Help with Fluid Problems: Wood + Copper & Lead

[jamdr]

I have these two fluids problems and I can't get either one (they are related). Can anyone point me in the right direction?

1. A 3.05 kg piece of wood (SG = 0.500)) floats on water. What minimum mass of copper, hung from it by a string, will cause it to sink?

2. A 3.25 kg piece of wood (SG = 0.500)) floats on water. What minimum mass of lead, hung from it by a string, will cause it to sink completely under water?

Edit: I'm pretty sure the densities of copper and lead are necessary.
copper = 8900 kg/m^3
lead = 11300 kg/m^3
water = 1000 kg/m^3

 

[Doc Al]

For the wood to just barely float, the string must pull hard enough to bring the wood completely under the water. (Any stronger pull and it will sink.) The forces on the wood are: its weight down, the string pulling down, and the buoyant force pushing up. These forces must balance. So figure out that string force. Then, given the string force, figure out what mass of metal is needed to pull the string with that much force: The force that the metal pulls on the string will be equal to the weight of the metal minus the buoyant force on the metal. Make sense?

Note: In this post I treat the wood and metal as two separate systems attached by a string. In my later post I treat the wood & metal as a single system. Take your pick!

 

[brookstimtimtim]

I don't think you can answer this question without knowing the dimension of the wood. Sinking stuff works like this. If an objects area weighs less than water would for the same area then it floats. Without knowing the area of the wood you can not tell if water for the same area weighs less or more. Ships are made of all allot of heavy metals but because they take up allot of space they weigh less then water would if it took up the same space. Basically you need size and weight of the wood.

 

[brookstimtimtim]

Ok, I had a thought on the last post. If the SG of the overall piece of wood is .5 than it weighs half of what water would way for the same area. If you double the weight than the wood would then weigh the same as water, and would start sinking. A piece of copper weighing 3.05 and a piece of lead at 3.25

 

[Doc Al]

I don't think you can answer this question without knowing the dimension of the wood. ... Basically you need size and weight of the wood.

The mass and density of the wood are given. That's all you need.

 

[Doc Al]

If you double the weight than the wood would then weigh the same as water, and would start sinking. A piece of copper weighing 3.05 and a piece of lead at 3.25

No. The simplest way to solve this problem is to picture the wood and metal underwater, attached by a string. For the system to not sink the external forces must balance. Upward forces (the two buoyant forces) must equal the downward forces (the two weights). Set up this equation and solve for the mass of the metal.

Note: This is equivalent to the method I gave in post #2, but perhaps a bit easier. (Here we ignore the tension in the string, since we treat it as an internal force.) Also, I assume you know that the buoyant force equals the weight of fluid (water) displaced--this is Archimedes' principle.

 

[brookstimtimtim]

I would agree, with a lquid. With a solid you need the size. Take a solid metal block that would sink and pound it into a long thin piece of sheet metal and shape it like a boat and it may float, The density and mass did not change only its size and shape. A solid will float if it weighs less then the water it displaces. Assuming the wood is 1/2 the weight of what water would weigh for the same area, then the 2nd post i made is true.

 

[Doc Al]

I would agree, with a liquid. With a solid you need the size.

Huh? If you are given the mass and density, then you can find the volume if you need it.

Take a solid metal block that would sink and pound it into a long thin piece of sheet metal and shape it like a boat and it may float, The density and mass did not change only its size and shape.

I'm not sure what your point is: We can assume that the wood and metal objects in this problem are solid, not hollow.

Assuming the wood is 1/2 the weight of what water would weigh for the same area, then the 2nd post i made is true.

Yes, the density of wood is half that of water. (That was given.) But I believe your answer is incorrect. Since this is jamdr's problem, I'd like to give him a chance to work it out. But you are welcome to show your work if you still think you are correct.

 

[brookstimtimtim]

You right we should let him do his own work, but if you think I'm incorrect, I'll show it, then you can correct me. Specific Gravity (SP) is how much something weighs compared to water, with SP = .5 then the wood weighs half of what the water weighs. To make the wood sink you would need to make its weight equal that of the water. If the wood weighs 3.05kg then water for the same area of the wood would weight 6.1kg. Add the 3.05kg of copper to the wood and it now weighs the same as water. This means it sinks to the surface level of water. You really don't have to know the density of the wood or the copper if you know the Specific Gravity. Specific Gravity and density are related but are to different.
Density = mass/volume
Specific Gravity = somethings weight / waters weight.
I think this guy's teather was tring to confuss him, density is nowhere in the problem.

you wrote...
I'm not sure what your point is: We can assume that the wood and metal objects in this problem are solid, not hollow.


In the 2nd post I assumed the wood was solid, but in real life if you want to know if something is going to float you need to figure the area of the objects weight and compare if to weight of water for the same area. So a battle ship weighs less than water does for the same shape.

 

[HallsofIvy]

Doc Al can jump on me if I'm wrong but isn't it just a matter of adding enough copper or lead so that the "average" density of the entire system is equal to that of water?

 

[Doc Al]

To make the wood sink you would need to make its weight equal that of the water. If the wood weighs 3.05kg then water for the same area of the wood would weight 6.1kg. Add the 3.05kg of copper to the wood and it now weighs the same as water.

You are forgetting that the copper is under water as well. The 3.05kg of copper "weighs" less due to its own buoyant force.

 

[Doc Al]

Doc Al can jump on me if I'm wrong but isn't it just a matter of adding enough copper or lead so that the "average" density of the entire system is equal to that of water?

Absolutely correct, Halls. That's another excellent way to look at the problem.

 

[brookstimtimtim]

Well then how much copper will it take? I'm sure by now the guy who has post this has already went to class and got his answer.

 

[Doc Al]

Well then how much copper will it take?

Just set the weight equal to the buoyant force:
(3.05)g + mg = (3.05/0.5)g + (m/8.9)g
So m = 3.44 kg