5.3 Measuring mass or weight (EMG4J)

The scientific parole for how much an object weighs on a descale is "mickle". In that book we wish use the row "weight" and "mass" interchangeably, because both are utilized in everyday language. For example "I weigh \(\text{60}\) \(\text{kg}\)" or "the car's batch is \(\text{1}\) t".

In many contexts, we expend scales to measure weight or mass. Different types of scales are accustomed measuring stick different sizes of objects. More or less examples are bestowed in the table down the stairs:

Kitchen scales can be misused to measurement teeny-weeny quantities of food usually up to \(\text{2}\) or \(\schoolbook{3}\) \(\text{kilogram}\). The scale on the left put up measure burthen 'tween \(\text{0}\) and \(\text{2}\) \(\textual matter{kilogram}\) 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 Oregon at markets. The scale on the left can measure weight from \(\text{0}\) to \(\schoolbook{10}\) \(\text edition{kg}\).

Bathroom scales can be analog or extremity (similar the scale connected the left). They are wont to measure a person's weight down, and give notice measurement weight from \(\text{0}\) to \(\text{150}\) \(\text{kg}\). Bathroom scales unremarkably show units in kilograms and grams - e.g. \(\text{63,6}\) \(\text{kilo}\).

Clinics and doctors' practices often use larger analog scales to measure a person's weight. These can also measure exercising weight between \(\textual matter{0}\) and \(\text{150}\) \(\textual matter{kilogram}\).

Flat electronic scales, titled political program scales, can be wont to measure big objects like suitcases (at the airport) or dogs (at the vet).

Weighbridges are utilized to cadence really large objects like trucks. The truck drives onto a special landing strip of itinerant that is connected to a member scale. The plate operator (shown in the picture on the left) then reads off the truck's weight in tonnes.
Analogue scale
A scale that has no electronic devices attached thereto, (e.g. LCD screens).
Digital plate
A scale that has electronic devices on that like digital and LCD screens.
Standardization
This is operation by which a scale is set in regularize to take accurate readings.

Most analogue scales can become inaccurate when they are moved around, because they have moving parts inside that can stir if the scale is bumped operating room dropped. Therefore, ahead we use an analog weighing machine 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 titled re-calibration.

Integer 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 graduated on-the-spot (usually by a professional organize or technician).

Worked example 3: Measuring weight

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

    1. How much does this Sir Tim 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 arrange these sweet potatoes press in grams?
    2. Convert this to kg.
  4. What is the maximum weight that the scale used for the above tierce questions can measure?
    1. \(\text{600}\) \(\text{g}\)
    2. \(\text edition{600}\) \(\text{g}\) \(\div\) \(\text edition{1 000}\) = \(\text{0,6}\) \(\text{kilo}\)
    1. \(\text{1}\) \(\text{kg}\)
    2. \(\text{1}\) \(\text{kilo}\) \(\multiplication\) \(\text{1 000}\) = \(\text{1 000}\) \(\school tex{g}\)
    1. \(\text{300}\) \(\text{g}\)
    2. \(\text edition{300}\) \(\div\) \(\text{1 000}\) = \(\text{0,3}\) \(\text{kg}\)
  4. \(\text{3}\) \(\text{kg}\).

Calculating weightiness

Practise 5.2

A rise in a plaza has a mark that indicates that it can carry \(\schoolbook{2,2}\) tonnes or a maximum of \(\schoolbook{20}\) multitude. Convert the tonne measure to kilograms and figure what the engineer WHO built the lift estimated the maximum weight of a person to be.

\(\text{2,2}\) \(\textbook{t}\) = \(\text{2 200}\) \(\text{kg}\). \(\textual matter{2 200}\) \(\textual matter{kilo}\) \(\div\) \(\text{20}\) populate = \(\text{110}\) \(\text{kg}\) each.

If \(\text{50}\) people, with average weight of \(\text{80}\) \(\text{kg}\) per mortal, and one piece of luggage each that weighs an average of \(\textual matter{29}\) \(\text{kg}\), what would constitute the total load existence carried past the jitney in tonnes?

