a block of stone has a density of 2.75 g/cm3. the block has a mass of 3.30 kg. it measures 6.00 cm wide by 8.00 cm high by L cm long.
how do i find L?
if the block was in water with density of 1000kg/cm3 what would the buoyant force on the block be?
anything helps!! thank u
D = 2.75 g/cm3.
M = 3.30 kg. = 3,300 g.
M = D * V.
3,300 = 2.75 * (6*8*L),
L = ?.
So L should be 68.6927cm? Thank you!!!
L = 3300/(2.75*6*8) = 25 cm.
To find the length (L) of the block, you can use the formula for density:
Density = Mass / Volume,
where Volume = Length x Width x Height.
Given that the density of the stone block is 2.75 g/cm^3 and the mass is 3.30 kg, you need to convert the mass to grams:
3.30 kg = 3,300 g.
Now, plug in the known values, and rearrange the formula to solve for L:
2.75 g/cm^3 = 3,300 g / (L cm x 6.00 cm x 8.00 cm).
To solve for L, divide both sides of the equation by 2.75 g/cm^3:
L = 3,300 g / (2.75 g/cm^3 x 6.00 cm x 8.00 cm).
Performing the calculation gives:
L ≈ 24.85 cm.
So the length of the stone block is approximately 24.85 cm.
Now, let's calculate the buoyant force on the block when it is submerged in water. The buoyant force can be calculated using Archimedes' principle, which states that the buoyant force is equal to the weight of the fluid displaced by the object. In this case, the fluid is water, and its density is given as 1000 kg/cm^3 (or 1 g/cm^3).
The volume of the stone block can be calculated as before:
Volume = Length x Width x Height = 24.85 cm x 6.00 cm x 8.00 cm.
Now, the weight of the water displaced by the block is given by:
Weight of water displaced = Density of water x Volume of block x Acceleration due to gravity.
Substituting the given values:
Weight of water displaced = 1 g/cm^3 x (24.85 cm x 6.00 cm x 8.00 cm) x 9.8 m/s^2
Converting cm to m:
Weight of water displaced ≈ 0.01 kg/cm^3 x (0.2485 m x 0.06 m x 0.08 m) x 9.8 m/s^2
Weight of water displaced ≈ 0.018 kg x 0.1188 m^3 x 9.8 m/s^2
Calculating the buoyant force:
Buoyant force = Weight of water displaced
Buoyant force ≈ 0.212 kg m/s^2
So, the buoyant force on the block when submerged in water would be approximately 0.212 kg m/s^2.