Young's Double Slit Experiment

The video below does a pretty good explanation of Young's double slit experient. This experiment demonstates the interference of light and therefore, confirms the wave nature of light. For our class purposes you are only required to watch the video up to 2:15. You can watch the rest of it if you like.

Adding Vectors and Scalars

Scalar quantities are added numerically, for example, 3kg + 5kg = 8kg.

When adding vector quantities, however, the direction must be taken into account.

Adding Forces

Forces are represented by lines drawn to scale. Its direction it the direction of the vector quantity. If we have a force of 5 N east we may use a scale where 1cm represents 1N. Therefore, the 5N force would be represented by a 5cm line.

Below we have three examples. In each case we have to add forces of 3N and 4N. We will calculate the resultant force of each.

Example1:

In this example, the two forces are parallel and in the same direction. Therefore, they produce a resultant force of: 4N + 3N = 7N, to the right. Note, you must state the direction.

Example 2:

In this example, the two forces are in exactly opposite directions. The resultant force is therefore: 4N - 3N = 1N, to the right. Note, you must state the direction.

Example 3:

Example 4:

In these cases, the Principle of Parallelogram of Forces must be applied. This principle states that if the two forces are represented in size and direction by the sides of a parallelogram drawn to scale, the resultant force is represented by the the diagonal drawn from the point where the force acts.

This video should show you how to calculate the resultant vector. If you still do not get it, you can use YouTube.

Result for SBA #12

Below is the table of results for SBA #12:

V/cm3	50.0	45.0	40.0	35.0	30.0	25.0	20.0	15.0
t1/s	0	13.06	26.7	42.19	58.37	75.66	94.38	115.88
t2/s	0	13.94	28.4	44.13	60.84	78.75	98.26	126.62
t/s

Results for SBAs #10 and 11

SBA #10

A = 0.52A
B = 0.26A
C = 0.16A
D = 0.08A
E = 0.52A

SBA #11

Number of Throws	Undecayed Atoms
1	47
2	20
3	12
4	6
5	4

The results for SBA #12 are not good so that will be done again.

Force, Mass and Weight

Force

A force can be defined as a push or a pull. It can change the size, shape or motion of a body. There are several different types of forces, some of which are:

• Gravitational force
• Electrical force
• Magnetic Force
• Nuclear force
  

Measuring Force

The spring balance is used to measure force. The spring balance is based on the fact that the extension of the spring is proportional to the force applied. The unit of force is the newton (N).

Stretching a Spring

We hang a wire spring from a retort stand. A pointer and a small pan are hung at the bottom of the spring. We set up a scale, marked in millimetres vertically by the side.

We add a series of small, equal weights which stretch the spring. We measure the extension i.e. the extra length, of the spring. Typical results are shown in the table below:

Force F/N	0	1.0	2.0	3.0	4.0	5.0
Extension e/cm	0	1.6	3.2	4.8	6.4	8.0

If a graph of extension against load is plotted, a straight line passing through the origin will be obtained. This means that extension if proportional to the load.

Elastic Limit of Springs

If we remove the weights the spring contracts to its original length. However, if we continue to add greater weights, eventually the spring stretches by different amounts. At this point, the extension is no longer proportional to the load.

When we remove the lager weights the spring does not return to its original length. We have gone beyond the elastic limit of the spring. The new graph looks like this:

Hooke's Law

Hooke's law states that the extension of a spring is directly proportional to the force applied, provided the elastic limit has not been exceeded.

We can obtain similar graphs for elastic bands and for straight metal wires. Elastic bands need smaller forces for a measurable extension and metal wires need much greater ones. 

The following video explains more on Hooke's Law:

Mass and Weight

Mass

The mass of an object is the measure of the amount of matter it contains. The mass of an object is also a measure of a resistance to a change in its motion. This resistance is known as the inertia of the body.

We measure mass using a triple beam balance as shown in the picture below. The unit of mass is the kilogram (kg). The mass of an object is constant everywhere.

Weight

The weight of an object is the force of gravity on the object. It acts towards the centre of the earth.

We measure weight using a spring balance as shown in the diagram below. The unit of weight is the newton (N). A mass of 1 kg has a weight of approxiamtely10N on earth. The weight of an object changes is the force of gravity changes.

