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If you have a 12.4 cm spring hanging from a ceiling, and it stretches down to a length of 19 cm when a 122 kg mass is attached to it, what is the spring constant of the spring?

Answer :

Final answer:

The spring constant of the spring is 18133 N/m.


Explanation:

To calculate the spring constant, we can use Hooke's law which states that the force required to stretch or compress a spring is directly proportional to the change in length from its equilibrium position. Mathematically, it can be represented as F = kx, where F is the force, k is the spring constant, and x is the change in length.

In this case, the change in length is given as 19 cm - 12.4 cm = 6.6 cm = 0.066 m. The force can be calculated using the formula F = mg, where m is the mass and g is the acceleration due to gravity. Plugging in the values, we have F = (122 kg) * (9.8 m/s^2) = 1196.4 N.

Now, we can rearrange the equation F = kx to solve for the spring constant k. Plugging in the known values, we get k = F / x = 1196.4 N / 0.066 m = 18133 N/m.


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