Hooke's Law

## Question:

Thank you Mr. Jones,

I just went on about my solution and reached the ratios. I also tried your solution and figured out that your solution was shorter and more efficient. Thank you very much.

I had a couple more questions regarding Spring Constant (Hooke's Law): 1) I was given force and extension of a spring. I have to calculate spring constant which i did using F=k*x. The next question was "Explain the meaning of Spring Constant and Its uses?" meaning part is all right but I couldn't get the uses other than it is used in the calculation of the potential energy stored in the spring using :

E=0.5 * k * x2

Can you help me with the other uses?

2) What factors would affect the spring constant of a rubber band?

Thank you once again Mr. Jones

The F=k*x expression you used to calculate the spring constant leads to other uses of the spring constant. Once k is known, we may use the displacement of the spring to determine the force applied to it. Then the spring constant becomes useful as a force measurement. As such, springs are used to measure the weight of objects in common household scales.

Also in a micro-gravity environment, as aboard the space shuttle, a spring can determine the mass of an object through the relationship of the spring constant to the period of an oscillation, where period=two times pi times square root of the ratio of mass to spring constant.

In an inertial navigation system such as used on submarines, where reference to external objects is difficult, the spring constant may be used to determine the ship's acceleration. The spring constant measures the force of acceleration on a known mass and through Newton's second law that force is converted to the ship's acceleration. The acceleration may then be integrated over time to give the velocity and the velocity integrated over time to give the change in position from the last known fix.

Regarding a rubber band, the spring constant will depend on the nature of the rubber, some varieties are stiffer than others. It will also depend on the thickness of the band. Thicker bands will tend to have higher spring constants. Also the length of the band will have an effect. For a given thickness, the longer the band, the less force it will produce for a given displacement. This is because there are a greater number of inter-molecular bonds to participate in the stretching so each bond suffers less strain. Rubber is sensitive to temperature changes so its spring constant will change with temperature, probably increasing as temperature decreases up to a point where it becomes inelastic at very low temperatures.

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