# Calculate velocity of an oobject falling trhough a medium

• SFB
In summary, to calculate for the velocity of a falling object through any medium at any given time, you need to consider the forces of buoyancy and viscous drag. Using Newton's law and taking into account the different forces and their directions, you can derive an equation for acceleration and integrate it to get an equation for velocity. If the drag force is velocity dependent, the object will eventually reach a terminal velocity.
SFB
How do I calculate for velocity of a falling object through any medium at any given time if I have to consider both buoyancy and viscous drag.

If I consider Newtons law , I assume that it would be something like

m(dv/dt)=Fnet =mg-Drag-Buoyant force

Am I supposed to get a dimensionless quantity while doing dimensional analysis for such a problem.Whats the name of that number.

Thanks

Since you are looking for a velocity, you wouldn't end with a dimensionless number. It would need to be in meters/second (or whatever distance/time measure you are using).

To do problems like this, consider all the different forces and the directions they are acting in. Then, use the sum of the forces equals mass*acceleration to get acceleration, and from there you can derive velocity.

For your problem, gravity is the only force acting to pull the object downward. Both viscous drag and buoyancy are acting upward, against gravity. So, your equation is correct (assuming down as the positive direction).

ma = Fg - Fd - Fb

Fg = force of gravity = mg
Fd = viscous drag force
Fb = buoyant force

From that, solve for acceleration (a) and integrate to get an equation for velocity.

a = (Fg - Fd - Fb)/m
v = [(Fg - Fd - Fb)/m]*t + Vo

where t = time and Vo = initial velocity.

Hope that helps!

If the drag force Fd is velocity dependent (Stokes or turbulent drag), the falling velocity will reach a terminal velocity. See

http://en.wikipedia.org/wiki/Drag_(physics )

Bob S

Last edited by a moderator:

## 1. What is the formula for calculating velocity of an object falling through a medium?

The formula for calculating velocity of an object falling through a medium is V = gt, where V is the velocity in meters per second (m/s), g is the acceleration due to gravity (9.8 m/s²), and t is the time in seconds.

## 2. Why is it important to calculate the velocity of an object falling through a medium?

Calculating the velocity of an object falling through a medium is important in understanding the motion of the object and predicting its behavior. It can also be used to determine the impact force of the object when it hits the ground or another surface.

## 3. How does the density of the medium affect the velocity of an object falling through it?

The density of the medium affects the velocity of an object falling through it by increasing the resistance and slowing down the object's acceleration. This means that the velocity will be lower in denser mediums, such as water, compared to less dense mediums, like air.

## 4. Can the velocity of an object falling through a medium change during its descent?

Yes, the velocity of an object falling through a medium can change during its descent. This can happen if the object encounters changes in the medium's density or if external forces, such as air resistance, act upon the object.

## 5. How accurate are calculations of velocity for objects falling through a medium?

The accuracy of calculations for velocity of objects falling through a medium depends on various factors, such as the precision of the measurements and the assumptions made in the calculation. Generally, the more accurate the measurements and the fewer assumptions, the more accurate the calculation will be.

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