has to do with gravity and speed?

Question

if an sphere is falling at max speed and it suddenly splits into two perfect halfs. the cut is in a perfect place so that the wind resistance stays the same as if it was whole. will the sphere slow down increase sped or do anything at all

Answer 1

OK, let's be perfectly clear...wind resistance (drag) is proportional to the cross sectional area A of the object. So the only way drag could remain the same is for the ball to split along the horizontal and flop open to present the areas of each hemisphere to be the same as the area of the sphere. That is very unlikely in free fall because the hemispheres would tend to streamline and present about 1/2 A each during the fall. Which means, all things equal, the drag forces on each hemisphere would be about 1/2 that of the complete sphere.

As f = ma = W - F; where m is the ball's mass, a is its acceleration, W is its weight and F is the drag force on the sphere; we find that a = (W - F)/m. For a hemisphere, we'd have a' = (W/2 - F/2)/(m/2) = (W - F)/m = a when it streamlines so its cross sectional area is A/2 of the sphere. Thus, in the realistic case, the accelerations and terminal velocities would be about the same as the whole sphere.

In the unlikely case you describe, we'd have a" = (W/2 - F)/(m/2) = (W - 2F)/m < (W - F)/m = a; so that a" < a for each hemisphere. Thus, the acceleration of the hemispheres (and the consequent terminal velocities) would be less than the whole sphere. But again...this is not likely to happen because the hemispheres would streamline and show A/2 cross sectional areas upon descending.

Answer 2

slow down
initially the force of drag will be the same, but it will be against half the weight force. so the 2 bits slow down

http://en.wikipedia.org/wiki/Drag_equation
(at terminal velocity Fd = weight)

what you would get, given only the weight changes, the terminal velocity will be 1/(root2) of what it was at the start
for each piece
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yep. it's not clear if the split you talk about is horizontal (so each piece would have the same drag as the sphere) or vertical (so the sum of the 2 is the same as the sphere)
or even if the 2 pieces come apart.
i presumed that the split was horizontal...

if it splits vertically, then A is 1/2 and weight is 1/2 so the V stays the same...
although this would require it to magically stay with the same orientation while it falls

Answer 3

the proposal is not possible but if it were there would be no change. Only two forces work on a falling object, friction and gravity. Gravity is constant so if frictions is constant...No change

Answer 4

if the wind resistance stays the same there is no acceleration and hence no change in speed...