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## Measuring mass or weight

The scientific word for how much an object weighs on a scale is “mass”. In this book we will use the words “weight” and “mass” interchangeably, because both are used in everyday language. For example “I weigh 60 kg” or “the car's mass is 1 tonne”.

In many contexts, we use scales to measure weight or mass. Different types of scales are used to measure different sizes of objects. Some examples are given in the table below:

 Kitchen scales can be used to measure small quantities of food usually up to 2 or 3 kg. The scale on the left can measure weight between 0 and 2 kg in weight. The units are divided into kilograms and grams. Scales for measuring larger quantities of food (like vegetables or fruit) are sometimes seen in shops or at markets. The scale on the left can measure weight from 0 to 10 kg. Bathroom scales can be analog or digital (like the scale on the left). They are used to measure a person's weight, and can measure weight from 0 to 150 kg. Bathroom scales usually show units in kilograms and grams - e.g. 63,6 kg. Clinics and doctors' practices often use larger analog scales to measure a person's weight. These can also measure weight between 0 and 150 kg. Flat electronic scales, called platform scales, can be used to measure bulky objects like suitcases (at the airport) or dogs (at the vet). Weighbridges are used to measure very large objects like trucks. The truck drives onto a special strip of road that is connected to a digital scale. The scale operator (shown in the picture on the left) then reads off the truck's weight in tonnes.
Definition 1: Analogue scale
A scale that has no electronic devices attached to it, (e.g. LCD screens).
Definition 2: Digital scale
A scale that has electronic devices on it like digital and LCD screens.
Definition 3: Calibration
This is process by which a scale is set in order to take accurate readings.

Most analogue scales can become inaccurate when they are moved around, because they have moving parts inside that can shift if the scale is bumped or dropped. Therefore, before we use an analogue scale we has to adjust the scale to make sure that it gives the most accurate readings possible. This process of adjusting the scales again is called re-calibration.

Digital scales are calibrated (adjusted for accuracy) in the factory when they are made and do not become inaccurate when they are moved. Other, larger scales like a weighbridge will be calibrated on-site (usually by a professional engineer or technician).

## Example 1: Measuring weight

### Question

Study the following pictures of food on a scale and answer the questions that follow:

1. How much does this rice weigh in grams?
2. Convert this to kilograms.
1. How much does this flour weigh in kilograms?
2. Convert this to grams.
1. How much do these sweet potatoes weigh in grams?
2. Convert this to kg.
1. What is the maximum weight that the scale used for the above three questions can measure?

1. 600 g
2. 600 g $$\div$$ 1000 = 0,6 kg
1. 1 kg
2. 1 kg $$\times$$ 1000 = 1000 g
1. 300 g
2. 300 $$\div$$ 1000 = 0,3 kg
1. 3 kg.

## Exercise 1: Calculating weight

A lift in a shopping mall has a notice that indicates that it can carry 2,2 tonnes or a maximum of 20 people. Convert the tonne measurement to kilograms and work out what the engineer who built the lift estimated the maximum weight of a person to be.

2,2 t = 2200 kg. 2200 kg $$\div$$ 20 people = 110 kg each.

A long distance bus seats 50 passengers and allows every passenger to each have luggage of up to 30 kg.

1. If 50 people, with average weight of 80 kg per person, and one piece of luggage each that weighs an average of 29 kg, what would be the total load being carried by the bus in tonnes?

2. If the bus weighs 4 tonnes, how much does it weigh in total (in kg) including all the passengers and the luggage?

1. (50 $$\times$$ 80 kg) + (50 $$\times$$ 29 kg) = 4000 kg + 1450 kg = 5450 kg = 5,45 t.

2. 4 t = 4000 kg. 4000 kg + 5450 kg = 9450 kg.

John applied for a job as a flight attendant but was told that he had to lose at least 5 kg before he met their maximum weight allowance (so that the plane - full of passengers, luggage and fuel - is not too heavy) and could reapply.

1. If John weighed 85 kg at the time he applied for the job, what is the maximum weight that he can weigh in order to re-apply for the job?

2. John weighs 78 kg when he weighs himself after six months. Do you think he can reapply for the job? Explain your answer.

1. 80 kg

2. Yes - he weighs less than 80 kg and has lost more than the minimum 5 kg.

Sweet Jam can be bought in bulk from a warehouse in boxes of 25 tins each.

1. Suppose that a trader buys a box of 250 g Sweet Jam tins for resale. Calculate the total weight of the tins in the box, in kg.

2. If he orders 15 boxes of Sweet Jam, calculate the total weight of his order in kg.

1. 250 g $$\times$$ 25 = 6250 g = 6,25 kg.

