Use the following data to determine the length L of a wire when a fore of 30N is applied, assuming Hooke's law is obeyed \(\begin{array}{c|c}\text{Force app...

Answer Details

Hooke's Law states that the force applied to a spring is directly proportional to the extension or compression of the spring, provided the elastic limit is not exceeded. This can be expressed mathematically as F=kx, where F is the force, k is the spring constant, and x is the extension or compression. To determine the length L of the wire when a force of 30N is applied, we need to first find the spring constant k. We can do this by calculating the extension x for each force applied, using the formula: x = (L - L₀) where L₀ is the original length of the wire (500.0 mm). From the data given, we can calculate the extensions as follows: For 0 N: x = (500.0 - 500.0) = 0 mm For 5 N: x = (500.0 - 500.0) = 0 mm For 10 N: x = (501.0 - 500.0) = 1.0 mm Using Hooke's Law, we can find the spring constant k for the wire: k = F/x = 10 N / 1.0 mm = 10 N/mm Now we can use Hooke's Law again to find the extension x for a force of 30 N: 30 N = 10 N/mm * x x = 3.0 mm Finally, we can find the length L of the wire when a force of 30 N is applied: L = L₀ + x = 500.0 mm + 3.0 mm = 503.0 mm Therefore, the length of the wire when a force of 30N is applied is 503.0 mm. Answer is the correct answer.