Question

A block of wood floats in a bucket of water placed in a lift. Will the block sink more or less if the lift starts accelerating up?

Answer 1

If the lift starts accelerating up, the Block will neither sink more nor less.

Normally, under floating condition, Force equation is given by,

• Upthrust = Weight
• Vidlg = Vdsg

then the fraction of volume of the block, immersed in water is given by,

• Fraction , F = Vi/V = ds/dl,

Where ds = density of the block

dl = density of the liquid.

When the lift is accelerating up with an acceleration a,

Then, We have the following forces on the block

• upthrust in the upward direction,
• Weight of the block downwards
• Acceleration of lift upwards.

Let Vi be the volume of block immersed

V be the total volume of the block.

Therefore,

• Net force = upthrust  - weight
• Ma = dlVi(g + a) - dsVg = dsVa
• We know fraction of volume immersed = Vi/V
• dlVi(g + a) = dsV(g + a)
• Vi/V = ds/dl = F

• Therefore fraction of volume immersed is same when the lift is at rest as well as when it is accelerating.

• Therefore there is no change in the volume immersed.
• Therefore the block neither sinks more nor less.