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Chapter 1: Problem 46

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?

Short Answer

Expert verified
The force required to stretch the spring 0.16 meter is 293.33 newtons.

Step by step solution

01

Identifying Given Values

The exercise provides the following given values:\n Force \(F_1 = 220\) newtons, \n Stretch \(d_1 = 0.12\) meter\n The target stretch \(d_2 = 0.16\) meter.
02

Applying Hooke's Law to Find the Constant of Proportionality (k)

Hooke's Law is given by \(F = kd\), where \(F\) is the force, \(d\) is the stretch, and \(k\) is the constant of proportionality. Solving for \(k\), we have \(k = F/d\). Hence with \(F=220\) N and \(d=0.12\) m, we get \(k = 220 / 0.12 = 1833.33\) N/m.
03

Using the Constant of Proportionality to Find the Required Force

We now need to find the force required to stretch the spring \(d_2 = 0.16\) meter. Substituting \(k = 1833.33\) N/m and \(d_2 = 0.16\) m into Hooke's Law \(F = kd\), the required force \(F_2 = 1833.33 * 0.16 = 293.33\) newtons.

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