Course:
Integrated Science
By the end of this lesson, you should be able to:
In this subject, you’ll interact with various quantities, which can be classified into two classes. A quantity is something measurable, and understanding these classifications is essential.
This indicates that a quantity can be either a scalar or a vector. Let’s explore each in detail.
This is a quantity characterized solely by its magnitude (size). Examples of such quantities include:
Time: For instance, Theo took 2 hours and 30 minutes to travel from Gaborone to Johannesburg.
Mass: As an example, Lesego has a mass of 70 kg.
Distance: The distance between Francistown and Gaborone is 432 km.
Speed: Thabo’s car was traveling at a speed of 80 km/h.
By making such statements, learner, you have effectively detailed the quantities that needed to be addressed. The examples of quantities mentioned earlier include time, mass, distance, and speed.
This is a quantity defined by both magnitude and direction. To fully characterize a vector, both elements must be provided.
Examples of these include:
Displacement: The distance from Gaborone to Francistown is 432 km to the northeast.
Force: A downward force of 45 N is being applied to this plank.
Velocity: Mpho’s car was moving at a speed of 80 km/h toward the right.
Learner, do the following activity to check if you can distinguish a scalar from a vector.
What exactly is length? It’s a term we encounter frequently and interact with on a daily basis. You utilize it regularly when estimating and sometimes measuring distances. Now, here’s a chance for you to define it—please write your answer in the space provided below.
If you defined length as the distance between two points, you’re absolutely correct! You engage with the concept of length every day; for instance, you might want to know the length of your shirt sleeve or the length of your pencil. All of these can be measured using various instruments designed for measuring length, each with different units.
The standard unit of length, which is also the SI unit, is the metre. SI units are internationally recognized and are specific to a wide range of different quantities we encounter.
The standard unit for length is the metre (m). For smaller lengths, we use centimetres and millimetres, while kilometres are used for measuring long distances.
To convert 200 km from Mahalapye to Gaborone into meters, you multiply by 1,000 to get 200,000 m. This illustrates the conversion of non-standard measurements to the standard unit, the meter.
Learner, can you recall moments when you’ve estimated length? For example, when planning a trip, you likely have a general idea of the distance between your current location and your destination before setting out. You might also estimate a friend’s height or measure the length of your shoe. Naturally, the units you select will vary based on the length you are considering.
All measuring instruments feature scales marked on them, and each scale includes a unit specified on the instrument itself.
Rulers are essential tools in daily life for measuring lengths, such as fabric for tailoring or parts in auto spare shops. It’s important to understand how to use a ruler correctly and follow precautions while measuring.
Figure 5 : A Worn out ruler
At B the reading is 8.9 cm
This means that the length of the block of metal is 8.9cm -1.0 cm = 7.9 cm
At A the reading is 1.0 cm
While making a reading , always keep the eye vertically above the mark you are reading. If you take the reading from any other angle, the reading will not be correct and this will make an error called Parallax error.
The area of a regular object, such as a football pitch, measures the size of its surface. The formula to calculate area is:
Area = length x width.
Figure 7: A rectangular box
The formula for area is:
Area = Length × Breadth
Calculating the area:
= 5 cm × 3 cm = 15 cm²
In this case, the length of the box is 5 cm, and its breadth is 3 cm. The area of the top and bottom surfaces of the box is determined as shown above:
You already learned in the previous lesson that the SI unit of area is the square meter (m²). The unit of length is the meter (m), and thus, it follows that…
Estimating measurements is an essential skill to develop, as measuring instruments may not always be available. Practicing estimation is important, so let’s begin with an activity.
One effective method for determining the area of a leaf is by utilizing graph paper. Follow these steps to make your calculations:
Trace the outline of the leaf onto the graph paper.
Count the number of complete squares that fall within the outline.
Count the squares that are covered by more than half of a square.
Combine the two totals.
The sum you arrive at will provide an estimate of the leaf’s area.
We often purchase soft drinks in 330ml or 500ml containers. Volume can be defined as the space occupied by an object. The standard unit of volume is cubic meters (m³), with smaller volumes expressed in cubic centimeters (cm³). Commonly used volume units include liters (l) and milliliters (ml)
1 mL = 1 cm³
1 L = 1000 mL = 1000 cm³
You may be curious about how milliliters (mL) and cubic centimeters (cm³) relate to the standard unit of measurement. Let’s explore their relationships.
Learner, volume can be measured in various ways, depending on the substance or object’s shape.
Examine your book or any other rectangular-shaped object. How would you determine its volume? Please record the formula in the space provided below.
If you have noted the following formula, you are completely correct.
Volume = length × width × height
Volumes of liquids are typically measured with a measuring cylinder, which comes in various sizes. The scale used on these cylinders is in cubic centimeters (cm³) or milliliters (ml). When using a measuring cylinder, it’s important to follow certain precautions. Please complete the following activity to learn about these safety measures.
To enhance your understanding, let’s begin with an engaging activity.
A sinking object is one that descends to the bottom of a liquid when submerged. There are two widely used methods for measuring its volume:
Using a measuring cylinder
Using a measuring cylinder along with a displacement can
Let’s explore each method in detail.
Remember, when measuring the volume of regular objects, such as your textbook, you would measure their dimensions and apply a formula to calculate the volume. But what about measuring the volume of an irregular object, like a stone, or a floating object, such as a piece of cork?
Let’s begin with an engaging activity.
A floating object is one that stays on the surface of a liquid rather than sinking to the bottom of its container. To measure the volume of such an object, it must be attached to a sinking object with a known volume. The sinking object will pull the floating object underwater until it is completely submerged. You can use either a measuring cylinder or a displacement method for this process.
(c) Using a measuring cylinder and a displacement can
Estimating volumes relies on the experience acquired from handling various object sizes. To effectively estimate the volumes of liquids and solids, I propose we kick off with an engaging activity.
Quantities can be divided into two categories: scalar and vector.
Scalar: A quantity defined solely by its magnitude (size).
Vector: A quantity defined by both magnitude and direction.
Length: This refers to the distance between two points.
SI Unit: Metre.
It is measured using rulers.
The error that may occur during length measurement is termed parallax error.
Area: This indicates the size of an object’s surface.
SI Unit: Metres squared.
Area can be measured in various ways:
For regular objects, it is calculated by multiplying length by width.
For irregular objects, such as a leaf, graph paper can be utilized.
Volume: There are multiple methods to measure volume, depending on the object or substance and its shape.
The volume of regular objects can be determined using specific formulae.
For irregular objects, measuring cylinders and displacement cans can be employed.
Certain precautions should be observed when using a measuring cylinder.
The process of changing a unit of measurement into another unit while maintaining its size.
An action taken beforehand to prevent potential danger.
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