# 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? – user80551 Jan 1 '14 at 7:27
• I really mean weight. That's why I said I don't know the density. – user4749 Jan 1 '14 at 7:29
• You could measure the terminal velocity and calculate the mass that way. – John Rennie Jan 1 '14 at 8:36
• Buoyancy is your best friend. Amount of volume of fluid overflown will be the measure. – Torsten Hĕrculĕ Cärlemän 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. – Olin Lathrop Jan 1 '14 at 13:07

## 2 Answers

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.

You could use cylindrical hollow capacitor and electrical bridge circuit and measure changes to the capacitance when the metal balls passing through it. As the ball pass through the capacitor, its capacitance will change due to the change in the dielectric properties inside the capacitor. The changes to the capacitance will be a function of the size of the balls (assume you are using same metal with constant density). So you should be able to calibrate the system with known masses and then use that to determine the unknown.