Diving into Buoyancy: Calculating the Apparent Weight of an Iron Block in Water
The weight of an iron block is 790N. What is the apparent weight of the same block when it is completely immersed in water? The density of iron is 7900 kg/m3. This lesson delves into the principles of buoyancy to find the answer.
Understanding the Concepts
Buoyancy, the upward force exerted by a fluid on a submerged or floating object, plays a crucial role in determining the apparent weight of the iron block. The apparent weight is the actual weight of the object minus the buoyant force, which is the upward force exerted by the fluid on the object.
Step-by-Step Calculation
To find the apparent weight of the iron block, follow these steps:
Step 1: Calculate the Volume of the Iron Block
The volume of the iron block can be calculated using its weight and density.
Given:
Weight of the iron block, W 790 N Density of iron, (rho_{iron} 7900 kg/m^3) Density of water, (rho_{water} 1000 kg/m^3) (approximately)First, calculate the mass of the iron block:
m frac{W}{g} frac{790 N}{9.81 m/s^2} approx; 80.4 kg
Now, calculate the volume:
V frac{m}{rho_{iron}} frac{80.4 kg}{7900 kg/m^3} approx; 0.01018 m^3
Step 2: Calculate the Buoyant Force
The buoyant force is equal to the weight of the water displaced by the iron block.
Buoyant force, F_b rho_{water} cdot V cdot g
Substitute the known values:
F_b 1000 kg/m^3 cdot 0.01018 m^3 cdot 9.81 m/s^2 approx; 100 N
Step 3: Calculate the Apparent Weight
The apparent weight is the actual weight minus the buoyant force:
Apparent weight, W_{apparent} W - F_b
Substitute the known values:
W_{apparent} 790 N - 100 N 690 N
Conclusion
The apparent weight of the iron block when it is completely immersed in water is 690 N. This solution emphasizes the key principles of buoyancy and provides a clear, step-by-step approach to solving such problems.
Additional Insights
This problem can also be solved through simpler means, using mental arithmetic:
Volume of the iron block: (frac{80.4 kg}{7900 kg/m^3} approx; 0.01018 m^3) or 10.2 L Buoyant force: 10.2 L of water weighs 100 N (100 N force) Apparent weight: 790 N - 100 N 690 NNote: When writing expressions using SI units, there is a required space between the coefficient and the unit symbol. Examples: “790 N” and “7900 kg/m3”.