In outer space there is no gravity, a 1kg mass has no weight. On the moon, where the gravity is about a sixth i.e. 1/6 that on the earth, a mass of 1 kg has a weight of about 1.6 N, as shown in the calculation below

Motion 2

Equations of Uniformly Accelerated Motion

When we have objects moving with a constant acceleration we can also use certain equations to solve problems. In these equations we use the following symbols:

You should be able to recall ALL of the following equations:

This implies that

The above equation can be rewritten as:

You should also know ALL of the following:

Falling Objects

We can drop a large stone and a piece of chalk from a height of 3 or 4 metres and they land simultaneously. However, a stone will reach the ground faster than a piece of paper. If the stone and paper are allowed to fall in a vacuum they fall together.

When objects fall in the air the resistance of the air has a greater effect on the light objects, such as the paper, than on heavy ones, such as the stone. Fluid friction (or viscous drag) always opposes the fall of objects through fluids, i.e. liquids and gases.

Acceleration due to Gravity

If the effects of air resistance are eliminated, or negligible, then all objects fall with the same acceleration. This is called acceleration due to gravity, g.

The acceleration due to gravity has slightly different values in different parts of the world but all values are about 9.81 metres per second squared. We often take g as 10 metres per second squared, as a convenient approximation.

SBAs

Note that all of your SBAs are posted to the blog. Try to get them all through. I will be collecting your books on Thursday, 27th March, 2014 to mark up to wherever you are at. You will collect your books the same day so you can finish up your labs.

The official deadline for your physics SBA books is next week Wednesday i.e. Wednesday, 2nd March, 2014. Try to be all through.

We are nearing the end so put in the effort. It will soon be all over.

Good luck!

Motion

Vectors and Scalars

Vector quantities have both size and direction. Examples of vector quantities are velocity, displacement, acceleration and force.

Scalar quantities have size but no direction. Examples of scalar quantities are speed, distance and mass.

Distance and Displacement

When total distance travelled by and object is calculated, we take no account of the direction in which it travels. Distance is scalar.

Displacement is defined as the distance moved in a particular direction. It id a vector quantity. The diagram represents a man walking on a football field. He starts at P and walks 50m due east - a displacement of 50m. He then walks 50m due north. 

His total distance travelled would be the distance from P to Q to R. However, his displacement would be the direct distance between his starting point and ending point, i.e, the direct distance between P and R.

Speed

Speed is defined as the rate of change of distance or distance moved per second. It is a scalar quantity. If speed does not vary (if it is constant or uniform) then

Distance is measured in metres per second 

Velocity

Velocity is defined as the rate of change of displacement or displacement per second. It is a vector quantity. If velocity is constant then

The unit of velocity is metre per second

For velocity to be constant, both the speed and direction must be constant.

Acceleration

Acceleration is defined as the rate of change of velocity i.e. the change of velocity per second. If acceleration is constant then

The unit of acceleration is metres per second squared

Acceleration is a vector quantity.

Representation motion using graphs

We use graphs to represent and analyse motion. The most useful to us are graphs of displacement against time, and velocity against time.

Constant Velocity

Ia a car is moving at a constant velocity of 

then every second it will travel a distance of 15 metres in the same direction.

Two graphs can represent this motion:

Displacement/time graph

The graph below represents the car's motion., The gradient of the line is 60/4 = 15. The gradient of a displacement/time graph always represents the velocity.

Velocity/time graph

The gradient of the graph represents the acceleration. In the example below the velocity constant, so the gradient and acceleration are zero.

The area under a velocity/time graph represents the distance travelled. So in 4 seconds, are = 15 x 4 = 60 and the distance travelled is 60m.

Velocity/time graphs are more useful than distance/time graphs. All four quantities are represented on a velocity/time graph: velocity, time, distance and acceleration.

Uniform Acceleration

If a car starts from rest and has an acceleration of 5ms^-2 each second its velocity increases by 5ms^-1

We can represent this in a velocity/time graph as shown below.

We can use the graph to calculate the distance travelled in 6 seconds. Remember that the distance travelled is represented by the are under the graph. The triangle has an area of

The distance travelled in 6 seconds is 90m.

Results for Lab #9

The results for lab #9 are as follows:

Good luck with the SBA :)

Specific Latent Heat of Ice (SBA #8)

Note: When doing labs, it helps to review the topic before doing the questions.

