2022 | 1ª Série | Matemática | Aula 2 - Sistema Internacional de Unidades (SI) II

Summary

In this lesson, teacher Eliane explains the International System of Units (SI), focusing on both base and derived units. The video covers key derived units such as area, volume, force, pressure, and power, highlighting their practical applications. Through real-life problems, viewers are guided to calculate areas, percentages, and convert units like velocity from meters per second to kilometers per hour. The lesson offers a comprehensive understanding of SI units and their real-world use, making complex concepts more accessible with detailed explanations and exercises.

Takeaways

• 😀 The International System of Units (SI) is based on seven fundamental quantities, but there are also derived quantities.
• 😀 Derived units are used to measure quantities like area, volume, mass concentration, speed, and acceleration.
• 😀 Examples of derived units include square meters (m²) for area, cubic meters (m³) for volume, and kilograms per cubic meter (kg/m³) for mass concentration.
• 😀 Some derived units have specific names and symbols, such as the Newton (N) for force and Pascal (Pa) for pressure.
• 😀 The concept of derived units can be seen in various everyday measurements like speed (m/s) and force (N).
• 😀 The class exercises in the script involve real-world applications, such as calculating the maximum area for building a house on a rectangular plot of land.
• 😀 In the house-building problem, the area of the house is determined by subtracting required setbacks from the total area of the plot.
• 😀 To calculate the percentage of the total land area used for construction, a proportion-based approach (rule of three) is applied.
• 😀 Another exercise explores converting between meters per second and kilometers per hour, showing how one meter per second equals 3.6 kilometers per hour.
• 😀 A final exercise demonstrates how to calculate speed in meters per second when given a speed in kilometers per hour, converting the value through a simple ratio.

Q & A

What are the seven base quantities of the International System of Units (SI)?

The seven base quantities of the International System of Units (SI) are: length (meter), mass (kilogram), time (second), electric current (ampere), thermodynamic temperature (kelvin), amount of substance (mole), and luminous intensity (candela).

What is a derived unit, and can you give examples of derived units?

A derived unit is a unit that is defined by combining the base units. Examples include area (square meter), volume (cubic meter), speed (meter per second), acceleration (meter per second squared), force (newton), pressure (pascal), and power (watt).

How is the area of a rectangular plot of land calculated in the context of the given exercise?

The area of a rectangular plot of land is calculated by multiplying its length and width. In the exercise, after accounting for the setbacks, the maximum area available for the house is 19 meters by 7 meters, resulting in an area of 133 square meters.

How do you calculate the percentage of the land used for construction in the given exercise?

To calculate the percentage of the land used for construction, divide the area of the house (133 m²) by the total area of the land (250 m²) and multiply by 100. The result is 53.2%, meaning the house occupies 53.2% of the land.

What is the unit conversion between meters per second (m/s) and kilometers per hour (km/h)?

To convert meters per second (m/s) to kilometers per hour (km/h), multiply the value by 3.6. For example, 1 m/s equals 3.6 km/h.

How can you calculate the speed of a runner in meters per second if you know the distance covered in kilometers per hour?

To calculate the speed in meters per second, convert the distance in kilometers per hour to meters per second by multiplying by 1000 (for kilometers to meters) and dividing by 3600 (for hours to seconds). For example, 18 km/h is equivalent to 5 m/s.

What is the unit of force in the International System of Units (SI), and how is it expressed?

The unit of force in the International System of Units (SI) is the newton (N). It is expressed as kg·m/s², which represents the force needed to accelerate a mass of one kilogram by one meter per second squared.

What are the basic principles behind the calculation of area in a problem involving setbacks, as shown in the exercise with the rectangular plot?

The calculation involves subtracting the setbacks from the total dimensions of the land to determine the available space for construction. In the exercise, setbacks of 4 meters at the front, 2 meters at the back, and 1.5 meters on each side reduce the total area where the house can be built.

Why is drawing a diagram helpful in solving problems like the one involving the construction of the house?

Drawing a diagram helps visualize the problem, making it easier to understand the given measurements and how the setbacks reduce the usable area of the land, thus simplifying the calculations.

What does the unit of pressure, Pascal (Pa), represent, and how is it expressed in terms of basic units?

The unit of pressure, Pascal (Pa), represents one newton per square meter (N/m²). It is expressed in terms of the basic units as kg/(m·s²), which reflects the force applied over an area.