# Calculate the Mass of a Ball Bearing (Millikan Experiment)

• rkimbel
In summary, the task is to calculate the mass of a single ball bearing using twelve cans, one of which is empty, and a balance. The equation used is Total Mass=Mo+n(mo), where total mass is the mass of the ball bearings, Mo is the smallest mass, n is the number of bearings, and mo is the mass of each bearing. The approach is to subtract the smallest mass from each of the masses, divide by 2.3 g, and then add the resulting numbers to find the total number of ball bearings. Finally, divide the total mass by the total number of ball bearings to find the mass of a single bearing.

#### rkimbel

1. Homework Statement
You are given twelve cans (one of which is empty) which are filled with a certain number of ball bearings. Using nothing more than a balance, calculate the mass of a single bearing

2. Homework Equations
Total Mass=Mo+n(mo)
Where total mass=mass of ball bearings
Mo=smallest mass
n=number of bearings
mo= mass of each bearing

3. The Attempt at a Solution
I realize the equation above is a little confusing (formatting in PF is not easy). The way I attempted this problem was by first trying to organize the mass of the twelve cans (after subtracting the mass of the empty can, of course). I found the smallest difference between two masses, which was 2.3 g. From this point, however, I'm not sure what to do. I could possible divide each mass by 2.3 g, giving me the theoretical number of ball bearings. But I don't see how I could verify my answer. Any help is appreciated. Thank you.

Your approach is on the right track. You are almost there. Instead of dividing each mass by 2.3 g, you need to subtract the smallest mass from each of the masses and then divide the result by 2.3 g. This will give you the number of ball bearings for each of the cans. Then simply add these numbers together and you will have the total number of ball bearings. Divide the total mass (from step 1) by the total number of ball bearings and you will have the mass of a single bearing.

I would suggest using the Millikan experiment to calculate the mass of a single ball bearing. This experiment involves suspending a charged oil droplet in an electric field and measuring its motion. By manipulating the electric field and measuring the motion, the mass of the droplet can be calculated. This method can be applied to the ball bearings by coating them with a thin layer of oil and suspending them in an electric field. By measuring the motion of the bearings, their mass can be calculated. This method is more precise and accurate compared to using a balance, as it takes into account the mass of the oil coating on the bearings.

## 1. What is the Millikan Experiment?

The Millikan Experiment is a famous physics experiment conducted by Robert Millikan in 1909 to determine the fundamental charge of an electron. It involved observing the motion of oil droplets in an electric field.

## 2. Why is calculating the mass of a ball bearing important in the Millikan Experiment?

The mass of the ball bearing is a crucial factor in the Millikan Experiment because it is used as a standard reference for the mass of the oil droplets. This allows for accurate calculations of the charge of the electron based on the observed motion of the droplets.

## 3. How is the mass of a ball bearing calculated in the Millikan Experiment?

The mass of a ball bearing can be calculated by using the density and volume of the bearing. The density can be measured using a density meter, and the volume can be determined by measuring the diameter of the bearing and using the formula for the volume of a sphere.

## 4. What are the potential sources of error in calculating the mass of a ball bearing in the Millikan Experiment?

Some potential sources of error in calculating the mass of a ball bearing in the Millikan Experiment include variations in the density of the bearing, inaccuracies in measuring the diameter, and external factors such as air resistance affecting the motion of the droplets.

## 5. How does the accuracy of the calculated mass of a ball bearing affect the results of the Millikan Experiment?

The accuracy of the calculated mass of the ball bearing directly affects the accuracy of the charge of the electron calculated in the Millikan Experiment. Therefore, it is crucial to have precise and accurate measurements of the ball bearing's mass to obtain reliable results.