How Much Lead Can a Tin Cup Carry Without Sinking?

In summary, the question is asking how many grams of lead shot with a density of 11.4g/cm^3 can a tin cup with a total volume of 0.012m^3 and a mass of 0.13kg carry without sinking in water. To solve this, you need to first calculate the force exerted by the tin cup on the water, which is 860N. Then, using Archimedes' Principle, you can find the buoyant force by calculating the weight of the water displaced by the cup. Once you have the buoyant force, you can set up the equation Ftin + Flead = Fwater to solve for the mass of lead shot needed to balance the forces and keep the
  • #1
r3dxP
A tin cup has a total volume of .012m^3 and mass of .13kg. How many grams of lead shot of density 11.4g/cm^3 could it carry without sinking in water?

the question i have here is what is equal to what and how to solve this?
so far.. i have.. Ftin = Vpg = .012m^3 * 7310kg/m^3 * 9.8m/s^2 = 860N
the tin alone pushes down 860N onto the water.
how can i find the force pushed by the water in the sink? cause once i find this force, i can set the equation.. Ftin + Flead = Fwater
once i get the Flead, i can solve for mass by Flead / g..
 
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  • #2
And Archimedes' Principle rears its attractive head for the second time in twenty-four hours.

The buoyant force will equal the weight of the water displaced by the cup.
 
  • #3
how can i solve for the buoyant force?
 
  • #4
You know the total volume of the cup - you therefore know the maximum amount of water it can displace, yes? Just find the weight of that much water and Bob's your uncle.

Clear?
 

Related to How Much Lead Can a Tin Cup Carry Without Sinking?

1. Why do some objects sink in water while others float?

Objects sink or float in water based on their density. If an object is more dense than the water, it will sink. If it is less dense, it will float. This is due to a principle called Archimedes' principle, which states that the buoyant force on an object is equal to the weight of the water it displaces. So, if an object is more dense than water, it will displace less water and therefore experience a greater downward force, causing it to sink.

2. How does the shape of an object affect its ability to float or sink in water?

The shape of an object can greatly affect its ability to float or sink in water. For example, a flat sheet of metal will sink, while a hollow metal ship will float. This is because the shape of an object affects its density and the amount of water it displaces. Objects with more surface area relative to their volume, such as a flat sheet, will have a higher density and sink, while objects with less surface area, such as a hollow ship, will have a lower density and float.

3. Can an object that is more dense than water still float?

Yes, there are some objects that are more dense than water but can still float. This is because of their shape and distribution of mass. For example, a boat made of steel can float because its overall shape and design allows it to displace enough water to counteract its density. Additionally, objects like icebergs can float because they are less dense than the surrounding water due to their high air content.

4. How does the temperature of water affect an object's ability to float or sink?

The temperature of water can affect an object's ability to float or sink in a few ways. First, colder water is more dense than warmer water, so an object will float more easily in colder water. Additionally, the temperature of water can affect the density of an object itself. For example, a helium balloon may float in room temperature water, but when the water is heated, it will sink because the gas inside the balloon expands and decreases the overall density of the object.

5. Can an object sink in a liquid other than water?

Yes, an object can sink in a liquid other than water. The same principles of density and buoyancy apply to other liquids as well. For example, if an object is more dense than oil, it will sink in oil just as it would in water. The only difference may be the amount of force needed to displace the liquid, as some liquids are more dense than others.

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