# Does a terminal velocity exist?

1. Aug 11, 2014

### Sagar98

Does a terminal velocity exist? Like when a free falling body is under the influence of gravity, does it stop accelerating after a certain velocity? If yes.. What's that velocity?

2. Aug 11, 2014

### Matterwave

A terminal velocity exists which depends on the aerodynamic properties of the object itself. The basic gist is that gravity is a constant force, while the aerodynamic drag depends on velocity (for simple approximations, a linear $v$ dependence is used, e.g. in introductory physics, for more complicated objects, obviously more complicated dependencies arise, starting first with a $v^2$ dependence). As the object speeds up, eventually, if it is falling from a high enough place, it should be moving so fast that the aerodynamic drag equals the force of gravity, and it should stop accelerating.

What this number is depends very much on the object itself. In this case, the mass of the object matters because the force of gravity is dependent on its mass, while the aerodynamic drag is dependent on the way it contacts the air (it's surface area properties). This is why a feather will, in the presence of an atmosphere, fall much slower than a bowling ball.

See here for a more detailed discussion: http://en.wikipedia.org/wiki/Terminal_velocity

3. Aug 11, 2014

### Staff: Mentor

In a vacuum, a falling body will continue to accelerate and gain speed until it hits the surface.

However, if the object is falling through air, there will be air resistance - and the greater thevspeed of the falling object, the greater the air resistance. Thus, an object falling in air will gain speed until the force of air resistance matches force of gravity, and then it will stay at that speed.

That speed where air resistance matches gravity is the terminal velocity.

4. Aug 11, 2014

### Sagar98

Thanks, But is there any specific value for that velocity that once attained, the body stops acceleration?

5. Aug 11, 2014

### jbriggs444

As Matterweave has pointed out, it depends. The terminal velocity for a feather is less than that for a bowling ball.

6. Aug 11, 2014

### SteamKing

Staff Emeritus
Yes, but it depends on the aerodynamic characteristics of the body. The terminal velocity of a brick, for example, will be different than for an object with a more streamlined shape, like a bird.

The NASA website has a page which discusses terminal velocity:

http://www.grc.nasa.gov/WWW/K-12/airplane/termv.html

7. Aug 11, 2014

### Sagar98

See, a feather, or a piece of paper etc. Are exceptions, due to high aur resistance acting on then and low weight. I'm talking about say a 10kg iron ball the size of a soccer ball gets dropped. *suppose* from the stratosphere.. Which is I'm not wrong is 50km from the surface of the earth. So it attains certain velocity after getting accelerated under free fall due to g . I'm asking what is the limit to this velocity. The boundary limit in numbers.

8. Aug 11, 2014

### Sagar98

Air*

9. Aug 11, 2014

### Staff: Mentor

No. It depends on the shape and the weight of the object. Skydivers know that the terminal velocity is much higher in a head-first vertical dive than if you're lying flat with arms and legs outspread.

10. Aug 11, 2014

### Sagar98

@streamKing, Thanks, That makes sense. I got it. Thanks a lot.

11. Aug 11, 2014

### sophiecentaur

A mouse would not die, if dropped from the Empire State Building. it is so light and its area is big enough to make its terminal velocity the same as being dropped from just a few metres.

12. Aug 11, 2014

### SteamKing

Staff Emeritus
It's SteamKing (no 'r'), but you're welcome.