A partially filled bucket of water sits on a scale and its weight is 4.8 N. A piece of metal is suspended from a thread and completely immersed in the bucket (but does not touch the bottom). The scale now reads 7.8 N. Find the volume of the metal.
The added weight represents the water displaced to provide (7.8-4.8)N bouyancy.
Volume=masswater/densitywater
= 3kg/9.8kg/m^3 / 1E3kg/m^3
= 3/(9.8*1E3) m^3
or 3/9.8 liters
To find the volume of the metal, we need to understand the principle of buoyancy. According to Archimedes' principle, the buoyant force on an object submerged in fluid is equal to the weight of the fluid displaced by the object.
Here's how we can solve this problem step by step:
1. Find the weight of the water displaced by the metal:
The weight of water displaced equals the difference between the initial weight of the bucket with water and the weight when the metal is immersed.
Weight of water displaced = Weight with metal - Weight without metal
= 7.8 N - 4.8 N
= 3 N
2. Convert the weight of the displaced water into mass:
We know that weight is mass times acceleration due to gravity (g). The acceleration due to gravity on Earth is approximately 9.8 m/s².
Weight = mass × g
3 N = mass × 9.8 m/s²
Rearranging the equation:
mass = 3 N / 9.8 m/s²
Therefore, the mass of the displaced water is approximately 0.306 kg.
3. Determine the volume of water displaced using the density of water:
The density of water is approximately 1000 kg/m³ (1 g/cm³).
Density = mass / volume
1000 kg/m³ = 0.306 kg / volume
Rearranging the equation:
volume = 0.306 kg / 1000 kg/m³
Therefore, the volume of the water displaced is approximately 0.000306 m³.
4. Since the volume of the metal submerged in water is equal to the volume of water displaced, the volume of the metal is also approximately 0.000306 m³.
Thus, the volume of the metal is approximately 0.000306 m³.