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SHM · Lecture 26 of 26

Floating body, U-tube liquid and a loaded wire: three SHMs

By Lalit, IIT Madras

Floating body, U-tube liquid and loaded wire, three SHMs for JEE: the extra buoyant force as −kx, and a rod or wire as a spring with k = YS/L.

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A chalkboard titled 'The same cube in a denser liquid' shows a cube of density ρ floating in a tank of liquid 3ρ with a/3 below the surface and 2a/3 above it, beside the rule that the largest amplitude equals the shorter length, under the surface or above it at rest, which gives a/3 for liquid 3ρ and a/2 for liquid 2ρ.

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What this lecture covers

Archimedes principle sets a floating cube's mean position. Pushed deeper by x, it is restored by the extra buoyant force, F = −2 rho a² g x, giving k effective and T. In a 3 rho liquid the cube floats higher, and its largest amplitude ends where F stops being −kx. A U-tube column is restored by a level difference of 2x. Last, a rod acts as a spring with k = YS/L, and a block hanging from it gets its top speed two ways.

In this lecture

  1. Play from The plan and Archimedes' principle
  2. Play from A floating cube: the mean position
  3. Play from Restoring force and k effective
  4. Play from T of the floating cube, unit check
  5. Play from The cube in a liquid of 3 rho
  6. Play from Largest amplitude of a floating cube
  7. Play from A liquid column in a U-tube
  8. Play from A rod as a spring: k = YS/L
  9. Play from A block hung on a rod, natural length
  10. Play from The top speed, also by energy