The density of water is about 3.6×104^-2 pounds per cubic inch. Any object with a density that is less than this will float. Objects with a density greater than the density of water will sink.
Suppose a block of wood has a density of 0.022 pounds per cubic inch. What is the density of water written in standard form?
The Correct Answer and Explanation is:
To express the density of water given as (3.6 \times 10^{-2}) pounds per cubic inch in standard form, we need to convert it to a more familiar numerical format.
Density of Water in Standard Form
The notation (3.6 \times 10^{-2}) means that the decimal point in the number 3.6 should be moved two places to the left. This results in the following calculation:
[
3.6 \times 10^{-2} = 0.036 \text{ pounds per cubic inch}
]
Thus, the density of water, in standard decimal form, is 0.036 pounds per cubic inch.
Explanation
Density is defined as the mass of an object divided by its volume, typically expressed in units like pounds per cubic inch (lb/in³) or kilograms per cubic meter (kg/m³). The density of water is crucial in determining whether an object will float or sink when placed in water.
In the context provided, an object with a density less than that of water will float, while an object with a density greater than water’s density will sink. This principle is based on buoyancy, which is governed by Archimedes’ principle, stating that the upward buoyant force exerted on an object immersed in a fluid is equal to the weight of the fluid that the object displaces.
The density of the block of wood mentioned is given as (0.022) pounds per cubic inch. Since (0.022) is less than (0.036), the block of wood will float when placed in water. This is a practical application of the density concept, as it helps predict the behavior of materials in fluid environments.
In summary, the density of water is (0.036) pounds per cubic inch in standard form, and this information is essential for understanding buoyancy and the behavior of objects in water. This understanding is not only important in physics and engineering but also has practical implications in fields such as marine biology, environmental science, and even everyday activities like fishing or swimming.