Suppose you have two 100-mL graduated cylinders. In each cylinder there is 40.0mL of water. You also have two cubes: one is lead(11.3g/ml), and the other is aluminum(2.70g/ml) Each cube measures 2.0cm on each side. After you carefully lower each cube into the water of the cylinder?
They both displace the same volume and mass of water so both weights are reduced by density of water * g * volume of cube
You asked this same question last night (actually you finished the question last night). Bob Pursely answered the question, you questioned his answer and I followed up with the same answer Damon has given you here. You may as well accept the answer because it's right; both cubes, if they have the same volume, displace the same amount of water. The old water volume is 40 cc, you displace 8 cc so the new water volume is 48 cc for BOTH. It makes no difference what the identity is. You can have 8 cc lead, 8 cc aluminum, or 8 cc of feathers and 40 + 8 = 48. Period.
To calculate what happens when you lower the cubes into the water in the cylinders, we can use the concept of density.
1. Calculate the volumes of the cubes:
- The volume of a cube is given by the formula: Volume = length^3
- For a cube measuring 2.0 cm on each side, the volume will be: Volume = (2.0 cm)^3 = 8.0 cm^3
2. Calculate the masses of the cubes:
- The mass of each cube can be calculated using the density formula: Mass = Volume x Density
- For the lead cube: Mass = 8.0 cm^3 x 11.3 g/cm^3 = 90.4 g
- For the aluminum cube: Mass = 8.0 cm^3 x 2.70 g/cm^3 = 21.6 g
3. Calculate the total volume of water in each cylinder:
- Each cylinder initially contains 40.0 mL of water.
4. Calculate the total volume of each cylinder once the cube is submerged:
- Since the cube is submerged in the water, its volume will displace an equal volume of water, resulting in a higher water level.
- For the lead cube:
- The cuboid's volume is 8.0 cm^3, which is equivalent to 8.0 mL.
- The total volume of water in the cylinder after submerging the lead cube will be: 40.0 mL + 8.0 mL = 48.0 mL
- For the aluminum cube:
- The cubic's volume is 8.0 cm^3, which is equivalent to 8.0 mL.
- The total volume of water in the cylinder after submerging the aluminum cube will be: 40.0 mL + 8.0 mL = 48.0 mL
5. Determine if the water level changed based on the total volume of water in each cylinder after submerging the cubes:
- The total volume of water in each cylinder after submerging the cubes is 48.0 mL in both cases, which is the same as the initial volume.
- Therefore, the water level will not change in either cylinder when the cubes are submerged.
In summary, when you carefully lower each cube into the water of the cylinders, the water level in each cylinder will not change.
To find out what happens after you carefully lower each cube into the water in the cylinder, we need to calculate the change in water level in each cylinder.
The volume of each cube can be calculated using the formula V = l^3, where l is the length of one side of the cube. In this case, the length is given as 2.0 cm.
For the lead cube:
V_lead = 2.0 cm * 2.0 cm * 2.0 cm = 8.0 cm^3
For the aluminum cube:
V_aluminum = 2.0 cm * 2.0 cm * 2.0 cm = 8.0 cm^3
Since 1 cm^3 is equal to 1 mL, the volume of both cubes is equal to 8.0 mL.
Now, let's determine the change in water level in each cylinder.
Start with the initial volume of water in each cylinder, which is 40.0 mL.
For the lead cube:
- The volume of water displaced by the lead cube is equal to the volume of the cube, which is 8.0 mL.
- Therefore, the change in water level is 8.0 mL.
For the aluminum cube:
- The volume of water displaced by the aluminum cube is also equal to the volume of the cube, which is 8.0 mL.
- Therefore, the change in water level is 8.0 mL.
To find the final water level in each cylinder, subtract the change in water level from the initial water level.
For the lead cube:
Final water level = Initial water level - Change in water level
Final water level = 40.0 mL - 8.0 mL
Final water level = 32.0 mL
For the aluminum cube:
Final water level = Initial water level - Change in water level
Final water level = 40.0 mL - 8.0 mL
Final water level = 32.0 mL
After carefully lowering each cube into the water of the cylinder, the water level in each cylinder will decrease by 8.0 mL, resulting in a final water level of 32.0 mL.