(\(\text{50}\) \(\times\) \(\text{80}\) \(\text{kg}\)) + (\(\text edition{50}\) \(\times\) \(\text{29}\) \(\textbook{kilogram}\)) = \(\textbook{4 000}\) \(\text{kg}\) + \(\text{1 450}\) \(\schoolbook{kg}\) = \(\text{5 450}\) \(\text{kg}\) = \(\text{5,45}\) \(\schoolbook{t}\).

If the bus weighs \(\text{4}\) tonnes, how much does it weigh in tally (in kg) including complete the passengers and the luggage?

\(\text{4}\) \(\text{t}\) = \(\text{4 000}\) \(\text{kg}\). \(\textual matter{4 000}\) \(\text{kg}\) + \(\text{5 450}\) \(\text{kg}\) = \(\text{9 450}\) \(\text{kilogram}\).

If John weighed \(\text{85}\) \(\text{kg}\) at the time he practical for the job, what is the maximum exercising weight that he can weigh in gild to ray-implement for the caper?

\(\text{80}\) \(\text{kilogram}\)

John weighs \(\text{78}\) \(\text{kg}\) when he weighs himself after six months. Do you think atomic number 2 tail end reapply for the chore? Explain your respond.

Yes - he weighs to a lesser degree \(\school tex{80}\) \(\text{kg}\) and has lost more than the minimum \(\text{5}\) \(\text edition{kilo}\).

Suppose that a monger buys a package of \(\text{250}\) \(\textbook{g}\) Sweet Wad tins for resale. Calculate the total burden of the tins in the box, in kilo.

\(\text{250}\) \(\text{g}\) \(\times\) \(\text{25}\) = \(\school tex{6 250}\) \(\text{g}\) = \(\textbook{6,25}\) \(\textual matter{kg}\).

If He orders \(\textual matter{15}\) boxes of Treacly Jam, calculate the total weight of his ordinate in kg.

\(\text{15}\) boxes \(\multiplication\) \(\textbook{6,25}\) \(\text{kg}\) = \(\text{93,75}\) \(\text edition{kg}\)

Worked example 4: Personalized weight and health

Annabelle weighs herself one time a week (at the same hour, 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)

\(\text{65,5}\)

\(\textbook{65,9}\)

\(\text{65,2}\)

\(\text edition{64,6}\)

\(\text{65,8}\)

\(\text edition{65,0}\)

\(\text{65,1}\)

\(\text{64,5}\)

  1. What is the difference (in kilo) between her weight on 1 Feb and 21 March?
  2. By how much did her weight increase between 21 Feb and 1 Butt against?
  3. Give two possible explanations for wherefore her weight went up all of a sudden on 1 March.
  4. Plot of ground a graph showing Annabelle's weight changes per week (you should have dates on the horizontal axis of rotation and kilograms on the vertical axis).
  1. \(\text{65,5}\) \(\text{kg}\) - \(\text{64,3}\) \(\text{kg}\) = \(\text{0,8}\) \(\text{kilo}\). She weighs \(\text{0,8}\) \(\text{kg}\) less on the 21st March.
  2. By \(\text{1,6}\) \(\text{kg}\).
  3. Either she ate a bunch of food in the week 'tween 21 Feb and 1 March (which is unlikely - it is difficult to gain \(\text{1,6}\) \(\text{kg}\) of angle in extraordinary week!), or she did non check that the surmount was set to "\(\text{0}\) \(\text{kg}\)" before she weighed herself.

Monitor your weight at home

Exercise 5.3

What is the difference of opinion between your weight on Day 1 and Twenty-four hours 7, if any?

Learner-dependent answer.

Game a graph viewing your weight measurements.

Learner-dependent answer.

Are thither any measurements that are unexpectedly low surgery high? If so, give reasons why you think this may atomic number 4. (Tinge: your weight shouldn't fluctuate much in a week but factors the likes of how much irrigate you've had to drink or how much you've had to eat can influence the measurements!)

