# If the length of a #44 cm# spring increases to #58 cm# when a #5 kg# weight is hanging from it, what is the spring's constant?

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To find the spring constant, you can use Hooke's Law formula: ( F = -kx ), where ( F ) is the force applied (weight), ( k ) is the spring constant, and ( x ) is the displacement from the equilibrium position.

First, calculate the force applied: ( F = mg ), where ( m ) is the mass (5 kg) and ( g ) is the acceleration due to gravity (approximately 9.8 m/s²).

Next, find the displacement (( x )): ( x = \text{final length} - \text{initial length} ).

Finally, use Hooke's Law to calculate the spring constant (( k )): ( k = -\frac{F}{x} ).

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