A particular object weighs 313 N in air and 264 N when immersed in alcohol of density 0.70 g/cm3. What is the volume (in L) and the density (in kg/m3) of the object?
I had origionally used the 264N as the force of buoyancy and did the Fb=density*volume*g, then solved for volume.
Then, I used the 313N and used Fg=mg to solve for the mass and then divided that by the volume to get the density.
for some reason, It says I'm wrong, and maybe it was in my conversions and such.
could you please calculate so I can compare? would be greatly appreciated :)
the buoyancy force is the difference in the air weight and immersed weight
Sure, I can help you with that.
To find the volume of the object, we can start by using the formula for buoyancy:
Fb = density of fluid × volume × g
Given that the force of buoyancy is 264 N and the density of the alcohol is 0.70 g/cm^3, we can rearrange the formula and solve for volume:
volume = Fb / (density of fluid × g)
Before proceeding, let's convert the density of the alcohol to kg/m^3:
density of alcohol = 0.70 g/cm^3 = (0.70 × 10^3) kg/m^3 = 700 kg/m^3
Next, we will convert the force of buoyancy from Newtons to kg·m/s^2 since the density is in kg/m^3:
Fb = 264 N = 264 kg·m/s^2
Now, we'll use the values to calculate the volume:
volume = 264 kg·m/s^2 / (700 kg/m^3 × 9.8 m/s^2)
By solving this equation, we get:
volume ≈ 0.038 m^3
To convert this to liters (L), we need to multiply the volume by 1000:
volume ≈ 0.038 m^3 × 1000 L/m^3
volume ≈ 38 L
Therefore, the volume of the object is approximately 38 L.
Now, let's find the density of the object. We can use the formula:
density = mass / volume
To find the mass, we'll use the weight of the object in air:
Fg = 313 N = 313 kg·m/s^2
Using the formula Fg = mg, where g ≈ 9.8 m/s^2 is the acceleration due to gravity, we can solve for mass:
mass = Fg / g = 313 kg·m/s^2 / 9.8 m/s^2
mass ≈ 31.94 kg
Finally, we can calculate the density:
density = mass / volume = 31.94 kg / 0.038 m^3
By solving this equation, we get:
density ≈ 840.53 kg/m^3
Therefore, the density of the object is approximately 840.53 kg/m^3.
I hope this helps! Let me know if you have any further questions.