Statement: A solid that is insoluble and floats on a liquid is less dense than the liquid, and it displaces a mass of liquid equal to its own mass.
The problem that goes with it is:
Approximately what fraction of its volume is submerged when a 1kg block of wood (d=.68g/cm^3) floats on water?
The answer is .68
But can someone explain how to get there?
So far, I've found the volume of the 1kg (1000 g) block which is 1470 cm^3.
Can someone explains what happens after that?
Thanks in advance and of course, 10 points!
The problem that goes with it is:
Approximately what fraction of its volume is submerged when a 1kg block of wood (d=.68g/cm^3) floats on water?
The answer is .68
But can someone explain how to get there?
So far, I've found the volume of the 1kg (1000 g) block which is 1470 cm^3.
Can someone explains what happens after that?
Thanks in advance and of course, 10 points!
-
"The mass displaced is 1000g.
And the density of water is 1. So that means the volume has to be 1000 cm^3?"
That's correct. The wood will float when it displaces 1000 g of water. If the block floated in a liquid with a higher density, it would not go as far into the liquid in order to displace 1000 g.
An example of this is the Dead Sea. If you float in the Dead Sea more of your body is above the water level than when you float in your pool. That's because the density of the Dead Sea water is rather high and you displace a mass equal to your body with less of your body underwater than compared to the density of the water in your pool.
"What if the mass of the block is something other than 1000. I don't understand what I would do if the mass is something other than 1000. "
If the mass of the block is greater than 1000, then its volume will be bigger and the 1000/1470 ratio will have different numbers, but it will still be a 0.68 ratio.
And the density of water is 1. So that means the volume has to be 1000 cm^3?"
That's correct. The wood will float when it displaces 1000 g of water. If the block floated in a liquid with a higher density, it would not go as far into the liquid in order to displace 1000 g.
An example of this is the Dead Sea. If you float in the Dead Sea more of your body is above the water level than when you float in your pool. That's because the density of the Dead Sea water is rather high and you displace a mass equal to your body with less of your body underwater than compared to the density of the water in your pool.
"What if the mass of the block is something other than 1000. I don't understand what I would do if the mass is something other than 1000. "
If the mass of the block is greater than 1000, then its volume will be bigger and the 1000/1470 ratio will have different numbers, but it will still be a 0.68 ratio.