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Is it possible to determine the spring constant of a spring in a situation in which it is being compressed when such certain length of compression is not known? If so, how can such calculation be determined? Values that are known include mass, velocity, total distance the object moves down a ramp, weight. Will the integral of force/potential energy be needed?

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"Values that are known include mass, velocity, total distance the object moves down a ramp, weight. " Do you also know the initial location of the spring? Can you deduce the compressed length from there? –  dmckee Mar 7 '13 at 18:55

1 Answer 1

The spring constant, $k$, is simply defined as:

$$ k = \frac{dF}{dl} $$

where $dF$ is the change in the force when you compress the spring by an infinitesimal distance $dl$. So you don't need to know the free length of the spring i.e. you don't need to know how much it has been compressed in total. All you need to do is compress or expand it a small amount and measure the change in force.

However if you're just presented with a compressed spring and you don't know how much it has been compressed or stretched and you're not allowed to compress or expand it even a small amount then you cannot measure the spring constant.

In principle you could calculate the spring constant from it's geometry and the elastic properties of the material it's made from. However in practice you'll struggle to get an accurate answer.

I get the impression there is more to this question because you mention things like total distance the object moves down a ramp. You might want to update your question with a bit more detail.

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