A paperweight, when weighed in air, has a weight of W = 6.8 N. When completely immersed in water, however, it has a weight of Win water = 4.3 N. Find the volume of the paperweight.
The 2.5 N reduction is due to buoyancy, which equals the paperweight volume multiplied by the weight density of water, which is 9810 N/m^3. Therefore
V = 2.5/9810 = 0.00025 m^3 = 250 cm^3
To find the volume of the paperweight, we can use Archimedes' principle, which states that the buoyant force acting on an object is equal to the weight of the fluid it displaces.
1. Calculate the buoyant force acting on the paperweight when it's completely immersed in water.
Buoyant force = Weight in air - Weight in water
Buoyant force = 6.8 N - 4.3 N
Buoyant force = 2.5 N
2. Determine the density of water.
The density of water is typically around 1000 kg/m³ or 1000 g/cm³.
3. Use the formula for buoyant force:
Buoyant force = Density of water * Volume of immersed object * Acceleration due to gravity
Rearrange the formula to solve for the volume:
Volume of immersed object = Buoyant force / (Density of water * Acceleration due to gravity)
Volume of immersed object = 2.5 N / (1000 g/cm³ * 9.8 m/s²)
(Note: Convert the density of water from g/cm³ to kg/m³)
Volume of immersed object = 0.025 m³
4. So, the volume of the paperweight is 0.025 cubic meters.
To find the volume of the paperweight, we need to use Archimedes' principle, which states that the buoyant force experienced by a submerged object is equal to the weight of the fluid displaced by the object.
First, we need to calculate the buoyant force acting on the paperweight when it is submerged in water. The buoyant force is equal to the weight of the water displaced by the paperweight, given by:
Buoyant force = Weight in water - Weight in air
Buoyant force = Win water - W
Buoyant force = 4.3 N - 6.8 N = -2.5 N
Since the buoyant force is negative, it means that the paperweight is denser than water and sinks.
Next, we can calculate the volume of the paperweight using the formula:
Volume = Buoyant force / Density of water
Here, the buoyant force is -2.5 N and the density of water is approximately 1000 kg/m^3.
Converting the units to SI units:
Volume = -2.5 N / (1000 kg/m^3 * 9.8 m/s^2) = -0.000255 m^3
Since the volume cannot be negative, we take the absolute value:
Volume = 0.000255 m^3
Therefore, the volume of the paperweight is 0.000255 m^3.