What is the kilowatt-hour?

The kilowatt-hour is the unit in which usage of electricity is measured in the home.

You would remember that the SI unit of energy is the Joule (J)  as you have seen in  work done, gravitational potential energy or kinetic energy.

Now as you know the rating of home appliances is its power and the unit of power is the Watt (W).

Now if a kettle with a rating of 1000 W is used for two hours, then the amount of energy used will be calculated as shown:

Power = Energy used / time taken

Energy used = power * time taken  = 1000 * (2 * 3600)

                    = 7200000 J

                     = 7.2 MW (Megawatt)

However as you can see such calculation is difficult and beyond someone that is not a Physicist.

Hence in order to make matter more simple we use the Kilowatt-hour.

If we use the example above we would need to use the equation below:

Energy used in kilowatt-hour = power of appliance in Kilowatt  x time in hour

Hence the energy used = 2 kW x 2 h

= 4  kilowatt-hour (kWh)

As you can see it is quite simple to determine the the energy used in kilowatt-hour.

What is a photon?

A photon also known as a corpuscle or a quantum is the basic unit of electromagnetic radiation.

You will remember that the electromagnetic spectrum is made up of different radiations. These radiations are waves and as such they are energy being moved from one place to another.

The photon is simply a small packet of energy and a beam of electromagnetic radiation is just a stream of these photons travelling in a particular direction.

So if the photon is a packet of energy then you should be able to determine the energy of a photon of electromagnetic radiation.

The following equation is used:

Energy of a photon = Planck’s constant * frequency of electromagnetic radiation

E = h * f

Planck’s constant = 6.63 x 10^-34 m² kg s^-1

If you want to calculate the energy of a photon read this post .

What is pressure ?

When you have a force that is applied on a surface over a given surface area then you say that a pressure is being exerted on the surface.

Fig 1

Fig 1 shows a small wooden block placed on a wooden sheet. As you know every object has a weight. This weight as you would remember is a force of attraction that the earth is exerting on the object. Thus it is a downward force.

Hence we can deduce that block of wood due to its weight is applying a force F on the sheet. The force F  would act as shown in fig 2 below.

Fig 2

But we also know that the weight of the object, the force applied on the wooden sheet, is being applied over a surface area A. That surface area is shaded black in fig 3 below.

Fig 3

The pressure exerted on the wooden sheet by the wooden blockis thus the force acting perpendicularly per unit surface area.

Hence to calculate the pressure we have to use the equation below:

Pressure exerted = Force applied / surface area

The unit of pressure is thus the N m^-2

The pressure is a scalar quantity since it is obtained by dividing a vector quantity by a vector quantity.

What is the weight of an object?

Every object has a quantity known as the mass. The mass is simply the quantity of matter that it contains.

When according to the law of gravitation, a mass that is situated inside the gravitational field of the earth would experience an attractive force, a pull, as shown in fig 1 below.

Fig 1

Now this pull on the object is called the weight.

Hence the weight can be defined as the gravitational pull that the earth exerts on an object. 

Since it is gravitational pull it is a  thus a force and its unit is the Newton (N).

The weight is calculated according to the equation below:

weight = mass * acceleration due to gravity

w  = mg 

Example

A stone has a mass of 5.0 kg. Calculate it weight if the acceleration due to gravity is 9.81 m s^-2 .

Weight w = mg

               = 5.0 * 9.81

                = 49.05 N

                = 49 N

What is linear momentum?

Linear momentum is a physical quantity that depends on the mass and the velocity of the object.

Fig 1 below shows an object that has mass m and is moving with a velocity v.

 

The linear momentum which is denoted by the symbol p and is calculated using the equation below

 

linear momentum  = mass of object  x velocity of object

p = mv

Hence the unit for linear momentum is kg m s^-1

The linear momentum is thus a vector quantity since it is the product of a scalar quantity (the mass) and the vector quantity (the velocity).

We can thus say that the linear momentum of a body is defined as the product of the mass of that body and its velocity

Types of distance-time graph

As we have seen in this post on distance-time graph, it is easier to extract information from a distance-time graph than from a paragraph or from a table of time and distance travelled.

We have seen in this post the gradient of the distance-time graph is the speed. Hence you must be able to deduce how the speed of an object varies according to the shape of its distance time graph.

