# If the length of a #22 cm# spring increases to #55 cm# when a #7 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, which states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position.

First, find the change in length of the spring: ΔL = L - L₀ ΔL = 55 cm - 22 cm ΔL = 33 cm

Next, calculate the force exerted by the weight: F = m * g F = 7 kg * 9.8 m/s² F ≈ 68.6 N

Then, use Hooke's Law to find the spring constant: F = k * ΔL 68.6 N = k * 0.33 m

Finally, solve for k: k = 68.6 N / 0.33 m k ≈ 208 N/m

So, the spring constant is approximately 208 N/m.

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The spring constant can be calculated using Hooke's Law, which states that the force exerted by a spring is directly proportional to its displacement from the 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, x is the displacement from the equilibrium position.

In this scenario, the spring's displacement (x) is the change in length, which is 55 cm - 22 cm = 33 cm.

The force exerted by the weight (7 kg) can be calculated using the formula F = mg, where: m is the mass (7 kg), and g is the acceleration due to gravity (approximately 9.8 m/s^2).

Thus, F = 7 kg * 9.8 m/s^2 = 68.6 N.

Now, using Hooke's Law, we can find the spring constant: 68.6 N = k * 0.33 m

Therefore, k = 68.6 N / 0.33 m ≈ 208 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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