# An experiment from which you can calculate terminal velocity

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1. Nov 22, 2015

### Zara-!@#$* "Describe an experiment that could be carried out in order to measure the terminal velocity of an object falling under gravity. Include any equations you would use or calculations you would make." The only formula I can think of is F=ma, but I don't see how that is relevent. My train of thought is currently that velocity is d/t. Therefore, I'd have thought that I would need to know the distance from which terminal velocity starts to when it hits the floor, and also the time spent in terminal velocity. But in order to find this I'd need to know how long it takes for drag to be in equilibrium with the weight, how long the object is falling, the distance from rest to the floor, the distance traveled before reaching terminal velocity and the weight. I have been ill for a while and missed the lesson on terminal velocity. Yes, I did it at GCSE, but I never had to calculate terminal velocity so I'm at a complete loss. 2. Nov 22, 2015 ### Heliosphan Terminal Velocity equation is sqrt( 2mg/density*Area of object * drag coefficient) Basically the idea is that this is the fastest possible velocity that an object can obtain through freefall. And when it's at it's fastest point The downward force of gravity (9.8 m/s^2) == the drag on an object, so it maintains a constant speed. There's a lot of variables that can change the drag on an object through. And you can see how the equation is derived on wikipedia. That's pretty much what I know about air drag. 3. Nov 24, 2015 ### Zara-!@#$*

I've looked into that equation before, but to find the drag coefficient, I'll need the velocity and I don't know how to find that.

4. Nov 24, 2015

### andrevdh

I would think that you would need to measure the speed of the falling object while it is in flight.
The speed normally increases without limit under the influence of gravity, but due to drag it will
only increase up to a point, at which stage it falls with a constant speed - its terminal velocity.
The drag on a falling object increases as the speed of the object increases, that is the drag force
is a function of the speed of the object and it increases as the speed of the falling object increases.
This means at some speeed the drag force will reach the same magnitude as the objects weight.
At this point the net force on the object is zero and it falls at a constant speed - the terminal velocity.
One detector that measures the objects speed is a sonic ranger. It bounces packets of sound off
the object and measures the duration for the sound packets to return to the detector. From these
periods and the known speed of sound in air (or via a calibration procedure) it can then calculate the
speed at which the object is moving.

5. Nov 24, 2015

### CWatters

One of the issues you need to address with your experiment is how to be sure that the velocity you measure is the terminal velocity. So describe how you would check that.

6. Nov 24, 2015

### Heliosphan

Well if we're on Earth, the gravitation acceleration is 9.8 m/s^2. However at terminal velocity the force of drag and the gravitational downward force equal out giving zero acceleration and a constant velocity. And here's a hint about the weight of the object, what's the weight of an object that's in free-fall.

7. Nov 24, 2015

### Staff: Mentor

If you have the form of the equation for the velocity as a function of time then you should be able to take several measurements along the trajectory (which aren't necessarily at terminal velocity) and fit such a curve to the data. From the fitted curve you should be able to extract the actual drag and predict the terminal velocity.