What is the weight of a granite cube with 25cm in each side (density of granite is 2.9g/cm^3). What is the weight of this cube when it is submerged in the sea.(the density of sea water is 1.03g/cm^3)
1st part ... 25^3 * 2.9 ... grams
2nd part ... 25^3 * (2.9 - 1.03) ... grams
weight is force, usually measured in Newtons
change grams to kilograms, then multiply by g
... g = 9.8 m/s^2
To find the weight of the granite cube, you can use the formula: weight = density × volume.
First, let's calculate the volume of the cube. Since the cube has 25cm on each side, the volume can be found by raising that length to the power of 3: volume = (25cm)^3.
Next, we need to convert the units of density to grams per cubic centimeter (g/cm^3). The density of granite is already given as 2.9 g/cm^3, so no conversion is needed. However, the density of sea water needs to be converted from 1.03 kg/L to g/cm^3. Since 1 L = 1,000 cm^3 and the density is 1.03 kg/L, the density of sea water becomes 1.03 g/cm^3.
Now we can calculate the weight of the granite cube out of water:
weight = density × volume
weight = 2.9 g/cm^3 × (25 cm)^3
Now, to find the weight of the submerged cube, we need to consider the buoyant force acting on the cube. The buoyant force is equal to the weight of the water displaced by the cube. When the cube is submerged, the volume of the cube will be the same, but it will displace a certain volume of water with a density of 1.03 g/cm^3.
We can find the weight of the submerged cube by calculating the difference between the weight of the granite cube and the buoyant force:
weight_submerged = weight_granite - buoyant force
The buoyant force can be found using the formula: buoyant force = density of fluid × volume of fluid displaced.
Therefore, the weight of the granite cube when submerged in sea water is:
weight_submerged = (2.9 g/cm^3 × volume) - (1.03 g/cm^3 × volume)