

Density of Ball and Distance Travelled
Name: Julie
Status: educator
Grade: other
Location: AL
Country: N/A
Date: 4/7/2005
Question:
Does the density of different balls effect the distance
that they travel?
Replies:
Julie,
If the only force affecting the ball is gravity, density does not matter.
Mass and size also have no effect. However, density does affect the motion
when a ball travels in air (or any other gas).
Air pressure depends on speed and size (specifically the crosssectional
area). For a ball, this is of course pi times the radiussquared. The
force of air resistance does not depend on the ball's mass. The contribution
to a balls acceleration due to air resistance (F/m) is proportional to the
ratio r^2/m. Density is proportional to m/r^3. If radii are similar, the
ball with the greater density is affected less by air resistance. A bowling
ball is larger than a tennis ball, but air resistance affects a bowling
ball's motion much less than it affects a tennis ball.
Ken Mellendorf
Math, Science, Engineering
Illinois Central College
Sure, Julie, due to air drag.
In a vacuum it would not matter,
but in our atmosphere it matters a fair amount to fastmoving balls.
As ball move slower and slower it will matter less and less.
Plastic wiffleballs are the same size as baseballs,
but they have less density and less mass.
They travel much less distance when hit hard.
To keep the same mass while varying the density,
you might find a big wiffleball with the same weight as a little golfball.
The higherdensity ball will travel farther in that case, too,
given the same speed.
There is an idea called "ballistic coefficient".
ballistic_coefficient = ( mass / frontal_area ).
Things with the same ballistic coefficient tend to travel
about the same distance through the air.
Things with higher ballistic coefficients tend to travel greater distances.
An arrow made of wood needs to be longer than an arrow made of iron,
to have the same ballistic coefficient.
This never exactly matches the idea of density.
density = ( mass / volume ).
You can reconcile them a little bit by understanding:
volume = ( frontal_area x length ) (approximately)
ballistic_coefficient = ( density * length )
So a big softball will travel farther than a little baseball of the same
density.
Jim Swenson
Short answer, Yes.
Long answer, only in an atmosphere. The greater the density of a ball, the
more mass it has at a given size. (Boulders are far more massive than
beach balls!) Whenever anything moves through the air, there is resistance
roughly proportional to its surface area. This resistance acts as a force
to slow that object down. The more massive the object, the more force
required to slow it.
So if you took the aforementioned beach ball, and a boulder of the same size,
and chucked them both with a catapult...
The beach ball would quickly slow to a near stop in the air, and drop to the
ground.
The Boulder would go sailing through the air with only a trivial drop in
its forward momentum.
All of this is of course assuming both objects are the same shape, and can be
launched at the same velocity.
Ryan Belscamper
Click here to return to the Physics Archives
 
Update: June 2012

