In this article, we will explore how to calculate the tension in a string supporting an iron object of mass 180 g when it is fully submerged in a liquid of density 800 kg/m3. We will use the principles of buoyancy and weight to find the solution step by step. We will also discuss the application of Archimedes' principle and the force formulas.
Introduction
The problem involves finding the tension in a string holding a solid iron object that is completely submerged in a liquid. The key concepts involved are the weight of the iron object, the buoyant force due to the liquid, and the tension in the string that balances these forces. Let’s go through the detailed calculation.
Given Data
Mass of the iron object, m 180 g 0.180 kg Density of the liquid, rho;liquid 800 kg/m3 Density of iron, rho;iron 8000 kg/m3Step-by-Step Calculation
Step 1: Calculate the Volume of the Iron Object
The volume of the iron object can be calculated using the formula for density:
V frac{m}{rho;iron}
About the calculation:
V frac{0.180 text{ kg}}{8000 text{ kg/m}^3} 2.25 times 10^{-5} text{ m}^3
Step 2: Calculate the Buoyant Force
According to Archimedes' principle, the buoyant force is equal to the weight of the liquid displaced by the object:
F_b rho_{text{liquid}} cdot g cdot V
F_b 800 text{ kg/m}^3 cdot 9.81 text{ m/s}^2 cdot 2.25 times 10^{-5} text{ m}^3 approx 0.00177 text{ N}
Step 3: Calculate the Weight of the Iron Object
The weight of the iron object can be calculated using the formula for weight:
W m cdot g
About the calculation:
W 0.180 text{ kg} cdot 9.81 text{ m/s}^2 approx 1.764 text{ N}
Step 4: Calculate the Tension in the String
The tension in the string is the difference between the weight of the iron object and the buoyant force:
T W - F_b
About the calculation:
T 1.764 text{ N} - 0.00177 text{ N} approx 1.76223 text{ N}
Conclusion
The tension in the string is approximately 1.762 N. This calculation demonstrates the practical application of buoyant force and gravitational force in determining the tension in a supporting string for an immersed object.
Note: The gravitational constant, g, is typically taken as 9.81 m/s2 unless otherwise specified.