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

Name: Problem 68, Chapter 3: College Algebra
Uploaded: 2022-01-16T21:22:26-08:00
Duration: 1 min 49 s
Channel: Tara Wells
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. (a) What force is required to stretch the spring 0.1 meter? (b) How far will a force of 90 newtons stretch the spring?

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. (a) What force is required to stretch the spring 0.1 meter? (b) How far will a force of 90 newtons stretch the spring?

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.
(a) What force is required to stretch the spring 0.1 meter?
(b) How far will a force of 90 newtons stretch the spring?

Key Concepts

Spring Constant

The spring constant, often denoted as k, is a measure of a spring's stiffness. It represents the ratio of the force affecting the spring to the displacement caused by it. A higher spring constant indicates a stiffer spring that requires more force for a given displacement, while a lower spring constant indicates a more easily stretched or compressed spring.

Algebraic Manipulation

Algebraic manipulation involves solving equations to find unknown variables. In problems using Hooke's Law, this means rearranging the equation F = kx to solve for the desired quantity, such as force or displacement, by isolating the variable of interest. This process is essential for applying the law to practical situations where certain values are known and others need to be determined.

Hooke's Law

Hooke's Law is a principle in physics that states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position. This relationship is typically expressed as F = kx, where F is the force applied, x is the displacement (stretch or compression), and k is the constant of proportionality known as the spring constant.

Direct Variation

The concept of direct variation refers to a relationship between two variables in which an increase in one variable leads to a proportional increase in the other. In the context of Hooke's Law, the displacement of the spring varies directly with the force applied, meaning that if the force is increased, the displacement increases proportionally, assuming the spring's properties remain unchanged.

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