Let us now look at some distance-time graph and see how the speed varies with time. We will then look at the corresponding speed-time graph for the object.

1. Fig 1 below shows a distance-time graph shows that the distance travelled by the object from time  0 s to t s  is 0 m. This means that the object has not moved at all and as a result it is motionless at the starting point.

The gradient of the graph is 0, hence it means that form time o s to time t s, the speed is 0 m/s.

The speed-time graph is thus as shown in fig 2.

Fig 1

Fig 2

2. Fig 3 below is a distance-time graph that shows an object whose distance travelled is constant form 0 s to time t s. We can thus assume that the object is stationary. The gradient of the graph is thus 0 which means that the speed is also  0 m/s from 0 s to t s. The speed-time graph would thus be as shown in fig 4 below.

Fig 3

 

Fig 4

3. Fig 5 below is a distance-time graph that shows an objects moving and the distance travelled is increasing.

The gradient of the graph is the speed. From the graph the gradient is a constant value but is not zero. Hence the speed-time graph is as shown in fig 6.

Fig 5

Fig 6

4. In fig 7 below we have a distance-time graph that shows an object that is moving as a result the distance travelled is increasing.

As we know the gradient of the graph is the speed and since the gradient is increasing then is it means that the speed is increasing. Hence the speed-time graph of the object is as shown in fig 8.

Fig  7

Fig 8

Past exam papers

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Planning and analysis

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Practical skills

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Medical Physics

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Telecommunications

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Radioactive decay, fission and fusion

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Quantum physics and photoelectric effect

What is a photon?

What is the electron volt (eV) ?

How to calculate the energy of a photon?

Charged particles

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Alternating current

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Electronics

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Electromagnetic induction

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Electromagnetism

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Magnet and magnetic field

What is a magnet?

Dc circuits

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Current electricity

What is a complete circuit?

What is an electric current?

What is the conventional current?

What is the electromotive force (e.m.f.)

What is the potential difference?

What is the kilowatt-hour?

Capacitors

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Static electricity, charges and electric field

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Sound

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Light, mirrors and lens

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Superposition, interference and diffraction

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Waves and the electromagnetic radiations

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Oscillations, damping and resonance

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Temperature and its measurement

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Ideal gases and gas laws

Under construction

Deformation of solids

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Matter and the kinetic model

Matter

What are atoms?

gravitation

What is gravitational force ?

Distance-time graph

The ability to draw graphs and to obtain information from them is one of the most important skills that a physicist needs to develop. You are also able to extract information more easily using graphs.

Example 1

A boy starts to walk at t = 0 s and walks from point A to point B a distance of 100 m for 10 s . He then stops and walk back towards his starting point in a time of 10 s.  The motion is as shown in fig 1.

 

Fig 1

If you use a table to present this information then it would be as follows:

time /s	Distance travelled /m
0	0
10	100
20	200

Table 1

After 10 s the boy has walked a distance of 100 m. And after 20 s the boy has walked a distance of 200 m( 100 m from A to B and another 100 m from point B to A).

Hence we can plot this on a graph as shown in fig 2 below.

Fig 2

As you can see from this graph the different coordinates will the give you the distance that the boy has walked after a particular time.

Now that you can plot the motion of an object on a graph. Let us see what you can do with a distance-time graph.

You would remember that the speed of an object is the rate of change of distance with time and that it can be calculated using the following equation

speed = distance travelled / time taken

With the distance-time graph the speed of an object at a particular time is the gradient of the line at that particular point.

Now what is the speed of he object at 5 s?

You will have to determine the gradient of the line at 5 s.

Hence the two coordinates that can be used are

(0,0)  and (10,100)

The gradient is thus

gradient = (y1 –y2)/(x1-x2)

                   = (0-100)/(0-10)

                   = –100/-10

                   10

Hence since the gradient a distance-time graph is the speed

speed at 5 s = 10 m/s

Moment, torque and equilibrium

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Pressure and upthrust

Pressure 

What is pressure?

Motion and equations of motion

Distance and displacement

Speed and velocity

Acceleration

Gradient and how to determine it?

Types of distance-time graph

First equations of motion

Second equation of motion

Third equation of motion

Errors and uncertainties

 

Rules to perform mathematical operations

 Addition and subtraction/Addition and subtraction

Multiplication and division/Multiplication and division

lg and ln

Uncertainty and errors

Addition and subtraction

Multiplication and division

root, powers, etc

Errors

What is an error?

