so the question is:

I whirl a mass m attached to a wire with length L and diameter d around my head in the horizontal plane. The mass takes t seconds to move around a circle. How far do the atoms in the wire move apart, compared to their spacing at rest? Young's modulus is given as Y.

I know the value of Young's Modulus(Y).

So: Y = Stress/Strain

For me to find the Strain I need to find the Stress first, which requires force(F) Stress = Force/A , A = cross-sectional area = pi*(d/2)^2

=> Y = (F/A)/strain = (F/(pi*(d/2)^2))/strain

So, to find the strain, I need to find the Force and from the answer I can find how far the atoms move.

My question is how to I go about to find the force?


  • 1
    $\begingroup$ Please try to use math formatting for better readability. $\endgroup$ – ja72 Aug 1 '14 at 19:10
  • $\begingroup$ The force you are looking for is the cetripetal force. It is the force your wire needs to excert on the mass in order to keep it on its circular path. $\endgroup$ – Neuneck Sep 2 '14 at 10:05

What you're looking for here is the equilibrium case when the wire has stretched out and has a constant length as you're swinging it. When the wire has a constant length each little piece of it with mass $m$ is executing circular motion with a radius $r$, and the force required to keep that piece of the wire moving in a circle is simply the centripetal force $mv^2/r$ or $m \omega^2 r$.

  • $\begingroup$ It seems that I'm on the right track. I took x as the angle between the tension and the horizontal motion plane and resolved. I got -Tcos x = m(-v^2/r) and Tsin x = mg. However, how will I find v? $\endgroup$ – Sab ಠ_ಠ Mar 31 '14 at 4:00
  • $\begingroup$ You have the period of the motion, so it should be easy to find the angular velocity. $\endgroup$ – Jordan Mar 31 '14 at 4:03
  • $\begingroup$ But still, r is not given. $\endgroup$ – Sab ಠ_ಠ Mar 31 '14 at 4:07

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