Question

State whether the following will sink or float when dropped into water. (a) $\mathrm{wax}(d=0.90\mathrm{g}/{\mathrm{cm}}^3)$ (b) marble $(d=3.5\mathrm{g}/{\mathrm{cm}}^3)$

Short answer

(a) Wax will float; (b) Marble will sink.

Step-by-step solution

Understand Density Concept

Objects with a density less than water's density (1.0 g/cm³) will float, while those with a higher density will sink. We'll compare each object's density to that of water.

Check Density of Wax

The wax has a density of 0.90 g/cm³. Since 0.90 g/cm³ is less than water's density of 1.0 g/cm³, the wax will float.

Check Density of Marble

The marble has a density of 3.5 g/cm³. Since 3.5 g/cm³ is greater than 1.0 g/cm³, the marble will sink in water.

Key concepts

Buoyancy

Buoyancy is the force that allows objects to float in a fluid, such as water. This force is proportional to the volume of the fluid displaced by the object. If the buoyant force on an object is equal to or greater than the gravitational force pulling it down, the object will float. When we talk about "floating," we are discussing this delicate balance of forces.
The buoyant force can be calculated using Archimedes' Principle, which states that the upward force, or buoyancy, is equal to the weight of the fluid displaced by the object. This is why a shape or a hollow object might float even if it is made of a dense material, like steel, provided it displaces enough water.

• An object that floats displaces a volume of water that weighs the same as or more than the object itself.
• An object that sinks displaces a volume of water that weighs less than the object.

Understanding buoyancy helps in predicting whether an object will float or sink by considering its density and how much water it displaces.

Floatation

Floatation is directly tied to buoyancy, as it describes the action of maintaining an object on the surface of a liquid without it sinking. The concept of floatation looks at whether an object will remain on top of a liquid based on its interactions with buoyancy.
When an object floats, it's because the buoyant force is balancing the gravitational pull on the object. In practical terms, floatation means stability on the surface. Floatation can vary depending on the shape and material of the object. For example, a boat floats even though it's made of heavy steel because it is designed to displace a lot of water and spread its weight over a larger area.

• If an object's density is less than that of the liquid, the object floats.
• Ballasts are sometimes used to adjust floatation by adding weight deliberately, like in a submarine.

Density Comparison

Density is a measurement of how much mass is contained in a given volume and is expressed as grams per cubic centimeter (g/cm³). When comparing densities, you can predict whether an object will sink or float in a fluid like water.
Let's pretend you have two objects. By comparing their densities with that of water, which is approximately 1.0 g/cm³, you can tell if they will sink or float:

• An object with a density less than 1.0 g/cm³, such as wax at 0.90 g/cm³, will float on the water's surface.
• An object like a marble, with a density of 3.5 g/cm³, will sink since its density is greater than that of water.

This concept can apply widely, from understanding why icebergs float even though they are made of dense ice, to designing ships and airplanes that maximize safety and efficiency.