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Chapter 1: Problem 69

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. The coiled spring of a toy supports the weight of a child. The spring is compressed a distance of 1.9 inches by the weight of a 25 -pound child. The toy will not work properly if its spring is compressed more than 3 inches. What is the maximum weight for which the toy will work properly?

Short Answer

Expert verified
The maximum weight for which the toy will work properly is approximately 39.47 pounds.

Step by step solution

01

Understand and Express Hooke's Law

For a spring obeying Hooke's Law, the compression \(d\) (in inches) is directly proportional to the force \(f\) (in pounds). The relation can be expressed as \(d = kf\), where \(k\) is a constant of proportionality.
02

Establish the Equation

Since a weight of 25 pounds compresses the spring by 1.9 inches, this gives the equation \(1.9 = k*25\). Solving for \(k\), we get \(k = 1.9 / 25 = 0.076\) inches/pound.
03

Find the Maximum Weight

We want to find the maximum weight \(f\) which wouldn't compress the spring by more than 3 inches. So, we set up and solve the equation \(3 = 0.076f\). Solving for \(f\), we find \(f = 3 / 0.076 \approx 39.47\) pounds.

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