Answer: Half of a Spring. (a) Suppose you cut a massless

Chapter 6, Problem 44E

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QUESTION:

Half of a Spring. 

(a) Suppose you cut a massless ideal spring in half. If the full spring had a force constant k, what is the force constant of each half, in terms of k? (Hint: Think of the original spring as two equal halves, each producing the same force as the entire spring. Do you see why the forces must be equal?)

(b) If you cut the spring into three equal segments instead, what is the force constant of each one, in terms of k?

Questions & Answers

QUESTION:

Half of a Spring. 

(a) Suppose you cut a massless ideal spring in half. If the full spring had a force constant k, what is the force constant of each half, in terms of k? (Hint: Think of the original spring as two equal halves, each producing the same force as the entire spring. Do you see why the forces must be equal?)

(b) If you cut the spring into three equal segments instead, what is the force constant of each one, in terms of k?

ANSWER:

Solution 44E

Step 1:

The spring constant is an inherent property of a spring.

Constant by meaning itself is an invariant.

But when you cut a spring into several parts, it is not the same spring any more. As, the mass of the spring also gets changed regardless of the invariance of mass.

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