Q#2 (Past Exam Paper – June 2016 Paper 11 Q20)
A number of identical springs are joined in four arrangements.
Which arrangement has the same spring constant as a single spring?
Solution:
Answer: C.
Answer: C.
Let the spring constant of a single spring = k
When 2 springs are joined end-to-end (in series),
Effective spring constant = (1/k + 1/k)-1 = k/2 [Choice A]
When 2 springs are joined side-by-side (in parallel),
Effective spring constant = k + k = 2k [Choice B]
Choice C may be considered to be as if the arrangement in B is in series with another similar one [or equivalently, the arrangement in A is in parallel with another similar one].
Considering the former case,
Effective spring constant = k/2 + k/2 = k
This has the same spring constant as a single spring.
Considering the latter case,
Effective spring constant = (1/2k + 1/2k)-1 = 2k/2 = k
Again, it has the same spring constant as a single spring.
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