Balanced and unbalanced forces on a body

3(b) describe the effect of balanced and unbalanced forces on a body 
3(c) describe the ways in which a force may change the motion of a body.

Newton's First Law Of Motion

"Every object continues in its state of rest or of uniform motion in a straight line unless acted upon by an external unbalanced force."

Balanced forces

To better understand the concept of balanced forces, you will have to know the meaning of the term resultant force. The topic is covered in this post here.

Now that you know about the term resultant force, we will come to balanced forces. When the resultant force in a system is 0, we will say that the forces are balanced in the system. Look at the following picture.

The toy car is initially at rest. A man pushes it in both the forward and the backward direction.The

Newton third law

Newton's third Law

Newtons third law also known as third law of motion is related to the forces

The Law states :

                      

           " Every action has an equal but opposite reaction."

Lets see the following diagram. If a hammer strikes a nail into the wall, we are applying a force on the nail. But this is not the only force that is being applied in the process. The nail also applies an equal but opposite force onto the hammer.

Lets see another example.

As you can see in the image the lady applies a force on the wall so that her skate board moves

How to calculate distance travelled from a speed-time graph

2(g) calculate the area under a speed-time graph to determine the distance traveled for motion with uniform speed or uniform acceleration.




Calculating Distance traveled a from speed-time graph

Speed time-graphs are mostly meant to be as velocity-time graphs in the CIE exams. What speed time graphs basically show us is the speed of an object at a particular time.

But from a speed time graph, we can also obtain the following quantities.

• Distance
• Uniform Acceleration and Deceleration

Distance from speed time graphs

Speed Time and Distance Time graphs

2(e) plot and interpret speed-time and distance-time graphs.

2(f) recognize from the shape of a speed-time graph when a body is
(1) at rest,
(2) moving with uniform speed,
(3) moving with uniform acceleration,
(4) moving with non-uniform acceleration.


Speed Time Graphs
Plotting a graph is simple enough. In a speed-time graph, the speed (m/s) is always on the vertical axis, that is the y axis. The time (s) is on the horizontal axis, that is the x axis. Head over here if you need more tips in making a graph.

 There are a few things you need to remember for a speed time graph. When an object is
 (1) At Rest

The graph would be like this.

Uniform and Non Uniform Acceleration

2(c) state what is meant by uniform acceleration and calculate the value of an acceleration using change in velocity/time taken

2(d) discuss non-uniform acceleration.
 

Acceleration.

Acceleration is the rate of change of velocity. Its formula is change in velocity (final velocity minus initial velocity) /time taken . From the formula, we can deduce its SI unit. By dividing m/s by seconds we get m/s square or m/s^2, which is the SI unit of acceleration.

Now I'll go into a bit more detail .By rate of change of velocity, it means by how much the velocity of an object is increasing or decreasing in one second. E-g if the acceleration of a car is 4 m/s square, it means that the velocity of that body is increasing by 4 m/s every second. So if the car was initially at rest, and it accelerated at 4m/s^2 for four seconds, its velocity after 4s would be 16m/s. As it is derived from velocity, acceleration is a vector quantity too.

How to calculate Acceleration

How to calculate speed

2 (b) calculate average speed using distance traveled/time taken.

The formula for calculating speed is distance traveled/ time taken. Lets say a car covered a distance of 300 m in 30 seconds, the speed of the car would be 300/30 = 10 m/s. If you are wondering where the units m/s came from, it is quite simple. The unit for distance is m, meters. The unit for time is s, seconds. As speed is distance/time, we can say it is m/s, which are the units of distance and time respectively. It means how much distance a body is covering in one second. So if an object is moving at a speed of 10m/s, it is actually covering a distance of 10 meters every second. Also, remember that the unit for speed and velocity is the same.

Speed and Velocity.

2 (a) state what is meant by speed and velocity.

Speed

Speed is defined as rate of change of distance. Its formula is distance/time. To put it simply, speed defines what distance a body covers in one second. So, if you say that something is traveling at a speed of 10m/s, it means that that object is covering a distance of 10m every one second. The standard unit for speed is m/s. The m stands for meters, which is distance while s represents seconds. Also, sometimes speed is stated as kilometer per hour, or km/h. From the formula, speed = distance/time, we can also deduce the formula for distance and time, by rearranging the equation. As the distance, is not in any particular direction, speed is a scalar.

