- #1
JC2000
- 186
- 16
- Homework Statement
- If a metal wire of length L, area of cross-section A and Young's modulus Y, behaves as a spring of spring constant k. Find the value of k.
- Relevant Equations
- Hooke's Law ##F= -kx## and Young's modulus, defined as ##Y = \frac {F*L}{x*A}##
Equating the two equations gives me ##k = -\frac {YA}{L}## but the correct answer of the same magnitude but opposite sign.
I think the nub of my misunderstanding is quite elementary (who would have guessed!) : When is it ##F=kx## and when is it ##F=-kx##? If I understand correctly, F is the restoring force or the 'stress' and x is the direction of displacement by the force which F opposes(?), thus with the origin at equilibrium (before any forces act), x and F would have opposing signs always?
What have I misunderstood here?
Thank you!
I think the nub of my misunderstanding is quite elementary (who would have guessed!) : When is it ##F=kx## and when is it ##F=-kx##? If I understand correctly, F is the restoring force or the 'stress' and x is the direction of displacement by the force which F opposes(?), thus with the origin at equilibrium (before any forces act), x and F would have opposing signs always?
What have I misunderstood here?
Thank you!
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