2. 15 boxes $$\times$$ 6,25 kg = 93,75 kg

## Example 2: Personal weight and health

### Question

Annabelle weighs herself once a week (at the same time of day, wearing similar clothes) for two months and records the following measurements:

 Date 1 Feb 7 Feb 14 Feb 21 Feb 1 March 7 March 14 March 21 March Weight (kg) 65,5 65,9 65,2 64,6 65,8 65,0 65,1 64,5

1. What is the difference (in kg) between her weight on 1 Feb and 21 March?
2. By how much did her weight increase between 21 Feb and 1 March?
3. Give two possible explanations for why her weight went up suddenly on 1 March.
4. Plot a graph showing Annabelle's weight changes per week (you should have dates on the horizontal axis and kilograms on the vertical axis).

1. 65,5 kg - 64,3 kg = 0,8 kg. She weighs 0,8 kg less on the 21st March.
2. By 1,6 kg.
3. Either she ate a lot of food in the week between 21 Feb and 1 March (which is unlikely - it is difficult to gain 1,6 kg of weight in one week!), or she did not check that the scale was set to “0 kg” before she weighed herself.

## Exercise 2: Monitor your weight at home

If you have a bathroom scale at home, monitor your weight every day for a week. Whilst you should weigh yourself at the same time and in the same kinds of clothes everyday to get consistent results, you may experiment with your measurements: for example, do you weigh more with your shoes on? Or do you weigh more before or after a meal? Don't forget to check that your scale is correctly calibrated before you take each measurement.

1. What is the difference between your weight on Day 1 and Day 7, if any?

2. Plot a graph showing your weight measurements.

3. Are there any measurements that are unexpectedly low or high? If so, give reasons why you think this may be. (Hint: your weight shouldn't fluctuate much in a week but factors like how much water you've had to drink or how much you've had to eat can influence the measurements!)

## Exercise 3: Calculating whether or not your school bag is too heavy

Read the following statements and complete the activities that follow:

According to mysafetyandhealth.com, you should never carry more than 15% of your body weight. Elias weighs 66 kg and his backpack, with school books, weighs 12 kg. Elizabeth weighs 72 kg and her school bag, with school books, weighs 8 kg.

1. Determine 15% of Elias's weight.

2. Is his bag too heavy for him?

3. Determine 15% of Elizabeth's weight.

4. Is her bag too heavy for her?

5. Using a bathroom scale, weigh your school bag, with your school books inside it.

6. Weigh yourself.

7. Do the necessary calculations in order to write the weight of your school bag as a percentage of your own weight.

1. 9,9 kg

2. Yes. It weighs more than 9,9 kg.

3. 10,8 kg

4. No. It weighs less than 15% of her body weight.

## Example 3: Calculating cost from weight

### Question

Khuthele School has two soccer fields. The grass need to be covered with fertiliser. A bag of 30 kg of fertiliser costs R 42,60. The school will need to buy 96 bags. How much will they pay for the fertiliser? How many kg will they buy altogether?

Number of bags $$\times$$ price: 96 $$\times$$ R 42,60 = R 4089,60

Number of bags $$\times$$ weight of one bag: 96 $$\times$$ 30 kg = 2880 kg

## Example 4: Calculating cost from weight

### Question

Mr. Booysens needs to buy sand to build a new room onto his house. Sand is sold for R 23 per kg. Suppose Mr. Booysens needs to buy 0,8 tonnes of sand in order to build the room.

1. Write the amount of sand needed in kg.
2. Calculate the total amount of money he will have to spend to buy enough sand for the project.
3. If sand is only sold in 50 kg bags, how many bags will Mr Booysens need to buy?

1. Remember that 1 tonne = 1000 kg

so he needs 0,8 tonnes $$\times$$ 1000 kg = 800 kg

1. Quantity of sand needed $$\times$$ Cost per kg
800 $$\times$$ 23 = R 18 400
2. 800 kg $$\div$$ 50 kg = 40 bags of sand.

## Exercise 4: Measuring weight and calculating costs

A chef is preparing a meal that needs 3,75 kg of rice and 1,5 kg of beef. The recipe will feed 8 people.

1. Rice is sold in packets of 2 kg. How many packets will he need for this meal?

2. Suppose it costs R 31,50 per 2 kg pack. Calculate the total cost of rice he will need.

3. If beef costs R 41,75 per kg, calculate the total cost of beef needed for this meal.

4. Calculate the total cost of preparing the meal. (Assume that all the other ingredients are available for free).

1. 2

2. 2 $$\times$$ R 31,50 = R 63,00

3. R 41,75 $$\times$$ 1,5 kg = R 62,63

4. R 63,00 + R 62,63 = R 125,63