Free falling speed for object?

Question

I'd like to find out what equations are involved for calculating this (including calculating the air resistance) and if possible could you provide an example calculation. You can assume any surface area for the object in question but could we assume the density of air (starting at 10,000 feet).

Answer 1

The required input data for this ? is:
mass of object
shape of object
size of object
air density = f(altitude)

I assume we are talking about the terminal velocity, which will not actually be constant, but vary with altitude.

The shape and size will determine the drag coefficient, Cd. Cd for various shapes are found in aerodynamic texts. The aerodynamic drag formula is
D = Cd*(ρV²/2)*A where ρ is the density, V the velocity, and A is the reference area the Cd is based on.
The driving force for the motion is simply mg, the weight of the object. At terminal condition, D = mg, and the above eqn becomes

mg = Cd*(ρV²/2)*A --->V² = 2mg/(Cd*ρ*A)

To give you some numbers to play with, the Cd of a teardrop shaped object is in the neighborhood of 0.10 based on its cross sectional (┴ to direction of travel) area. Air density @ 10Kft = .001758 sl/ft³ and at sea level =.00238 sl/ft³. You can assign any mass and area you like to put in the eqn. Area is in ft² and mg is pounds. Velocity will be in feet /sec.

GOOD LUCK!

Answer 2

The acceleration for any falling object is 9.8 meters/second^2.
The force of air resistance for large objects is:
Fair=1/2DpA(v^2)
D=drag coefficient, p is density of air, and A is cross sectional surface area, and V is the velocity of the object

To determine the force on on abject by the earth, you would use F=ma
F=9.8m
m being the mass of the object

you would then draw a force diagram, with the upward component on the object being the force of air resistance, and the downward force being the force of gravity.

The difference of these two forces would vary, and a system of equations must be created.

----basically, it varies with each object. Given numbers it can be better calculated.

The density of the air also depends on the temperature.


random fact -- terminal velocity of a human is about 120 miles/hour

Answer 3

Acceleration due to gravity, g = GM/(R+h)^2 G = Universal gravitation constant =6.6742 x 10^(-11) N.m^2 / kg^2 M = Mass of earth = 5.98 x 10^24 kg R = Radius of earth = 6 371 km (average) h = Height of falling body g remains constant for a short distance Total acceleration reduces due to higher air friction resistance at higher speed and at certain speed, total acceleration will reduce to zero >> achieving constant speed If distance h in the above equation changes substantially, g will increase - not for speed but for reduced height above the earth surface

Answer 4

Doug is correct; however, assume normal gravitational force and a normalized density of air, you could use the fomulae given at http://www.ac.wwu.edu/~vawter/PhysicsNet/Topics/Kinematics/FreeFall.html to figuere out your result.

Not too difficult, a minute at most. Good luck!

Answer 5

That is, in general, a very difficult question. Aerodynamics is, in many ways, something of an 'ad hoc' science in that if an equation works for a particular situation, you try it in other, similar, situations and analyze its predictions against measurement. There really aren't any 'easy' equations for what you're asking and all of them are dependent upon a bunch of other factors.


Doug

Answer 6

I jumped out of an airplane at 12,000 feet and free fell for 20 seconds at 120 mph.