A beaker of mass m beaker containing oil of mass m oil (density =ρ oil ) rests on a scale. A

step 1 Question number 64. First of all, we will find the reading of the spring scale. To find it first

A beaker of mass m beaker containing oil of mass m oil ...

A beaker of mass $m_{\text { beaker }}$ containing oil of mass $m_{\text { oil }}$ (density $=\rho_{\text { oil }} )$ rests on a scale. A block of iron of mass $m_{\text { iron }}$ is suspended from a spring scale and completely submerged in the oil as in Figure $\mathrm{P} 14.63 .$ Determine the equilibrium readings of both scales.

Key Concepts

Archimedes' Principle

This principle states that a body completely or partially submerged in a fluid experiences an upward force equal to the weight of the fluid that it displaces. It is fundamental in determining the magnitude of the buoyant force acting on immersed objects and is applicable irrespective of the depth at which the object is submerged.

Buoyant Force

The buoyant force is the net upward force exerted by a fluid on an object immersed in it. It is equal to the weight of the displaced fluid and is the main reason why objects feel lighter when submerged. In equilibrium problems, this force counteracts part of the object's weight and affects measurements taken by scales.

Apparent Weight

Apparent weight is the weight that an object seems to have when it is immersed in a fluid, which is less than its actual weight due to the upward buoyant force. This concept is critical in analyzing forces in fluids, particularly when calculating the readings of scales or tension in supporting springs.

Force Equilibrium in Fluids

Analyzing force equilibrium involves accounting for all forces acting on an object, including gravitational forces, buoyant forces, and any applied forces such as tension in a spring. In equilibrium, the sum of these forces equals zero, which is essential for determining system parameters such as scale readings.

System Weight and Force Transmission

In systems where components are connected and interact through fluids, the weight measured by a supporting scale includes contributions from all objects and fluids in the system. Understanding how forces, such as buoyant forces on submerged objects, are transmitted through the system is key to correctly interpreting scale readings and overall system behavior.

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