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I have been working on a program which should simulate all the forces on a spherical object. Right now those are balls, but they can easily be changed to something else. These are the formulas I use for the forces so far. My question is, if all of them are correct for this situation and if I get the correct resultant force.

$$\matrix{ F_{zw} &=& g m \\ F_d &=& \frac12 \rho v_y^2 C_d A \\ F_b &=& \rho V g \\ Fres &=& F_{zw} + F_d - F_b \\ } $$

Would this work when the ball is falling down? Will I have to change the sign of one of these forces when the ball is going up? (It's a bouncing ball)

EDIT:

$$\matrix{ m &=& 0.0425\,\text{kg} \\ \text{radius} &=& 0.125\,\text{m} \\ } $$

To get the speed I get the acceleration ($F_{res} / m$) and then multiply that by the difference in time.

$F_{zw}$ is gravity, $F_b$ is buoyancy, and $F_d$ is drag.

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closed as off-topic by Emilio Pisanty, Dan, BebopButUnsteady, Nathaniel, Dilaton Jul 25 '13 at 21:55

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1 Answer

In reality there will be many forces on it, but those are probably the three most important ones. Gravity will always point "down" (towards its source). Drag will always point in the direction opposite to velocity, so it will change direction when it's coming up. Buoyancy will always point in the direction opposite to gravity.

Another detail is, it's not clear exactly how you plan to integrate the motion, to me -- acceleration won't be constant because v is changing, and F depends on v here. You have to choose some tiny "time constant" to integrate over, but maybe you know this.

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