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.
if i found L to be 68.6927cm by doing m=D*V, is that right? Also if it was in fresh water (density=1000kg/cm^3), would the buoyant force be 32,313,050? I feel like that number is WAYY too big, but i did Fb=pgV and that's what I got. Help please!!
watch your sig figs
you're mixing g and kg
also , water density is 1000 kg/m^3
... or 1 g/cm^3
V = 3300 g / 2.75 g/cm^3
convert V to m^3 and use 9.81 for g
... Fb will be in Newtons
To find the length (L) of the block, you can use the formula m = D * V, where m is the mass, D is the density, and V is the volume. Rearranging the formula, you have V = m / D.
Since the mass of the block is given as 3.30 kg and the density is 2.75 g/cm³, you need to convert the mass to grams to maintain consistent units. Therefore, the mass is 3300 g and the density is 2.75 g/cm³.
Using V = m / D, you can now calculate the volume:
V = 3300 g / 2.75 g/cm³
V ≈ 1200 cm³
Now that you have the volume, you can use the given measurements of the block to find the missing length (L). The block measures 6.00 cm wide, 8.00 cm high, and L cm long. To find the volume, you multiply these measurements together:
Volume = width * height * length
1200 cm³ = 6.00 cm * 8.00 cm * L cm
To solve for L, divide both sides by 48 cm²:
L = 1200 cm³ / (6.00 cm * 8.00 cm)
L ≈ 25 cm
So, the length (L) of the block is approximately 25 cm, not 68.6927 cm as you mentioned.
Now, let's consider the buoyant force when the block is submerged in fresh water with a density of 1000 kg/m³ (not kg/cm³). The formula for buoyant force (Fb) is Fb = p*g*V, where p is the density of the fluid, g is the acceleration due to gravity (9.8 m/s²), and V is the volume of the object submerged.
First, convert the density of water from kg/m³ to g/cm³. It is 1000 g/cm³.
Next, calculate the volume of the block submerged using its dimensions:
Volume_submerged = width * height * length_submerged
Volume_submerged = 6.00 cm * 8.00 cm * 25 cm
Volume_submerged = 1200 cm³
Finally, calculate the buoyant force:
Fb = p * g * V
Fb = 1000 g/cm³ * 9.8 m/s² * 1200 cm³
Fb = 11,760,000 g*cm²/s²
Note that the units for the buoyant force are g*cm²/s², which can be a bit confusing. To simplify it, you can convert it to Newtons (N) by dividing by 980 cm/s² (which is equivalent to 9.8 m/s², the acceleration due to gravity).
Fb = 11,760,000 g*cm²/s² / 980 cm/s²
Fb ≈ 12,000 N
Therefore, the buoyant force exerted on the block when submerged in fresh water is approximately 12,000 N, not 32,313,050 N as you calculated.