What is a zero error?

What is a parallax error?

What is angular velocity ?

As we have seen in this post an object undergoing circular motion has an angular displacement.

Hence the object will also have an angular velocity.

You will recall that velocity is the rate of change of displacement.

Let us look at an example of an object that is undergoing circular motion.

Fig 1                                              Fig 2                                                           

In fig 1 above a person moves in a circular path moving from A to B.

Thus the person can have an angular displacement θ in a time t.

We can thus calculate the angular velocity according to the equation below:

What if the person completes one complete turn?

Then the angular displacement will be 360^o or 2π rad.

The time taken to perform the complete turn will be the time period denoted by the letter T.

Thus the angular velocity will be calculated using the following equation:

Introduction to circular motion

Circular motion as the name suggest is the motion of an object in a circular path.Examples of circular motion is the motion of a car around a roundabout, a satellite around the earth or a stone tied to a string being whirled by the hand.

Centre of rotation

In fig 1 below you can see a circular path and a person is  moving in that circular path.

 

Fig 1

The person would move in such a way that at all time it would remain at the same distance from a point that we call the centre of  rotation. It is usually indicated by the symbol O in a diagram as you can see in fig 1.

Fig 2

Radius of circular path

As you can in Fig 2 I have draw the person at a point A and two other points B and C that the person would be during its motion later on. As is shown in the diagram the person would be at the same distance from the centre of rotation O. This distance is known as the radius of the circular path and is denoted by the letter r.

Angular displacement

In linear motion the movement is describe in term of the displacement of the object. In circular motion the movement of the object is describe in term of angular displacement. The angular displacement is simply the angle covered by the object during the circular motion.

Fig 3

In the first diagram of fig 3, you can see a person moves from point A to point B. In so doing it covers and angle θ of 120^o or 0.66 Pi rad. Hence the person would have an angular displacement of  120^o or 0.66 Pi rad. In the second motion the person starts from point A and moves along the circular path and finally back to A. In so doing the person covers an angle of 120^o or 2pi rad. Thus the angular displacement would be 120^o or 2pi rad

What is the gradient and how to determine it?

The gradient of a line or the slope of a line is an indication of how steep a line is at a particular point. The gradient is particularly important in Physics and as a result it is particularly important that you understand how to calculate it perfectly.

Gradient of a straight line

We have in fig 1 below two straight lines that have different slopes. We are going to see how to determine the gradient of both straight lines.

As you can see, there are two straight lines: a blue one and a red one.

It is clear that the red one is steeper than the blue one and as a result its slope would be greater. Consequently the gradient of the red line is greater than that of the blue line.

But do you know how to determine the gradient of the two straight lines mathematically?

Let us look at the red line first and then you are going to look at the blue line.

Loot at the line and the take two coordinated off the line.

I have taken (1,2) and (4,8)

These two coordinates would be considered as (x1,y1) and (x2,y2) such that

From the first coordinate you have x1 =1 and y1=2

from the second coordinate you have x2 =4 and y2 = 8

In order to calculate the gradient of the red line we are going to use the equation below

Hence using the equation above the gradient of the red line is calculated as shown

gradient of red line = (8-2)/(4-1) =6/3 = 2

If you want to check if you can calculate the gradient of the blue line you can do so by repeating the process above.

What you would also find is that any pair of coordinates that you take will give you the same gradient. Which mean that at any point along the straight line the gradient is the same.

Gradient of a curve

The method to calculate the gradient at a point along a curve is slightly different. In that you first have to draw a tangent to the curve at the point that you want to calculate the gradient.

Fig 2

As you can see in fig 2 above, I want to calculate the gradient of the curve at the point (3, 27) as a result I have drawn a tangent to the curve at that point. If you do not know how to draw a gradient I can show you later on in a later post.

Now that you have drawn a tangent at the point that we want (3,27) you will need to choose any two coordinates on the tangent line.

I have chosen (2.5 , 4) and (4 , 60). You can choose any coordinate on the tangent.

Hence using the coordinated below the gradient of the curve at the point (3,27) is

Gradient of curve at point (3,27) = (60 – 4)/(4 - 2.5)= 56/1.5 = 37.3 =37 (2 sf)

As you can see it is easy to calculate the gradient of a straight line or a curve at a particular point.