How to perform addition and subtraction in physics

In physics we often encounter calculations where you have to add two numbers together or we had to subtract one number from another. This is particularly important when data from practical sessions are processed even though additions and subtractions are often met in the syllabus.

However, as I have said in the introduction, the answer must be given to a certain number of decimal place. If you cannot say what the number of decimal place a number has, please refer to this post on decimal place.



Addition

Now let us see an example on how to add two numbers.

4.43

7.6    +

_____

12.03

____

12.0     Final answer.

So how do you give the answer to the appropriate number of decimal places? Add the two numbers and you get the answer 12.03. But this is not the final answer to the addition.

Before you write the final answer, look at the two numbers and determine the number of decimal places for each.

4.43    2 decimal places

7.6      1 decimal place

Now what is the smallest number of decimal places in the two numbers?

7.6 has 1 decimal place so the answer must have 1 decimal place. So the final answer is 12.0 with 1 decimal place.

Let us have a look at a second example.

67.54             2 decimal places

45.345            3 decimal places

______

112.885

112.89            Final answer2  decimal places

This is not the final answer. The two numbers used has 2 and 3 decimal places. So the final answer must be given to 2 decimal places. So the final answer is 112.89

Easy isn’t it.



Subtraction

Now we are going to see how subtraction is done. Here an example.

34.9

32.09  -

____

2.81

2.8      Final answer

So have you guessed how the answer is obtained?

The first number has 1 decimal place and the second number has 2 decimal places. As a result the answer must have 1 decimal place.

Let us have a look at a second example.

123.7             1 decimal place

3.433         3 decimal places

______

120.267

120.3             Final answer

1 decimal place

Have you got it? Let me summarise this with a rule.

When an addition or a subtraction is performed the answer is given to the same number of decimal places as the number used that has the smallest number of decimal places.

It is very important that you remember this law.

It is now time to do some exercises.

1. 12.45 + 34.555


2. 2.3 + 23.4445


3. 3.444 - 545


4. 34.3 – 34.111


5. 44.009 – 23.2

Do the following exercises and leave the answer in the comment section. I will give the correct answer later on when a few of you have submitted your answers.

What is a physical quantity?

Physical quantities

A physical quantity is a property of an object that can be measured with a measuring instrument.For example length, width, time, weight, etc.

It is important for you to be able to say which instrument is used to measure which physical quantity.The table below shows a few examples of physical quantities and the instruments used to measure them.

Physical quantity Instrument

Length                                                        Metre rule

Temperature                                            Thermometer

Time                                                             Stopwatch

Volume                                                       Measuring cylinder

Of course as we go through the different chapters we will be able to introduce more physical quantities and their measuring instruments.

Basic and derived quantities

Quantities can be divided into two types :

1. Base quantities

2. Derived quantities

Basic quantities

Basic quantities are the fundamental quantities that are not related to each other and that are use to derive all other quantities.

There are seven basic quantities. They are

1.  length

2.  time

3. mass

4. Thermodynamic temperature

5. electric current

6. amount of substance

7. luminous intensity

Derived quantities

Derived quantities are just quantities that are derived from one or more basic quantities.

For example area is a derived quantity because it is derived from the basic quantity length.

Area = length * length

Volume is a derived quantities because it is derived from the basic quantity length.

volume = length * length * length

density is a derived quantity because it is derived from length and mass, two basic quantities.

density = mass/(length * length * length)

As you can see all other quantities apart from the 7 basic quantities are derived from the seven basic quantities and it can easily be shown as in the example above.

Can you show what are the basic quantities that are used to derive the following derived quantities?

a) force

b)  kinetic energy

c) power

d) pressure

I would give the answer after a few of you would have give your answers.

Good luck and see you next time.

What is power?

Power is the rate of doing work.

From the definition we can deduce the following equation

Power = Work done /Time taken

The unit of power is the Watt (symbol W) or the Joule/second (J/s)

Example 1

A boy pushes a box and as a result does 120 J of work in 10 s. What is the power developed by the boy?

Power = Work done / time taken

= 120 /10

= 12 W or J/s

There is another definition for power that is often used. It is

Power is the rate of dissipation of energy or the rate of change of energy conversion.

Power = Energy dissipated / Time taken

Example 2

A girl climbs a staircase gaining 500 J of gravitational potential energy in 10 s.

What is the power developed by the girl?

Power = Energy conversion / Time taken

= 500 / 10

= 50 W or J/s

Example 3

During the boiling of some water 4000 J of heat energy is dissipated in the kettle’s heater in a time of 8 s. What is the power of the heater?

Power = Energy dissipated/Time taken

= 4000/8

= 500 W or J/s

It is now time to do some questions. It will give these questions after a few of you have supplied your answers.

1. A trains of mass 50000 kg accelerated form rest and reaches a velocity of 50 ms^-1 in 60 s.

(a) Calculate the kinetic energy gained by the train.

(b) Calculate the power of the train engine.

2. A lamp is rated 80 W. If it is switched on for two hours, how much light energy is dissipated.

Work done

Work done is a very important concept in Physics as it is used in fields, in deriving gravitational potential energy and kinetic energy, etc.

So what is work done?

Let us look at the diagram above. A force F acts on the box at A. During the time the force is acting, the box moves in the direction of the force. When the application of the force stopped the box has moved a distance d.

Using the definition

Work done is the product of the force acting on an object and the distance moved by the object in the direction of the force.

We can deduce that the equation to calculate work done is

Work done = Force * distance moved in the direction of the force

Work done = F *d

Let us have a look at an example.

Example

A man pulls a table by exerting a force of 100 N on it moving it by a distance of 3.9 m.

Calculate the work done by the man?

Work done = Force * distance moved in the direction of the force

Work done = F *d

= 100 * 3.9

= 3900 J

If you have understood the concept do the question below.

Question

A braking force of 2.3*10⁴ N is applied to a car and as a result the car stops in a distance of 23 m. Calculate the work done in stopping the train.

Good luck.

Physical quantities and units

Physical quantities

What is a physical quantities?

Subject of formula

Subject of formula: The basics

Vectors

What is a vector and how to add vector

Scalar and vector quantities

How to subtract one vector from another

Units

Base Units
Derived units

Homogeneity of equations 

Prefixes

Prefixes  and how to use them

Measurement of physical quantities

Volume and volume of irregular objects

Prefixes

How to use prefixes

Introduction

Hello my pupils,

I have been a physics teacher for the last eight years. Though the subject is very difficult, I have found that there are very few resources available on the internet where students can interact with the students. Hence I have decided to set up this blog . The aim of this blog is to gradually build a series of posts that would explain the difficult concepts in physics. Students would be able to ask questions and interact with the other students and with the teacher.

I hope that this attempt would bhelpful to us all and would help our students to better understand physics.

John Tan