A plastic ball is pushed inside the tank and then released, can anyone plot velocity vs time and velocity vs height as long as ball is completely inside the water? For simplicity we can assume no viscous forces

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    – Solar Mike
    Jun 6 at 6:52

1 Answer 1


If we ignore viscous forces:

at the full immersion, the buoyancy is the weight of water the sphere of the ball has displaced.

$$F_{B}=V_{ball}*1000kg/m^3= \frac{4}{3}\pi R^3$$

And the ball will emerge with an acceleration of $\alpha= F/m$

As the ball partially emerges from the water there will be a growing cap of the ball standing above the water until the ball is fully ejected.

The cap volume is

$$V_{cap}=\frac{1}{3}\pi h^2(3R-h)$$

The buoyancy force, Fb is

$$F_{b}= F_{Bfull-Bcap}= \frac{4}{3}\pi R^3-\frac{1}{3}\pi h^2(3R-h)$$

  • m= mass of the ball
  • R= radius of the ball
  • h= height of the cap measured from the top of the ball to water level

I would slice the ball into say 20 sections and write an excel formula using the above EQ to calculate the force and speed at any given height, h.


cap volume


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