# If the length of a #35 cm# spring increases to #86 cm# when a #9 kg# weight is hanging from it, what is the spring's constant?

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The spring constant (k) can be calculated using Hooke's Law: F = k * x, where F is the force applied, k is the spring constant, and x is the displacement from the equilibrium position. Rearranging the equation to solve for k: k = F / x. Given that the weight is 9 kg (which can be converted to Newtons by multiplying by the acceleration due to gravity, 9.8 m/s^2) and the displacement is the change in length of the spring from its original length of 35 cm to 86 cm, the displacement (x) is 86 cm - 35 cm = 51 cm. Converting the displacement to meters (since the standard unit for force is Newtons and meters for displacement), we have x = 0.51 meters. The force (F) is the weight, which is 9 kg * 9.8 m/s^2 = 88.2 N. Therefore, k = 88.2 N / 0.51 m ≈ 172.94 N/m. So, the spring constant is approximately 172.94 N/m.

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