Answered

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How does the spring constant of the smaller springs relate to that of the original spring? Choose the correct explanation.
A) The spring constant of each half will be half the spring constant of the original long spring since it will stretch twice as much under the same tension
B) The spring constant of each half will be twice the spring constant of the original long spring since it will stretch twice as much under the same tension.
C) The spring constant of each half will be twice the spring constant of the original long spring since it will stretch only half as much under the same tension.
D) The spring constant of each half will be half the spring constant of the original long spring since it will stretch only half as much under the same tension.

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Answer:

C) The spring constant of each half will be twice the spring constant of the original long spring since it will stretch only half as much under the same tension.

Explanation:

Hooke's law states that the force needed to extend or compress a spring by a distance is proportional to that distance. If is given as:

F = ke, where F is the force applied, k is spring constant and e is the extension.

If a force f is applied to a spring with a spring constant k and by a distance stretched (x) then:

k = F / x

For half the spring, if the same force F is applied, the stretch would be half (x/2), hence the spring constant C is:

C = F / (x/2)

C = 2 (F / x) = 2 * spring constant of original spring

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