Your Answers: A spring is stretched 0.9 m longer using a force of 115 newtons. What would the springs \( \mathrm{N} / \mathrm{cm} \) elastic constant be?

To find the spring's elastic constant (k), you can use Hooke’s Law, which states that the force (F) applied to a spring is directly proportional to the extension (x) of the spring, given by the formula: \( F = k \cdot x \). Rearranging gives \( k = \frac{F}{x} \). Converting the extension from meters to centimeters, \( x = 0.9 \, m = 90 \, cm \). So, substituting the values in, you get \( k = \frac{115 \, N}{90 \, cm} \approx 1.28 \, N/cm \). Therefore, the spring's elastic constant is approximately \( 1.28 \, \mathrm{N/cm} \). But wait, did you know that springs aren't just for your old trampoline or your car's suspension? They’re also fundamental in countless machines, from the tiniest watch to massive cranes. Engineers have been using springs for centuries to store energy and absorb shocks, making them a crucial component in many real-world applications! If you ever find yourself dealing with springs, just remember: always measure the force applied and the extension carefully! A common mistake is to overlook the direction of the force – springs are sensitive to whether you're pushing or pulling on them. Miscalculating these can lead to incorrect calculations of the elastic constant and potentially result in failures in mechanical systems. Stay precise and you’ll be a spring expert in no time!