(a) Determine the force that a vertical string exerts on a...

(a) Determine the force that a vertical string exerts on a 0.80-kg rock of density of 3300 $kg / m^{3}$ when it is fully submerged in water of density 1000 $kg /m^{3} .(b)$ If the force exerted by the string supporting the rock increases by 12% when the rock is submerged in a different fluid, what is that fluid’s density? (c) If the density of another rock of the same volume is 12% greater, what happens to the buoyant force the water exerts on it?

Key Concepts

Density

Density is defined as the mass per unit volume of a substance. It is a fundamental property that helps determine whether an object will float or sink in a fluid, as it is compared with the fluid's density. It is also critical when relating the mass and volume of an object to derive other properties like buoyant force.

Apparent Weight

The apparent weight of an object in a fluid is the net weight observed when the buoyant force is taken into account. It is the actual weight minus the buoyant force. This concept helps in understanding how weights measured in fluids differ from those measured in air, particularly in problems involving support forces like those exerted by strings.

Archimedes' Principle

This principle states that any object wholly or partially immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced by the object. It explains why the apparent weight of an object in fluid is less than its true weight in air, forming the basis for analyzing buoyant forces in fluid mechanics.

Buoyant Force

Buoyant force is the upward force exerted by a fluid on an object submerged in it. It is calculated as the product of the density of the fluid, the volume of the displaced fluid, and gravitational acceleration. This force is crucial in understanding how objects float or sink in different fluids.

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