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Chapter 4: Problem 39

A spring with spring constant \(k=340 \mathrm{N} / \mathrm{m}\) is used to weigh a 6.7-kg fish. How far does the spring stretch?

Short Answer

Expert verified
The spring would stretch approximately 0.196 meters or 19.6 centimeters.

Step by step solution

01

Calculate fish weight

Firstly, calculate the weight of the fish by using the formula \(F = m \cdot g\), where \(m = 6.7 \mathrm{kg} \) (mass of the fish) and \( g = 9.81 \mathrm{m/s^{2}} \) (acceleration due to gravity). It should give the weight of the fish in Newtons (N).
02

Calculate spring stretch

Next, use the weight of the fish from step 1 as the force in the Hooke's law formula (\(\Delta x = \frac{F}{k}\)) to find how far the spring stretches. Remember to use \(k = 340 \mathrm{N/m}\) for the spring constant.
03

Result

The final step is to compare the calculated value with the correct answer to confirm the solution.

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