For a project i need to separate items based on their mass in real time. I like to explore measuring weight of an object (round metal ball) by taking photographs (several) during free fall and calculate mass from the pictures. Even if I cannot find the real mass I like to get a good estimate of the mass delta among many samples in real time.
The basic logic is that I can measure velocity and acceleration from images with good accuracy. And use this data to calculate approximate mass. The density of the object is not controlled tightly neither the volume.
Does this approach make sense?
Best Answer
This approach will not work. Let's assume we are doing the experiment in vacuum for now. As you are saying, the basic logic is that you can measure velocity and acceleration from images with good accuracy. The problem is that any metal ball, irrespectively of their mass or weight will have exactly the same velocity and acceleration and therefore you cannot measure weights this way. To see that the acceleration will be the same: $$F=ma \Rightarrow mg=ma \Rightarrow g=a$$ So the acceleration is always g no matter what the object. Similar arguments hold for the velocity.
If we are doing the experiment in air then you might want to take into account the effects of the air resistance as well as the buoyancy as mentioned in the comments. However, intuitevely we would expect that the effect of the air resistance is small and also for freefalls of small duration (I imagine you cannot capture the motion on camera for too long) the metal ball will probably not reach terminal velocity. You will also need a good hold on the density, drag coefficients, etc and very good accuracy in your experiment which I think is unrealistic with your apparatus.