# How does inertia affect an object suspended in a fluid?

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.

• very intriguing question , slight correction: buoyant force does change as density of fluid increases with depth Commented Mar 11, 2023 at 15:11
• Please, add a video supporting your question. If a rigid body moves in a fluid, it experiences as forces only its weight and the contribution of surface stress: this latter contribution reduces to "buoyant force" due to pressure only in static conditions, while it includes viscous stresses if it moves. If you're doing an experiment with a body immersed in a constant density fluid, there would be no restoring force (as the one described in an answer below), but only a "drag force" reducing the acceleration to zero, implying constant sinking speed Commented Mar 11, 2023 at 18:57

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.

• I was surprised that nobody else has mentioned friction which is key here. a carefully inserted egg of the same density as the surrounding fluid would come to rest in spite of inertia. Commented Mar 13, 2023 at 16:56

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.

• Liquids aren't anywhere near compressible enough for this to be correct. Commented Mar 11, 2023 at 23:39
• Increasing pressure by 1 atmosphere decreases the volume of water by about 46 parts per million. It takes about 10 meters of water depth to increase pressure by 1 atmosphere. Going down 10 cm would only increase density by about 0.46 parts per million, an utterly negligible effect far too small to measure with an egg in a glass of water. It would be completely swamped by other effects. Commented Mar 12, 2023 at 0:35
• In any practical situation, the object will stop rising or sinking because it hits the surface or the bottom long before the compressibility of the liquid has any significant effect. Even at the bottom of the Mariana trench, 11 km deep, the water density is only about 5% greater than at the surface. (In the egg experiment, the egg stops sinking because it hits a carefully-prepared layer of salt water, and the buoyancy changes because of the salinity, not because the water is significantly compressed.) Commented Mar 12, 2023 at 7:08
• And at the kinds of extreme depths where you would actually have to consider the compressibility of the fluid, you would also have to consider the compressibility of the object. It may even be more compressible than the surrounding fluid, causing the buoyant force to actually decrease instead of increasing as the object sinks. Commented Mar 12, 2023 at 7:13
• Thank you for your comments. The question I address is why Newton’s second law doesn’t send a weight upward or downward in a fluid without limit. I added a note about layer stratification to address that particular case. Commented Mar 12, 2023 at 20:21

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.

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.

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.