How does inertia affect an object suspended in a fluid?

Question

When I asked my physics teacher how fully submerged objects are suspended in fluids, she told me it was because the object's density was equal to that of the fluid's as a result of the net force acting on the object being 0 which would then mean the acceleration of the object would be 0 as well.

But that explanation doesn't make sense to me. Wouldn't inertia cause the object to continue sinking downwards with constant velocity? Before, $mg > F_B$ which caused the object to accelerate downwards and in turn its velocity vector to be downwards as well.

As I understand it, when partially submerged objects float on the surface of a fluid sink further down due to inertia, the buoyant force acting on them increases and accelerates the object upwards. Then, gravity accelerates it downwards when not enough of it is submerged, eventually resulting in the object's final position in the fluid.

However, once an object is fully submerged, its buoyant force remains constant because the difference in pressure above and below it is the same. So what is it that's causing the object's velocity to slow to 0?

I have a feeling my understanding of inertia here is wrong so if anyone can clarify how inertia affects objects in a fluid or provide an explanation as to how this:

works, that would be very much appreciated.

Answer 1

If a submerged object is in hydrostatic equilibrium, that is the buoyancy force and the gravitational force on it exactly balance, it will stop moving because of friction with the fluid it is in. This friction, which is due to the viscosity of the fluid, does not behave in exactly the same way as friction between two solid objects, but it still has the effect of stopping an object from moving relative to the fluid.

Other answers have noted that there may be a gradient in the buoyancy force. This would determine the depth where buoyancy and gravity balance. Viscosity will ensure the object stops at this depth rather than continuing to oscillate around this depth.

Answer 2

You could ask the same question about an object hung from a mechanical spring: If the forces at the final equilibrium position sum to zero, why isn’t the object still moving, or why did it ever decelerate from its initial downward velocity?

And the answer is the same: Although the downward weight is constant, the upward force—sometimes termed the restoring force—increases with progressive downward movement. (In the buoyancy case, it’s because the density of the liquid increases with increasing depth, with the weight of the liquid above compressing it. Alternatively, stratification of layers with different compositions would lead to sudden density changes.) In fact, the behavior of a bobbing object in liquid can exactly be modeled as damped-spring oscillation.

Does this get at what you’re asking about?

Answer 3

The experiments of eggs floating in a glass of water normally involve adding salt, until it floats. If we add afterwards small amounts of water step by step, the floating egg starts to move down, progressively deeper as the solution gets more dilute.

The only explanation is that the linear relation $P = \mu gh$ for $\mu$ constant is no more valid. $\mu$ increases with $h$. For example, if $\mu$ is linear with $h$ the relation between $P$ and $h$ is quadratic. In this case it is clear that $\frac{dp}{dh}$ increases with $h$, and the upward force over the egg is bigger as $h$ grows.

The presence of salt is important because any fluctuation of salinity in the glass results that saltier portion of the solution sinks, because it is denser. So, the equilibrium is not an equally concentration of salt, but a gradient of concentration, bigger as $h$ grows. And the same for density because bigger salt concentration means a denser solution.

Answer 4

Experiments like these involve creating two separate layers: one dense, salty layer on the bottom, and one warm, fresh water layer on top, without giving them time to mix. For example, quoting instructions from the BeardedScienceGuy video just linked (no affiliation):

Step 1: Fill a tall vase halfway with room temperature water.

Step 2: Mix in enough salt to create a saturated solution. I used about ½ cup.

Step 3: Stir the saltwater solution until dissolved.

Step 4: Pour the saltwater solution into a tall vase, filling it about ½ way.

Step 5: Wait 1-2 hours until the salt water is no longer cloudy, and any excess salt collects at the bottom.

Step 6: Pour warm, freshwater carefully into the vase to fill it up. Be sure to use warm water. The goal is to keep the saltwater on the bottom and the fresh water on top.

Step 7: Drop an egg into the vase and observe.

The floating object is denser than the fresh water layer, but less dense than the salt water layer. It thus floats on the boundary between the two layers, at the point where it displaces the right balance of salt water and fresh water that the buoyant force matches its weight. This is similar to a boat floating on the boundary between ocean and air, but both layers are liquid in this experiment instead of one being air.

If the object sinks below the equilibrium point, it displaces more salt water and less fresh water, increasing the buoyant force and pushing it back up. If the object rises a bit, it displaces more fresh water and less salt water, decreasing the buoyant force, so it sinks back down.

If you mix the layers, there will be no boundary for the egg to float on. It will sink to the bottom or float to the surface, depending on how salty the resulting solution is.

Answer 5

Your understanding of inertia is in no way wrong.

Lets say you have an object suspended in water. Lets say that the increase of density in the fluid with depth is negligible:

There is no reason in particular why the object should not be buoyant at point A or B, as gravity and buoyancy balance each other in any of these points. The object would only stop because of the fluids viscosity.

Lets say the object was moving perpendicularly to the pull of gravity. Why would it stop? Neither buoyancy nor gravity contribute to stopping or accelerating the movement and there would need to be a third force (a non-conservative one) slowing the object down.

Answer 6

I haven't done physics since A-Level in 2017 so I'm a bit rusty but inertia as far as I'm aware is a constant force,but only in a perfect vacuum.

Basically in the real world air resistance and friction are a thing (though only got as far as questions and equations that don't account for friction (I loved seeing "ignore air resistance or friction)).

So think of friction as a pool of water. Resistance takes a little water out the pool until it's empty and inertia is zero. Because no force is being applied to it.

Now buoyancy will put the object in equilibrium until the net forces (including gravity) equal zero at rest after the force or inertia reduces. Think of throwing a tennis ball into a pool. At first it goes down into the water, then as the inertia is sucked away it stops and even has enough buoyancy to reverse direction and come out the water but the inertia is sucked away by gravity and friction so it falls back down where it's inertia is stopped by water surface tension or landing on the ground or someone catching it.

Hope I wasn't too far off am looking for ideas.

Answer 7

The answer is here: Bouyancy and pressure

The upwards force and pressure are greater at a greater depth.