Question

If a solid block of glass, with a volume of exactly 100 in. \({ }^{3},\) is placed in a basin of water that is full to the brim, then of water will overflow from the basin.

Short answer

When the solid block of glass with a volume of 100 in.\(^{3}\) is placed in the basin, 100 in.\(^{3}\) of water will overflow from the basin.

Step-by-step solution

Identify the volume of the glass block.

We are given that the solid block of glass has a volume of exactly 100 cubic inches.

Determine the amount of water displaced by the glass block.

Since the block is fully submerged in water and the volume of water displaced is equal to the volume of the glass block, the amount of water displaced by the block is also 100 cubic inches.

Calculate the amount of water overflow from the basin.

The amount of water overflowing from the basin is equal to the amount of water displaced by the glass block, which is 100 cubic inches. Therefore, 100 cubic inches of water will overflow from the basin when the solid block of glass is placed in it.

Key concepts

Volume Displacement

Understanding the concept of volume displacement is critical in several scientific fields, including chemistry and physics. Essentially, volume displacement refers to the amount of fluid that is moved out of the way when an object is submerged in that fluid.

Let's say you have a container filled to the brim with a liquid, such as water, and you place an object inside the container. The object will displace a volume of water equivalent to the volume of the part of the object that is submerged. This is exactly what happens in the exercise, where a glass block with a specified volume displaces the same amount of water when it's completely submerged.

One practical application of this concept is measuring the volume of irregularly-shaped objects, which is difficult to calculate using simple mathematical formulas. By submerging the object in water and measuring the volume of water displaced, one can accurately determine the object's volume. This method is especially crucial in fields that require precise volume measurements, such as material science and engineering.

Water Displacement Method

The water displacement method is a practical technique that's often used for measuring the volume of an object. According to the method, the volume of water displaced by an object when submerged in water is equal to the volume of that object.

In our exercise scenario, the solid glass block has a known volume of 100 cubic inches. When this block is submerged in a basin full of water, it pushes out an equal amount of water – this is the 'displacement' part. This is how the water displacement method confirms the principle of volume conservation; the space taken up by the object in the fluid is precisely accounted for by the fluid that gets pushed out.

Steps to Use the Water Displacement Method:

• Fill a container with water to the brim.
• Carefully submerge the object into the water.
• Collect the displaced water in another container, if necessary.
• Measure the volume of the displaced water to find the volume of the object.

For most accurate results, it's essential for the water level to be exactly at the brim and for the object to be fully submerged without any air pockets. Educators often use this method in classrooms to visually demonstrate the conservation of volume and to teach about displacement.

Archimedes' Principle

One of the foundational principles in fluid mechanics is Archimedes' principle. It states that any object, wholly or partially submerged in a fluid, is buoyed up by a force that is equal to the weight of the fluid displaced by the object. This principle is what the water displacement method is based upon.

The classic story of Archimedes discovering this principle in his bath led to the famous exclamation 'Eureka!' As he submerged himself in the bath, he noticed the water level rise and realized that the volume of water displaced was equal to the volume of the part of his body submerged in the water. This principle not only explains why objects float or sink but is also the principle behind calculating the volume of objects through displacement.

Implications of Archimedes' Principle:

• It helps explain the buoyant force of fluids.
• It is essential for the design of ships and submarines which must have calculated buoyancy to float.
• It can be used to measure the density and specific gravity of objects.

Archimedes' principle extends beyond water; it applies to all fluids, including gases. Students learning Archimedes' principle can experiment with objects of different densities and shapes to understand how the force of buoyancy is influenced by the volume of fluid displaced.