The spring constant can be calculated using Hooke's Law, which states that the force needed to extend or compress a spring by some distance is proportional to that distance. The formula is:

F = kx

Where:
F is the force applied,
k is the spring constant,
x is the distance the spring is stretched or compressed.

We can rearrange the formula to solve for k:

k = F/x

However, we are given the energy used (8 J) and the distance (0.1 m), not the force. We can use the formula for the elastic potential energy stored in a spring, which is:

E = 1/2 kx^2

We can rearrange this formula to solve for k:

k = 2E/x^2

Substituting the given values:

k = 2 * 8 J / (0.1 m)^2
k = 16 J / 0.01 m^2
k = 1600 N/m

So, the spring constant is 1600 N/m.

Question

The spring constant can be calculated using Hooke's Law, which states that the force needed to extend or compress a spring by some distance is proportional to that distance. The formula is:

F = kx

Where:
F is the force applied,
k is the spring constant,
x is the distance the spring is stretched or compressed.

We can rearrange the formula to solve for k:

k = F/x

However, we are given the energy used (8 J) and the distance (0.1 m), not the force. We can use the formula for the elastic potential energy stored in a spring, which is:

E = 1/2 kx^2

We can rearrange this formula to solve for k:

k = 2E/x^2

Substituting the given values:

k = 2 * 8 J / (0.1 m)^2
k = 16 J / 0.01 m^2
k = 1600 N/m

So, the spring constant is 1600 N/m.

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