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# The apparent weight Watch

1. I am puzzled by this question

What is the apparent weight for a piece of wood has density 1.10 g/cm3 if it displaced 786 ml from water when it was immersed in lake
2. (Original post by MAA_96)
I am puzzled by this question

What is the apparent weight for a piece of wood has density 1.10 g/cm3 if it displaced 786 ml from water when it was immersed in lake
Archimedes Principle states that the wood will experience an upwards force (upthrust) due to the weight of the water it displaces.
Find the weight of 786ml water. This is the reduction in the measured weight of the wood.
The wood's normal weight can be found from its mass. (Volume x density)
3. The clue is in the 'displaced 786 ml of water' statement and the difference in density between the wood and water.

You know that the wood will float on water when the force of gravity pulling it down (it's weight) is equal to the 'upthrust' of the water stopping it from being pulled down any further. (Archimedes). At that point the forces on the wood are balanced.

When that happens the amount of water displaced will be exactly the same as the weight of the wood.

So to answer the question you need to know:

a) How to convert 786 ml of water into cm3 of water.

b) What the weight of 786 ml of water is.

c) Using this information, work out the 'apparent' weight of the wood.
4. (Original post by uberteknik)
The clue is in the 'displaced 786 ml of water' statement and the difference in density between the wood and water.

You know that the wood will float on water when the force of gravity pulling it down (it's weight) is equal to the 'upthrust' of the water stopping it from being pulled down any further. (Archimedes). At that point the forces on the wood are balanced.

When that happens the amount of water displaced will be exactly the same as the weight of the wood.

So to answer the question you need to know:

a) How to convert 786 ml of water into cm3 of water.

b) What the weight of 786 ml of water is.

c) Using this information, work out the 'apparent' weight of the wood.
But what do you mean in step "a"? They are basically the same ml and cm^3.
5. (Original post by MAA_96)
But what do you mean in step "a"? They are basically the same ml and cm^3.
Yes. The statement was to check your understanding that ml's apply to liquids which therefore take up the shape of their container, whereas cm3 is a volume with dimensions 1 x 1 x 1 cm.

So as you point out, 1cm3 is a defined shape = 1 ml in any shape.
6. (Original post by uberteknik)
Yes. The statement was to check your understanding that ml's apply to liquids which therefore take up the shape of their container, whereas cm3 is a volume with dimensions 1 x 1 x 1 cm.

So as you point out, 1cm3 is a defined shape = 1 ml in any shape.
that's what I thought but I have one more question .How can I find the weight of the water in step "b" do I have to only multiply by 9.8 ?
7. (Original post by MAA_96)
that's what I thought but I have one more question .How can I find the weight of the water in step "b" do I have to only multiply by 9.8 ?
Mass = Volume x Density

Force = Mass x Acceleration

Weight = Mass x Acceleration due to gravity

So yes to work out the weights, you need to use acceleration due to gravity = 9.81 m/s2

Apparent weight is given by the formula:

actual weight of object - weight of displaced liquid

You already have the volume of water displaced in ml so convert that to cm3 to get the volume of the wood in cm3.

You can work out the actual weight of the wood by using:

weight = density x volume x gravity. (plug in the numbers for the density and volume of the wood and the)

You can also work out the weight of the water displaced by the same formula but you need to know the density of water to do that.

Once you have both of those weights, you cab plug them both into the apparent weight formula and you have your answer.

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Updated: April 12, 2013
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