# Measure mass difference of an object without a scale

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?

• All free-falling objects have the same acceleration, ignoring air resistance. By weight, you mean mass right? Jan 1 '14 at 7:27
• I really mean weight. That's why I said I don't know the density. Jan 1 '14 at 7:29
• You could measure the terminal velocity and calculate the mass that way. Jan 1 '14 at 8:36
• Buoyancy is your best friend. Amount of volume of fluid overflown will be the measure. Jan 1 '14 at 9:06
• Really!? It's been 400 years since we've known that all objects fall at the same speed, ignoring air resistance. Go see what Mr Galilei had to say about this. Surely this is out there in many places, so pointless to repeat here. Jan 1 '14 at 13:07

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.