Register to reply

Projectile motion with air resistance

by guysensei1
Tags: motion, projectile, resistance
Share this thread:
guysensei1
#1
Sep9-13, 07:05 AM
P: 22
Without air resistance, bodies travel in a parabola.

What is the curve that is travelled when air resistance is included?

I found that there are different air resistances, which curves would these types produce?
Phys.Org News Partner Physics news on Phys.org
Physicists unlock nature of high-temperature superconductivity
Serial time-encoded amplified microscopy for ultrafast imaging based on multi-wavelength laser
Measuring the smallest magnets: Physicists measured magnetic interactions between single electrons
mfb
#2
Sep9-13, 09:28 AM
Mentor
P: 11,589
With air resistance, you don't get a nice curve (such as a simple parabola). I don't think there is a special name for all those types of curves you can get.
arildno
#3
Sep9-13, 09:40 AM
Sci Advisor
HW Helper
PF Gold
P: 12,016
Quote Quote by mfb View Post
With air resistance, you don't get a nice curve (such as a simple parabola). I don't think there is a special name for all those types of curves you can get.
For air resistance proportional to the velocity, you may derive analytical expressions for the curve, that typically(if I remember correctly) involves the hyperbolic functions and their inverses.

cjl
#4
Sep9-13, 11:53 AM
P: 1,008
Projectile motion with air resistance

Quote Quote by arildno View Post
For air resistance proportional to the velocity, you may derive analytical expressions for the curve, that typically(if I remember correctly) involves the hyperbolic functions and their inverses.
Unfortunately, for the vast majority of cases, this is not a physically realistic solution, since air resistance is proportional to the square of the velocity (and there is no nice, analytical solution for that).
arildno
#5
Sep9-13, 12:01 PM
Sci Advisor
HW Helper
PF Gold
P: 12,016
Quote Quote by cjl View Post
Unfortunately, for the vast majority of cases, this is not a physically realistic solution, since air resistance is proportional to the square of the velocity (and there is no nice, analytical solution for that).
Your point being?
cjl
#6
Sep9-13, 12:18 PM
P: 1,008
Quote Quote by arildno View Post
Your point being?
My point being that if you care about physical reality, rather than mathematical prettiness, the existence of a solution for drag proportional to velocity isn't terribly useful or relevant.
arildno
#7
Sep9-13, 01:17 PM
Sci Advisor
HW Helper
PF Gold
P: 12,016
Quote Quote by cjl View Post
My point being that if you care about physical reality, rather than mathematical prettiness, the existence of a solution for drag proportional to velocity isn't terribly useful or relevant.
Any relevance to my first post?
mfb
#8
Sep9-13, 03:44 PM
Mentor
P: 11,589
Some objects (mainly small objects) can have laminar flow where drag grows linear with the velocity.
Unfortunately, their typical timescale is so short that you cannot really call their motion "falling".
voko
#9
Sep9-13, 03:49 PM
Thanks
P: 5,677
Quote Quote by guysensei1 View Post
Without air resistance, bodies travel in a parabola.

What is the curve that is travelled when air resistance is included?

I found that there are different air resistances, which curves would these types produce?
This question is not well posed. When there is air resistance, there is also lift. Both depend on the shape and the mass distribution of the body, and its orientation and rotation. These effects can be very significant, in which you can certainly convince yourself by comparing the flight of a glider and a ball.
cjl
#10
Sep9-13, 05:00 PM
P: 1,008
Quote Quote by mfb View Post
Some objects (mainly small objects) can have laminar flow where drag grows linear with the velocity.
Unfortunately, their typical timescale is so short that you cannot really call their motion "falling".
It's not so much that the flow is laminar, it's that the flow (for very low reynolds numbers) is dominated by viscous, rather than inertial forces. Laminar (but inertially-dominated) flow still has drag that scales as v2. As you noted, in air, the only time you would have viscous-dominated flow is for very small, slow moving objects. There are however some physical cases where this could occur at larger scales. In a fairly viscous fluid (corn syrup, for example), a BB, marble, or even golf-ball sized object could have drag that scales with v rather than v2. Most of the time, though, when people ask about drag, they aren't thinking of a marble falling through corn syrup
Khashishi
#11
Sep9-13, 05:24 PM
P: 886
Short answer: there is no simple closed form except in very extraordinary circumstances.
arildno
#12
Sep9-13, 05:33 PM
Sci Advisor
HW Helper
PF Gold
P: 12,016
Quote Quote by mfb View Post
Some objects (mainly small objects) can have laminar flow where drag grows linear with the velocity.
Unfortunately, their typical timescale is so short that you cannot really call their motion "falling".
Quite so.

And?

It doesn't follow from this that what I wrote in my post was wrong. I pointed out that there were cases with air resistance in which analytical expressions could be found, I did not say that that was generally true.


Register to reply

Related Discussions
Projectile Motion and Air resistance Introductory Physics Homework 15
Projectile Motion with Air Resistance Classical Physics 8
Projectile motion and air resistance Introductory Physics Homework 0
Projectile motion with air resistance Introductory Physics Homework 7
Projectile motion with air resistance Introductory Physics Homework 4