Question

A turtle is hanging from a spring which is attached to the ceiling. The turtle has a mass of 25 kg. This causes the spring to stretch a distance of 0.52 meters. What is the value of the spring’s spring constant k?

Answer 1

To calculate the spring constant k, apply Hooke's Law using the formula F = k * x. The turtle's weight provides the force, and dividing this by the spring's stretch distance x yields the spring constant k.

Step-by-step explanation:

To calculate the spring constant k for the spring from which a turtle is hanging, we can use Hooke's Law. Hooke's Law states that the force F needed to extend or compress a spring by some distance x is proportional to that distance. It's represented by the formula F = k * x. In this scenario, the force exerted by the turtle due to gravity (its weight) is the force stretching the spring, which can be calculated by multiplying the turtle's mass m by acceleration due to gravity g (approximately 9.81 m/s2).

So, weight F = m * g = 25 kg * 9.81 m/s2. The distance that the spring stretches, x, is given as 0.52 meters. To find the spring constant k, we rearrange the formula to k = F / x. After calculating the weight F, we can divide it by x to get the value of k.