A paperweight weighs 6.9N in air. When it is completely submerged in water it appears to weigh 4.3N. A) What is the volume of the paperweight? B) What is the density paperweight? The density of water is 1000kg/m3.
Fb = 6.9 - 4.3 = 2.6 N. =Buoyancy force
= Wt. of water displaced.
m*g = 2.6 N.
m = 2.6/g = 2.6/9.8 = 0.2653 kg. = Mass
of water displaced.
A. Vp = Vw = mass/Dw=0.2653/1000kg/m^3=
2.653*10^-4 m^3 = Vol. of paperweight =
Vol. of water.
B. m*g = 6.9 N.
m = 6.9/g = 6.9/9.8 = 0.7041 kg.
Density = m/V = 0.7041/2.653*10^-4 =
2654 kg/M^3.
To find the volume of the paperweight, we can make use of Archimedes' principle, which states that the buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
A) The buoyant force experienced by the paperweight when submerged in water is equal to the weight of the water displaced by the paperweight. So, we can calculate the weight of the water displaced.
Step 1: Calculate the weight of the water displaced:
The weight of the paperweight in air is 6.9N, and the weight of the paperweight in water is 4.3N. The difference between these weights (6.9N - 4.3N = 2.6N) is the weight of the water displaced.
Step 2: Convert the weight of the water displaced to mass:
Using the formula F = mg, where F is the weight, m is the mass, and g is the acceleration due to gravity, we need to divide the weight of the water displaced by the acceleration due to gravity (9.8 m/s^2) to obtain the mass.
m = F / g = 2.6N / 9.8 m/s^2 = 0.265 kg
Step 3: Calculate the volume using the density of water:
Since density (ρ) is defined as mass per unit volume (ρ = m / V), we can rearrange the formula to solve for the volume:
V = m / ρ = 0.265 kg / 1000 kg/m^3 = 0.000265 m^3
Therefore, the volume of the paperweight is 0.000265 cubic meters.
B) To find the density of the paperweight, we can divide the mass of the paperweight by its volume:
Step 1: Calculate the mass of the paperweight:
Using the formula F = mg, the weight of the paperweight in air (6.9N) is equal to the product of its mass and the acceleration due to gravity (9.8 m/s^2). We can rearrange the formula to solve for the mass:
m = F / g = 6.9N / 9.8 m/s^2 = 0.704 kg
Step 2: Calculate the density of the paperweight:
Using the formula ρ = m / V, where ρ is the density, m is the mass, and V is the volume, we can divide the mass of the paperweight by the volume obtained earlier:
ρ = m / V = 0.704 kg / 0.000265 m^3 = 2650 kg/m^3
Therefore, the density of the paperweight is 2650 kg/m^3.