A tank containing oil of sp gr =0.80 rests on a scale and weighs 78.6 N. By means of a very fin

step 1 Find the tension of the wire. To find our tension in our wire, we need our weight of our aluminu

A tank containing oil of sp gr =0.80 rests on a scale and...

A tank containing oil of sp gr $=0.80$ rests on a scale and weighs $78.6 \mathrm{~N}$. By means of a very fine wire, a $6.0 \mathrm{~cm}$ cube of aluminum, sp gr $=2.70$, is submerged in the oil. Find $(a)$ the tension in the wire and $(b)$ the scale reading if none of the oil overflows.

Key Concepts

Tension in the Wire

In situations where an object is suspended in a fluid by a wire, the tension in the wire is reduced by the buoyant force acting upward. The tension is essentially the difference between the object's weight in air and the buoyant force due to the displaced fluid. This concept applies widely in determining forces in systems that involve suspended weights in fluids.

Buoyant Force

Buoyant force is the upward force exerted by a fluid on any object immersed in it. According to Archimedes' Principle, this force equals the weight of the fluid that has been displaced by the object. Calculating this force requires knowledge of the displaced fluid's volume and density, making it essential for problems involving submersion and equilibrium in fluids.

Scale Reading in a Displacement System

When an object is submerged in a liquid contained within a tank on a scale, the displaced liquid’s weight is effectively added to the overall system weight that the scale measures. Even though the object is supported by a wire (reducing the tension measured there), the fluid transmits the additional load to the container, thereby increasing the apparent weight recorded by the scale. This concept connects directly with the conservation of forces within the system.

Specific Gravity

Specific gravity is the ratio of the density of a substance to the density of a reference substance, typically water. It allows one to easily compare the densities of different materials without directly dealing with units, and it is crucial for converting volume into mass (or weight) using the known density of water as a baseline.

Archimedes' Principle

Archimedes' Principle states that any object submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces. This principle is fundamental in determining both the buoyant force acting on the object and how that force affects measurements such as tension in a supporting wire or the apparent weight on a scale.

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