Finding block volume from weights in water and alcohol

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ZeroXD
Hi everyone,

im having some difficulties with a certain homework problem I'm on.
Up until now I've solved all buoyancy problems knowing its weight in air and its weight submerged in a liquid (generally water).

In this particular problem, it gives the weight of the block completely submerged in water as 25 Newtons, and the weight of the blocked cmpletely submerged in alcohol as 25.7 Newtons. Then it states the density of the alcohol is 806 kg/m^3. How would I go about solving for volume of the block?

thanks in advance.
 
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Archimedes' principal states that an object, immersed in a liquid, displaces a volume of liquid equal to its own volume and its weight is reduced by the weight of the liquid displaced.

Let W be the (weight) density of water and A the (weight) density of alcohol.

Let V be the volume of the object and G its weight.

The weight of water displaced is WV so the weight of the object in water is G- WV= 25 Newtons.

The weight of alcohol displaced is AV so the weight of the object in alcohol is G- AV= 25.7 Newtons.

Since you know both W and A, you can eliminate G from the two equations and solve for V.
 


Hi there,

It seems like you are having some difficulty applying Archimedes' Principle to this specific problem. Let's break it down step by step to make it easier to understand.

First, let's review Archimedes' Principle. It states that the upward buoyant force on an object submerged in a fluid is equal to the weight of the fluid that the object displaces. In other words, the weight of the fluid that is pushed aside by the object is equal to the upward force that keeps the object afloat.

Now, let's apply this principle to your problem. We know that the weight of the block submerged in water is 25 Newtons and the weight of the block submerged in alcohol is 25.7 Newtons. This means that the upward buoyant force on the block is equal to the weight of the fluid it displaces in both cases.

Next, we need to find the weight of the fluid that is displaced by the block in each case. This can be calculated by multiplying the density of the fluid by the volume of the block. In this case, the density of alcohol is given as 806 kg/m^3.

So, to solve for the volume of the block, we can set up the following equation:

Weight of block in water = Density of water x Volume of block

25 Newtons = 1000 kg/m^3 x Volume of block

Volume of block = 25 Newtons / 1000 kg/m^3 = 0.025 m^3

Similarly, for the block submerged in alcohol, we can set up the following equation:

Weight of block in alcohol = Density of alcohol x Volume of block

25.7 Newtons = 806 kg/m^3 x Volume of block

Volume of block = 25.7 Newtons / 806 kg/m^3 = 0.0319 m^3

Therefore, the volume of the block is 0.025 m^3 when submerged in water and 0.0319 m^3 when submerged in alcohol. I hope this helps you solve your homework problem. If you have any further questions, don't hesitate to ask. Best of luck!