To compress spring 1 by 0.23 m takes 188 J of work. Stretching spring 2 by 0.27 m requires 211 J of work. Find the force constants.

K1 =
K2 =

I have derived the formula for k as

k = W/(2x^2) but when i plug in the values the answer isn't correct.

Formula?

W= 1/2 kx^2

k= 2W/x^2

To find the force constants, we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position.

Hooke's Law formula: F = kx

Where:
F is the force applied to the spring,
k is the force constant (also known as the spring constant),
x is the displacement from the equilibrium position.

We are given the work (W) done to compress spring 1 and spring 2. We can relate the work done to the force constant using the equation:

W = (1/2)kx²

Given:
W1 = 188 J (work done on spring 1)
W2 = 211 J (work done on spring 2)
x1 = 0.23 m (displacement for spring 1)
x2 = 0.27 m (displacement for spring 2)

To find the force constants, we need to rearrange the equation and solve for k:

k = (2W) / x²

Let's calculate the force constants:

For spring 1:
k1 = (2W1) / x1²
= (2 * 188) / 0.23²
= 2 * 188 / 0.0529
≈ 7150 N/m

For spring 2:
k2 = (2W2) / x2²
= (2 * 211) / 0.27²
= 2 * 211 / 0.0729
≈ 5824 N/m

Therefore, the force constants are:
K1 = 7150 N/m
K2 = 5824 N/m

To find the force constants (k1 and k2), we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position.

Hooke's Law can be expressed as: F = kx

Where:
F is the force applied to the spring
k is the force constant (also called the spring constant)
x is the displacement from the equilibrium position

Given that 188 J of work is required to compress spring 1 by 0.23 m, and 211 J of work is required to stretch spring 2 by 0.27 m, we can use this information to find k1 and k2.

For spring 1, we can use the formula:

k1 = W1 / x1^2

where W1 is the work done on the spring and x1 is the displacement.

Plugging in the values:
W1 = 188 J
x1 = 0.23 m

k1 = 188 J / (0.23 m)^2 = 188 J / 0.0529 m^2 ≈ 3556 N/m

So, k1 is approximately 3556 N/m.

Similarly, for spring 2:

k2 = W2 / x2^2

where W2 is the work done on the spring and x2 is the displacement.

Plugging in the values:
W2 = 211 J
x2 = 0.27 m

k2 = 211 J / (0.27 m)^2 = 211 J / 0.0729 m^2 ≈ 2900 N/m

So, k2 is approximately 2900 N/m.

Therefore, the force constants for spring 1 (k1) and spring 2 (k2) are approximately 3556 N/m and 2900 N/m, respectively.