Question

The force required to streach a hooke's-law spring varies from 0 n to 33.7 n as we stretch the spring by moving one end 18.5 cm from its unstressed position.

Find the force constant of the spring.

Answer 1

To find the spring constant 'k' for a spring obeying Hooke's law, divide the force (33.7 N) by the displacement (0.185 m) to achieve k = 182.16 N/m.

Step-by-step explanation:

The force required to stretch a Hooke's law spring varies with the displacement of the spring from its equilibrium position, which can be formulated as F = kx, where F is the force applied, k is the spring constant, and x is the displacement of the spring from its equilibrium position.

Given that the force varies from 0 N to 33.7 N as the spring is stretched by 18.5 cm (which is 0.185 m), the spring constant can be calculated using the equation for Hooke's law. Rearranging the formula to solve for k, we get k = F / x. Substituting the maximum force and displacement into the equation, we have k = 33.7 N / 0.185 m, which gives us the spring constant k.

Therefore, the correct option answer for the force constant of the spring is k = 182.16 N/m (rounded to two decimal places).