Lecture on Buoyant Forces and Archimedes' Principle

Introduction

• Discussion of weight measurement outside and inside water.
  • Object's weight outside water: 10 Newtons
  • Object's weight in water: 2 Newtons

Buoyant Force

• Definition: Upward force exerted by water, counteracting the object's weight.
• Calculation:
  • Difference in weight outside and in water = 10N - 2N = 8 Newtons.
  • Buoyant force = 8 Newtons, indicating water's upward force.

Archimedes' Principle

• Principle: Buoyant force is equal to the weight of the water displaced by the object.
• Equation:
  • Weight of water displaced = Volume of water displaced x Density of water x Gravity
  • Calculation of volume displaced:
    • Density of water = 1000 kg/m³
    • Gravity = 9.8 m/s²
    • Derived volume = (\frac{8}{1000 \times 9.8} = 8.2 \times 10^{-4}) cubic meters

Practical Application

• Experiment suggestion: Measure oneself outside and inside a pool using a waterproof scale to calculate personal volume.
• Volume calculation: Estimating surface increase to measure displaced water volume.

Volume and Surface Area

• Conversion to familiar units:
  • Volume of the object = approximately 0.02 square feet or 34 square inches.
  • Suggests a size of approximately 3-inch cube.

Example Problem: Balsa Wood

• Density of balsa wood: 130 kg/m³
• Problem: Determine percentage of balsa wood cube submerged in water.

Solution Steps

1. Force Equilibrium:

   • Buoyant force = weight of balsa wood
   • Formula: Volume of wood x Density of wood x Gravity = Volume of submerged wood x Density of water x Gravity
   • Simplification: Cross out gravity from both sides.

2. Algebraic Manipulation:

   • (\frac{\text{Volume submerged}}{\text{Volume of balsa wood}} = \frac{\text{Density of balsa wood}}{\text{Density of water}})
   • Calculation: (\frac{130}{1000} = 0.13)

3. Percentage Submerged:

   • Result: 13% of balsa wood block will be submerged in water.
   • Demonstrates applicability to different shapes (e.g., shaped like a horse).

Conclusion

• Understanding buoyant forces and Archimedes' principle helps in determining the volume of submerged objects and their interaction with water. Further problems and examples can deepen comprehension.
• Final Note: These principles apply to objects of any shape.