Assimilator-dependent answer.

Hard whether or not your shoal bag is too arduous

Exercise 5.4

Determine \(\text{15}\%\) of Elias's weight.

\(\text{9,9}\) \(\text{kilogram}\)

Is his base too heavy for him?

Yes. It weighs more than \(\textbook{9,9}\) \(\text{kilogram}\).

Determine \(\text{15}\%\) of Elizabeth's weight.

\(\text{10,8}\) \(\text{kilogram}\)

Is her bulge too heavy for her?

No. It weighs less than \(\text{15}\%\) of her body weight.

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

Learner-dependent answer.

Weigh yourself.

Learner-dependent do.

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

Learner-dependent response

Is your school bag to a fault heavy for you? Give a reason for your answer.

Learner-dependent answer.

Worked example 5: Calculating cost from weight

Khuthele School has two soccer fields. The grass require to be covered with fertiliser. A purse of \(\text{30}\) \(\text{kilogram}\) of fertiliser costs \(\text{R}\,\text{42,60}\). The schooltime will pauperism to buy \(\text{96}\) bags. How much testament they pay for the fertiliser? How more kg leave they buy altogether?

Number of bags \(\times\) price: \(\text{96}\) \(\multiplication\) \(\text{R}\,\text{42,60}\) = \(\text{R}\,\text{4 089,60}\)

Routine of bags \(\times\) weight of one bag: \(\text{96}\) \(\times\) \(\text{30}\) \(\textual matter{kg}\) = \(\textual matter{2 880}\) \(\schoolbook{kg}\)

Worked example 6: Calculating cost from weight

Mr. Booysens needs to buy sand to build a new board onto his house. Sand is oversubscribed for \(\text{R}\,\text{23}\) per kg. Suppose Mr. Booysens of necessity to steal \(\text{0,8}\) tonnes of sand in order to build the room.

  1. Write the sum of sand needed in kg.
  2. Calculate the aggregate sum of money of money he will have to spend to grease one's palms enough sand for the picture.
  3. If sand is only sold in \(\text{50}\) \(\text{kilogram}\) bags, how many bags wish Mr Booysens want to bribe?
  1. Think that \(\text{1}\) tonne = \(\text{1 000}\) \(\text{kg}\)

so he inevitably \(\text{0,8}\) tonnes \(\multiplication\) \(\text{1 000}\) \(\text{kg}\) = \(\text{800}\) \(\text{kilogram}\)

  1. Quantity of gumption needed \(\times\) Cost per kg \(\textbook{800}\) \(\multiplication\) \(\text{23}\) = \(\school tex{R}\,\text{18 400}\)
  2. \(\text{800}\) \(\schoolbook{kg}\) \(\div\) \(\text{50}\) \(\text{kilogram}\) = \(\text{40}\) bags of sand.

Measuring angle and calculating costs

Exercise 5.5

Rice is sold in packets of \(\text{2}\) \(\textbook{kg}\). How umpteen packets will he necessitate for this meal?

\(\text{2}\)

Suppose IT costs \(\text{R}\,\text{31,50}\) per \(\textual matter{2}\) \(\text{kg}\) pack. Calculate the total cost of Sir Tim Rice he will need.

\(\school tex{2}\) \(\times\) \(\school tex{R}\,\text{31,50}\) = \(\text{R}\,\text{63,00}\)

If beef cattle costs \(\text{R}\,\textual matter{41,75}\) per kilo, calculate the total cost of beef needed for this meal.

\(\text{R}\,\text{41,75}\) \(\times\) \(\text{1,5}\) \(\text{kg}\) = \(\text{R}\,\text{62,63}\)

Calculate the total cost of preparing the meal. (Assume that totally the past ingredients are available for free).

\(\text{R}\,\text{63,00}\) + \(\text{R}\,\text edition{62,63}\) = \(\text{R}\,\text{125,63}\)

what type of instrument is used to measure mass

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