Final answer:
The displacement of the rubber band is 0.0667 meters, or 6.67 centimeters, when a force of 12 N is applied and the spring constant is 180 N/m.
Step-by-step explanation:
To calculate the displacement of a rubber band given the force exerted and the spring constant, we use Hooke's Law, which states that the force (F) applied to a spring is directly proportional to the displacement (x) it causes. The spring constant (k) is the constant of proportionality. The formula derived from Hooke's Law is F = kx, where x is the displacement.
To solve for x, we rearrange this equation to get x = F/k. Given that the child exerts a force of 12 N and the spring constant is 180 N/m, we substitute these values into the formula to find the displacement:
x = 12 N / 180 N/m = 0.0667 m
This means the rubber band's displacement is 0.0667 meters, or 6.67 centimeters, when the child exerts a force of 12 N.