Question

Hooke's law describes a certain light spring of unstretched length 33.6 cm. when one end is attached to the top of a doorframe and a 6.89 kg object is hung from the other end, the length of the spring is 43.2 cm.

Answer 1

Hooke's law, represented as F = -kx, describes the linear relationship between the displacement of a spring and the restoring force exerted by it, with k being the force constant.

Step-by-step explanation:

Hooke's law states that the force (F) needed to extend or compress a spring by some distance (x) scales linearly with respect to that distance. That is, F = -kx, where F is the restoring force exerted by the material and k is the force constant of the system. The negative sign indicates that the direction of the restoring force is opposite to the direction of displacement.

When an object, such as a 6.89 kg mass, is hung from a spring, it stretches the spring, causing a displacement. The length of the spring increases from its unstretched length, and the force due to the object's weight causes this elongation. By measuring this extension (the difference between the stretched length and the unstretched length) and knowing the weight of the object, we can calculate the spring's force constant (k).

Answer 2

Missing question: "What is the spring's constant?"

Solution:
The object of mass m=6.89 kg exerts a force on the spring equal to its weight:

`F=mg=(6.89 kg)(9.81 m/s^2)=67.6 N`
When the object is attached to the spring, the displacement of the spring with respect to its equilibrium position is

`\Delta x=43.2 cm-33.6 cm=9.6 cm=0.096 m`
And by using Hook's law, we can find the constant of the spring:

`k= (F)/(\Delta x)= (67.6 N)/(0.096 m)=704.2 N/m`