# How Does Liquid Density and Viscosity Influence Free Fall Braking?

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• Arbegator
Arbegator
TL;DR Summary
If two objects with big diffrence in density but the same size travel through a liquid closer to the density of one of the objects, does it slow down the free fall?
In mine hypothesis I want to slow down free fall for diffrent density objects in liqudies. I have a stone wich i roughly a denisty of 2,7 g/ml and gold with 19,7 g/ml. They have the same size. Liquied glucose has the density of roughly 1,5 g/ml. In my example, I drop at the same time in a 1 meter pipe with glucose. How does the density affect the buoyancy with free fall? Does Viscosity matter in this case? Will gold fall faster?
Thank you for your help with trying to sort this out.

Welcome to PF.

It certainly seems like it will have some effect. Can you post links to the reading you have been doing so far on this question?

Also, is this question for schoolwork? Thanks.

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Arbegator said:
How does the density affect the buoyancy with free fall? Does Viscosity matter in this case?
Density is important because the driving force is due to the weight, less the buoyancy of the object in the fluid.

Viscosity is critical in that it is part of the drag equation. Terminal velocity is reached when the falling body drag balances the driving force.
https://en.wikipedia.org/wiki/Drag_(physics)#Very_low_Reynolds_numbers:_Stokes'_drag

russ_watters

## 1. How does the density of a liquid affect the deceleration of an object in free fall?

The density of a liquid directly affects the deceleration of an object in free fall because a denser liquid provides more resistance or drag force against the object. This increased resistance slows down the object's velocity more quickly upon impact, resulting in a greater deceleration.

## 2. Is there a mathematical relationship between the density of a liquid and the braking force experienced by a falling object?

Yes, the braking force experienced by a falling object in a liquid is often modeled using fluid dynamics principles. The drag force can be calculated using the drag equation: F_d = 0.5 * C_d * ρ * A * v^2, where F_d is the drag force, C_d is the drag coefficient, ρ is the density of the liquid, A is the cross-sectional area of the object, and v is the velocity of the object. This equation shows that the drag force increases with the density of the liquid.

## 3. Does the shape of the object affect how density influences its braking in a liquid?

Yes, the shape of the object affects how density influences its braking in a liquid. Different shapes experience different drag coefficients (C_d), which impact the overall drag force. Streamlined shapes experience less drag, whereas blunt or irregular shapes experience more drag. The effect of the liquid's density on braking will be more pronounced for shapes with higher drag coefficients.

## 4. How does the terminal velocity of an object in a liquid vary with the liquid's density?

The terminal velocity of an object in a liquid decreases as the liquid's density increases. Terminal velocity is reached when the drag force equals the gravitational force on the object, resulting in zero net acceleration. In a denser liquid, the drag force is higher, so the object reaches terminal velocity at a lower speed.

## 5. Can the density of a liquid completely stop an object in free fall upon impact?

While a very dense liquid can significantly slow down an object in free fall, it typically cannot completely stop it instantaneously upon impact. The object will decelerate rapidly, but it will still penetrate the liquid to some extent before coming to a stop, depending on the object's initial velocity, shape, and the liquid's viscosity in addition to its density.