Calculating Maximum Lead Shot Capacity of Tin Can

In summary, a tin can with a total volume of 1200 cm^3 and a mass of 130g is being considered in terms of how much lead shot of density 11.4 g/cm^3 it can carry without sinking in water. The buoyancy force equation, which states that the buoyancy force is equal to the mass of the displaced fluid multiplied by the acceleration due to gravity, is used to determine the amount of lead shot needed for the can to reach the verge of sinking. The question remains as to how much lead shot is needed to make the mass of the displaced water equal to the combined mass of the can and lead shot.
  • #1
drobtj2
5
0

Homework Statement


A tin can has a total volume of 1200 cm^3 and a mass of 130g. How many grams of lead shot of density 11.4 g/cm^3 could it carry without sinking in water?


Homework Equations



Bouyancy force= mass of displaced fluid*g



The Attempt at a Solution



no idea!
 
Physics news on Phys.org
  • #2
The can will sink when mass of the displaced water becomes less than the mass of the can plus lead shot, right? How much lead shot do you need to make them equal when the can is on the verge of sinking (i.e. has displaced all of the water it possibly 'can')?
 
  • #3


I would approach this problem by first determining the maximum volume of lead shot that the tin can can hold without exceeding its total volume of 1200 cm^3. This can be calculated by dividing the total volume by the density of lead shot (11.4 g/cm^3), which gives a maximum volume of approximately 105.3 cm^3.

Next, I would calculate the mass of this volume of lead shot by multiplying the volume by the density, which gives a maximum mass of approximately 1200 g. This is the maximum amount of lead shot that the tin can can hold without sinking in water, since it has the same mass as the displaced water.

To verify this, I would use the equation for buoyancy force, where the mass of the displaced fluid is equal to the mass of the lead shot (1200 g) and the acceleration due to gravity is 9.8 m/s^2. This would give a buoyancy force of 11,760 N, which is greater than the weight of the tin can (130 g * 9.8 m/s^2 = 1274 N). Therefore, the tin can would not sink with a maximum capacity of 1200 g of lead shot.

In conclusion, the maximum lead shot capacity of the tin can is 1200 g, based on the given information.
 

1. How do I calculate the maximum lead shot capacity of a tin can?

To calculate the maximum lead shot capacity of a tin can, you will need to know the volume of the can, the diameter of the lead shot, and the packing factor. The formula for calculating the maximum lead shot capacity is: (Volume of can)/(Diameter of lead shot)^2 x Packing factor.

2. What is the packing factor and how do I determine it?

The packing factor is a value that represents the amount of space that is taken up by the lead shot when it is packed together in the tin can. It is typically between 0.55 and 0.65 for spherical lead shot. To determine the packing factor, you can either consult a table or measure the volume of the lead shot when it is packed tightly in a container and divide it by the volume of the container.

3. Can I use any type of tin can for calculating maximum lead shot capacity?

No, it is important to use tin cans that are specifically designed for storing and transporting lead shot. These cans have been tested and have a known packing factor, ensuring accurate calculations. Using a different type of tin can may result in an incorrect maximum lead shot capacity calculation.

4. Are there any safety precautions I should take when calculating maximum lead shot capacity?

Yes, it is important to wear protective gear, such as gloves and safety glasses, when handling lead shot. Lead is a toxic substance and can be harmful if ingested or inhaled. It is also important to work in a well-ventilated area and to properly dispose of any lead shot or containers that have come into contact with it.

5. Can I use this calculation for other types of shot or materials?

No, this calculation is specifically for lead shot and may not be accurate for other types of shot or materials. Each type of shot or material will have a different packing factor, which will affect the maximum capacity calculation. It is important to use the appropriate formula for each type of shot or material being used.

Similar threads

  • Introductory Physics Homework Help
2
Replies
38
Views
1K
Replies
7
Views
890
  • Introductory Physics Homework Help
Replies
10
Views
891
  • Introductory Physics Homework Help
2
Replies
44
Views
3K
  • Introductory Physics Homework Help
Replies
16
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
5K
  • Introductory Physics Homework Help
Replies
16
Views
2K
  • Introductory Physics Homework Help
Replies
16
Views
1K
Replies
2
Views
779
  • Introductory Physics Homework Help
Replies
3
Views
1K
Back
Top