Question

The force required to stretch a Hooke’s-law spring varies from 0 N to 70.7 N as we stretch the spring by moving one end 6.52 cm from its unstressed position. Find the force constant of the spring. Answer in units of N/m.

Answer 1

The force constant of the Hooke's-law spring is calculated using the formula k = F / x, which yields an approximate value of 1084.04 N/m.

Step-by-step explanation:

To find the force constant of a Hooke's-law spring with a force range from 0 N to 70.7 N over a stretch of 6.52 cm from its unstressed position, we use Hooke's law, which states F = kx, where F is the force applied, k is the spring constant, and x is the displacement from the equilibrium position.

Rearrange this to k = F / x to find the spring constant. Substitute the given values: k = 70.7 N / 0.0652 m (we convert 6.52 cm to meters by dividing by 100).

Therefore, the spring constant k is approximately 1084.04 N/m.