Velocity 

Velocity is defined as rate of change of displacement. Its formula is the same as speed, which is distance/time. The units are the same too, m/s. The only difference is that as displacement has a specific direction, velocity is also in a praticular direction. This means that velocity can only be in a specific direction i-e if i say that the velocity of the car was 20km/h, the car must be moving with that speed in a particular direction only. Thus velocity is also a scalar quantity. 

 

Symbols, Units and Prefixes

1(f) Symbols, Units and Prefixes

Physics is known as the science of Measurements. It obviously has many physical quantities.

A physical quantity is written as a numerical magnitude followed by a suitable unit. In physics , SI units i.e. the International System of units is adopted.

There are a few Base quantities and some Derived Quantities in Physics. The following are the base quantities.

Derived quantities are quantities made from a combination of the base quantities. Some examples are the following.

Area = Length (m) * Width (m)                       Units: meter(square)

Volume =Length (m) *Width(m)*Height (m)      Units: meter(cube)

Speed = Distance travelled (m) / Time taken(s)     UNITS: m/s

PREFIXES AND THEIR SYMBOLS

The other thing that should be kept in mind are Prefixes. Prefixes are placed before the SI units to give them a specific value.

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For example, a centimeter is a meter multiplied by 10. I hope you now understand what prefixes are.

Vernier Caliper, Micrometer and other length measuring devices

 1 (d) Describe how to measure a variety of lengths with appropriate accuracy using tapes, rules, micrometers and calipers using a vernier as necessary.



In this part we are going to focus on how to measure different lengths, using the appropriate equipment. First, here are the most commonly used units for length

1km = 1000m

1m = 100cm 

1cm = 10mm

Back to the topic, the instrument's we need to know about are the following .....

 1) Vernier Caliper

Vernier caliper is used to measure short lengths i.e. 0 to 15 cm. It is accurate to 0.01 cm. A pair of vernier calipers consists of a Main Scale and a Vernier Scale as shown in the diagram below. The outside jaws, are used to measure the outer dimensions of an object and the inner jaws for the inner ones. The stem is used to measure the depth.

 

To measure , gently grip the object with the straight edges of outside or inside jaws.

  How to take reading

How to measure time

1e) Describe how to measure a variety of time intervals using clocks and stopwatches.

 Here we are going to talk about the physical quantity Time. SI units seconds (s).

Measuring Instruments for time are

1) Pendulum clock
2) Clock
3) Stopwatch

( a simple stop watch )

                     

 ( a simple stop clock)

Measuring time using stop watch and stop clock

Measuring time using stop watches and stop clocks is very easy. The only thing needed is the accuracy in pressing the start button at the right time. To avoid errors experiment can be repeated again so that an average of reading can be taken.

 

 Avoid Errors

Now due to introduction of digital stop watches reading of the time has become easier but still when an analogue stop watch (stop clock) is used,  parallax error should be avoided.

Repeating the experiment is important for getting an accurate reading as by taking an average of the readings, errors can be reduced. Human reaction error can also generate a difference in the time recorded and original time.

An important part of measuring time in o level course is measuring time period using a Simple pendulum. Details of it are discussed below.

 

A Simple Pendulum

(image above shows a simple pendulum)


A simple pendulum makes use of a swing (oscillation)  of the metallic bob to measure time period.

Note:  The oscillation refers to a swing of bob from left to right and back to the starting position.

The Time period of the pendulum is the time taken for one complete oscillation. Remember the time period is very dependent on the length of the pendulum(i.e. distance from fixed point to the bob see next image) and the gravitational force . when the length increases time period increases while when the gravitational force increases time period decreases.

One more thing that you should keep in mind is the definition of frequency. Frequency is the number of oscillations of the pendulum in one second.

How to find time period using a Simple pendulum.

• First measure time for 20 complete oscillations using a stop watch or a stop clock (remember measuring time period of just one oscillation will not be accurate and can introduce errors)
• Find T1 (time period 1) using formula TOTAL TIME FOR 20 OSCILLATIONS/20
• Once you have found T1 repeat the experiment for next four times to find T2 T3 T4 T5
• In end to get an accurate reading of time period  take average of the 5 time periods i.e. T1+T2+T3+T4+T5/5

Different Scalars and Vectors

1 (c) List the vectors and scalars from distance, displacement, length, speed, velocity, time, acceleration, mass and force.

