 265 newtons stretches a spring 0.15 meter (see figure). (a) How far will a force of 90 newtons stretch the spring? (b) What force is required to stretch the spring 0.1 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 265 newtons stretches a spring 0.15 meter (see figure).
(a) How far will a force of 90 newtons stretch the spring?
(b) What force is required to stretch the spring 0.1 meter?

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Key Concepts

Hooke's Law

Hooke's Law is a principle of physics that states the force needed to extend or compress a spring by some distance is proportional to that distance. This fundamental relationship applies as long as the material's elastic limit is not exceeded, meaning the spring returns to its original shape when the force is removed.

Direct Variation

Direct variation describes a relationship between two variables in which one variable is a constant multiple of the other. In the context of Hooke's Law, this means that the distance a spring stretches is directly proportional to the force applied, enabling the use of a constant of proportionality to solve for unknown values.

Proportionality Constant

The proportionality constant in problems involving direct variation represents the fixed multiplier that relates the two quantities. In Hooke's Law, this constant (often referred to as the spring constant) quantifies the stiffness of the spring, allowing one to calculate the displacement from any applied force by multiplying the force by this constant.

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