# If the length of a #15 cm# spring increases to #28 cm# when a #2 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 the displacement of the spring from its equilibrium position.

The formula for Hooke's Law is F = kx, where F is the force exerted by the spring, k is the spring constant, and x is the displacement from the equilibrium position.

Given that the weight hanging from the spring is 2 kg and the displacement of the spring is from 15 cm to 28 cm (which is 13 cm or 0.13 meters), we can use this information to find the spring constant.

First, we need to calculate the force exerted by the weight using the formula F = mg, where m is the mass and g is the acceleration due to gravity (approximately 9.8 m/s^2).

F = (2 kg)(9.8 m/s^2) = 19.6 N

Now, we can use Hooke's Law to find the spring constant:

19.6 N = k(0.13 m)

Solving for k:

k = 19.6 N / 0.13 m

k ≈ 150.77 N/m

So, the spring constant is approximately 150.77 N/m.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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