# If the length of a #25 cm# spring increases to #79 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, we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to its displacement from equilibrium. The formula is:

F = k * x

Where: F is the force exerted by the spring (in Newtons), k is the spring constant (in Newtons per meter), and x is the displacement from equilibrium (in meters).

Given that the length of the spring increases from 25 cm to 79 cm, the displacement is: x = 79 cm - 25 cm = 54 cm = 0.54 meters

The force exerted by the weight can be calculated using the formula: F = m * g

Where: m is the mass (in kilograms), and g is the acceleration due to gravity (approximately 9.8 m/s^2).

So, F = 5 kg * 9.8 m/s^2 = 49 N

Now, we can use Hooke's Law to find the spring constant: 49 N = k * 0.54 m

k = 49 N / 0.54 m ≈ 90.74 N/m

Therefore, the spring constant is approximately 90.74 N/m.

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