I already explained the terms scalars and vectors in my post here. It is extremely easy to differ between a scalar and a vector, and to pick them out once you have understood the two terms. I'll now explain how each of the quantities listed above is a scalar or a vector.

• Distance

Distance can be defined as the space between two fixed points. It has a magnitude i.e 5, and a unit km. But it has no specific direction.

• Displacement

 Displacement can be defined as the shortest distance between two points. As the shortest distance is always in a straight line, it has a direction. Therefore it is a vector. Remember both distance and displacement have the same unit. To better help you understand the difference between distance and displacement, I'll present a scenario to you.

A car travels from Multan to Lahore over a total distance of 300 km. Now, the car does not travel in a straight direction towards Lahore from Multan, but has to travel by road.

You can see the car does not have any particular direction while going by road. Now if an airplane was going to Lahore instead, it would travel in a straight direction.

• Length

Graphical representation of Vectors

1 (b) Determine the resultant of two vectors by a graphical method.

In the previous post, we learned that vectors are quantities which have a magnitude and a direction. As vector quantities have a direction too, we can represent them graphically. Graphical representation of vectors is extremely easy. All it takes is some practice and understanding, and you will be on your way to master this topic.

In graphical representation of vectors, what we do is represent vectors on a sheet of paper, in two dimensions. Usually in exams, the questions come about the resultant of two vectors. The first thing we need to learn about is the addition of vectors.

Head to Tail Method for addition of Vectors

The head to tail method is a simple way to add vectors. Lets say we have to vectors, A and B. 

 Now we need to draw them such that the tail of vector B is in contact with the head of vector A like this.

 The resultant vector, let's name it R, is found out by joining the tale of the first vector with the head of the second vector. Note that the tale of vector R is at the tale of vector A, the first Vector. And the head of vector R is at the head of vector B, the second vector.

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Now that you understand the method for addition of vectors, I'll come back to the main topic. To graphically represent vectors, the first thing we need to do is to take a suitable scale. By scale, i mean the ratio of the vectors and the lengths that we are going to use to represent those vectors on a paper e-g 1 cm to represent 1000 N. The next step is to draw the two vectors on a piece of paper according to the scale and the direction given. The resultant vector is then found out by the head to tail method of addition of vectors.




To help you better understand the topic, I'll be solving a simple question for you, and fill in the details step by step.

Question: A man walks 1200 m towards the North, and then 600 m towards the East. Find the resultant displacement of the man by graphical representation.

Solution.

Scalar and Vector

1 (a) Define the terms Scalar and Vector.

What is magnitude?

To understand the terms Scalar and Vector, you will have to first learn what the term Magnitude means. Magnitude can be defined as 'the degree or extent of something'. Sounds confusing? OK, here's an example. "Ali walked twenty miles that day." Now in this sentence, TWENTY is the magnitude of the distance Ali walked a specific day, for it tells us how much he walked that day, or as mentioned in the definition earlier, 'the extent of the distance he covered a specific day'.

Now here's a question for you to practice. "The temperature of the room was 20 degree Celsius". What is the magnitude of the quantity in this sentence?

Scalar

Hopefully, you have understood the meaning of magnitude. Now I'll come to Scalars. Simply put, a scalar quantity is 'a quantity that has a magnitude and a suitable unit only'. Examples include distance, time, mass, temperature etc. Now you might be thinking what do i mean by the word 'only'. By that, it means that scalar quantities do not have any direction.

Let's say, "Ahmad worked for 20 minutes". In this sentence, 20 is the magnitude, and minutes is the unit that represents time. Together, they represent time, which is a scalar quantity, as it does not have any direction.

Vector

 Vectors are quantities "that have a magnitude as well as a direction and a suitable unit". Examples include velocity, displacement, weight, acceleration, forces etc. Displacement is a vector because it is distance covered in a particular direction, e-g " Ali walked 20 km towards the east". In the example, 20 is the magnitude, km is the unit and East represents the direction of the quantity, therefore combining up to  represent displacement, which is a vector.  

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