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Help With Understanding Hooke's Law
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[QUOTE="RPinPA, post: 6072130, member: 651116"] That is exactly correct. ##F = kx## says that applied force is proportional to the amount of stretch. ##k## is the constant of proportionality. For your example, ##k = (5 \text { N}) / (0.030 \text{ mm}) = 167 \text{ N/m}##. Every N of applied force will stretch it by 1/167 of a meter or 6 mm. But ##k## is a property of this particular spring. Make it out of a different material, or use a thicker wire or a thinner one, or a longer or shorter piece of the same wire, and you'll have different a ##k##. That's correct, force is proportional to the change in length. I thought you were asking how you go from force being proportional to ##(x/L)## to force being proportional to ##x## and my answer is that if it's proportional to ##x## times a constant ##(1/L)##, it's proportional to ##x##. Force can't be equal to change in length anyway, since they have different units. There HAS to be a proportionality constant. I didn't add R. You did. You implied there's a constant. I'm just giving a name to the proportionality constant in your original statement: Stress is proportional to strain. That means stress equals a constant times strain. When you have a proportion, you have a proportionality constant. I gave that constant the name ##R## but in fact I think it's the thing called Young's Modulus and there's some different symbol which is standard. Every material will have a different Young's Modulus. Rubber is stretchier than steel, and steel is probably stretchier than wood. I didn't "change proportional to equal". Saying "a is proportional to b" and saying "a equals some constant times b" are equivalent statements. "a equals some constant times b" is the same as saying "a/b is always the same number" which is the same as saying "a is proportional to b". You seem to understand the concept of "proportional" just fine, but feel free to ask more questions. Physics is full of these kinds of proportions, and when we have a proportion, that requires a proportionality constant, which we often give a name. For instance, Newton figured out that gravitational force between two masses ##m_1## and ##m_2## at distance ##r## was proportional to ##m_1 m_2 / r^2##. He didn't say it's equal, he said it's proportional. So we multiply that thing by a proportionality constant, which we call G, which is a property of the universe and which depends on what units we're using. ##F = G * (m_1 m_2 / r^2)##. He just knew it was proportional, he didn't know what G was. That had to be measured, much later. Physics is full of these kinds of constants that have to be measured, many of them depending on the type of material and tabulated, and the vast majority of them are just names given to a proportionality constant in some proportion. It's a lot more common to have a proportion than to have an equality. [/QUOTE]
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