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2 \times 3
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Comments
That's easy.if the bock goes a distance x then the the change in the total length is 3x.(2x for the string+x for the spring)so the total is 3x.ad there are 2 forces.the spring force +the rod(the one that connects the pulley to block)so the net force is 3T as the tension=force of spring.so the net force on block is 33xk=9kx.and since we displace by x the effective is 9kx/x =9k
In you can think in 2 ways.I)consider the leftmost pulley.I guess its ideal then we can safely consider that the net torque cting on it is zero.which means you are left with fr-Tr=0 implying T=f.or you my thing it as tension will be constant throughout because if we consider the fbd of a small element the net force is zero(as its massless)which means I can extend the same throughout.
hey , sorry please don't bother about options, yes it is asking about some extension,but I think I will be able to solve it myself.But I am not able to understand how is the whole pulley system being replaced by a spring of force constant 9K.
Easy Math Editor
This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.
When posting on Brilliant:
*italics*
or_italics_
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or__bold__
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[example link](https://brilliant.org)
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\(
...\)
or\[
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to ensure proper formatting.2 \times 3
2^{34}
a_{i-1}
\frac{2}{3}
\sqrt{2}
\sum_{i=1}^3
\sin \theta
\boxed{123}
Comments
That's easy.if the bock goes a distance x then the the change in the total length is 3x.(2x for the string+x for the spring)so the total is 3x.ad there are 2 forces.the spring force +the rod(the one that connects the pulley to block)so the net force is 3T as the tension=force of spring.so the net force on block is 33xk=9kx.and since we displace by x the effective is 9kx/x =9k
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but why should the tension be equal to spring force?
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In you can think in 2 ways.I)consider the leftmost pulley.I guess its ideal then we can safely consider that the net torque cting on it is zero.which means you are left with fr-Tr=0 implying T=f.or you my thing it as tension will be constant throughout because if we consider the fbd of a small element the net force is zero(as its massless)which means I can extend the same throughout.
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@Spandan Senapati
What to find.I am not able to get the com question
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equivalent spring constant. the answer is given as 9K.
Hey the first 2 options dimensions looks like they are asking for some extensions etc.why don't you repost it with a complete question
hey , sorry please don't bother about options, yes it is asking about some extension,but I think I will be able to solve it myself.But I am not able to understand how is the whole pulley system being replaced by a spring of force constant 9K.