On 01/22/2011 08:39 PM, David Jonsson wrote:
> Hi
>
> Imagine a ball lying on a plane. The wheight is the mass times the
> gravitational acceleration.
>
> Imagine a bouncing ball. Momentarilly the force from it on the plane
> is higher and when it is in the air the force is zero.
>
> My question is if the time averaged force from the two different
> situations are the same or if either ball has a higher time averaged
> force on the plane below.
Time averaged force is the same; otherwise momentum isn't conserved.
Assume a cycle takes time 't'.
Net change in the ball's momentum over one cycle is zero (since it ends
up going at the same speed, in the same direction, as it was to start
with). Therefore, total momentum added to the ball during one cycle,
from all sources, must sum to zero.
Total momentum from gravity is g*m*t.
Total momentum from the bounce force is F*T, where F is the force of the
bounce and T is the duration of the bounce.
The two must be equal, so F*T = g*m*t.
Average upward force is
A = F * (T/t)
so
A = (F*T)/t = (g*m*t) / t = g*m
**************************
And when a truck full of chickens with 3 ton gross weight is about to
drive over a bridge rated at 2 tons, it doesn't do the driver any good
at all to bang on the side of the truck. The chickens all fly up into
the air inside the truck, but none the less, it still requires 3 tons of
upward force on the wheels to support the truck and chickens. ('Course,
if he's got a ton of chickens on board, chances are they're too fat to
fly, anyway.)
>
> Good night ( 02:38 AM in Stockholm),
> David
>
> David Jonsson, Sweden, phone callto:+46703000370
>