For this lab, you are required to find the specific latent heat of ice using the method of mixtures. Therefore, you need all of the following information:

• The mass of ice used m_i
• The mass of water used m_w
• Initial temperature of water (temperature after heating up the water) θ₁ 
• Final temperature of water (temperature after ice was completely melted) θ₂
• Specific heat capacity of water (4200 J kg^-1 K^-1)

In this experiment, it is assumed that the total energy lost by the heated water was transferred to, or gained by the ice. This implies that:

Total energy lost by water = Total energy gained by ice

Energy needed to change the temperature of a substance is found by the following formula:

The ice gained energy from the water and was changed to a liquid. This change from ice to water is called a change of state. Therefore the energy needed for a change of state from ice to liquid is found by the following equation:

Since the energy lost by the water is equal to the energy gained by the ice then

In words:

the mass of water X specific heat capacity of water X temperature change = mass of ice X latent heat of ice

You can then rearrange the formula to find the specific latent heat of fusion of ice. Hope this helps you.

Good luck!!! :)

Magnetism

Permanent Magnets

Some materials can be defined as magnetic whereas others are non-magnetic. A magnetic material is one which is affected by magnetism.

Some materials which are strongly attracted to magnets (magnetic) are:

• Iron and steel
• Other alloys of iron, cobalt or nickel
• Alloys containing a mixture of iron, colbalt and nickel

Some materials which are not attracted to magnets (non-magnetic) are:

• wood
• plastic
• leather

Properties of Magnets

Poles

Poles are the regions on a magnet to which materials are attracted. All magnets have two poles, a north pole and a south pole. Hence, they are called magnetic dipoles.

The two poles of a magnet are either south-seeking or north seeking. A suspended magnet always settles with its poles pointing in the same direction. The north pole of the magnet will always point toward the geographical north pole of the earth hence it is called the north seeking pole or simply the north pole. The south pole of the magnet will always point toward the geographical south pole of the earth hence, it is called the south seeking pole or simply the south pole. This video explains this some more. Because of the property explained above, magnets are used to make the magnetic compass.

Forces between magnets

If two opposite poles of a magnet are brought into close proximity, a force of attraction between the two magnets is observed. Also, if two similarly poles of a magnet are brought into close proximity a force of repulsion is observed. Therefore, "like poles repel and unlike poles attract".

Magnetic Induction

When an unmagnetised iron alloy is brought near to a magnet it is attracted to the magnet. This is a result of temporary magnetism being induced in the material. Magnetic induction always results in attraction, never repulsion. Also, there is always a pair of induced poles.

Permanent and Temporary Induced Magnetism

Refer to page 276 of your text book.

Iron alloys like steel and magnadur are hard to magnetise, hence they are called hard magnetic materials. Materials which are easier to magnetise such as iron and mumetal are called soft magnetic materials. Soft magnetic materials are used to make temporary magnets whereas hard magnetic materials are used to make permanent magnets.

Magnetic Forces

The magnetic field around a magnet is the region in which forces act on other magnets and on magnetic materials by inducing magnetism in them. The direction of a magnetic field at a particular place is the direction of the force it produces on a free magnetic north pole. Remember, field lines always go from north to south.

Magnetic Field Diagrams

You should be able to draw the field lines:

• Around a strong single magnet
• Around and between two strong magnets which are oriented parallel, anti-parallel, and pole to pole with each other just as you did in your SBA. (Page 280 of your text has a few diagrams)

Read up on this entire topic in your text books people. It is important.

Measurements and Mathematics

Measurement and Significant Figures

When we calculate the value from our results the answer should we written to the same number of significant figures as the original results. For example, is the two sides of a rectangle are measured as 24.2 cm and 18.3 cm, then the are of the triangle is 24.2 cm x 18.3 cm = 442.86 cm²

Since the sides of the triangle were given at three significant figures, then the answer should also be to three significant figures. Therefore, the answer is 443 cm²

Reading Scales

Many readings in physics are taken from a scale on an instrument e.g. thermometers, ammeters, voltmeters etc. When reading a scale you make an estimate when the pointer is not actually on a mark on the scale. In the example below of an ammeter, the result would be taken as 1.34 A.

Accuracy of Results

For an experiment to be useful we must obtain accurate results. There are certain steps that can be taken to increase the certainty of our results. These are:

1. Take the same reading more than once can calculate an average value.
2. Measure a large number of a quantity and calculate the value for one. For example, if we have to find the thickness of a sheet of paper, we can measure the thickness of 300 sheets. We then divide our result by 300 to find the thickness of one sheet.
3. We can select and instrument which is appropriate to the reading. If a current of about 0.4 A is being measured we use an ammeter with a range of 0 to 1 A, not 0 to 5 A.
4. We take care to avoid parallax error. Always try to read scales from directly over the mark.

 Large and Small Numbers

When we have very large and small numbers there are useful alternative ways to write them.

 Standard Form

In standard form we write numbers in two parts as follows:

You should be able to multiply and divide numbers in standard form:

 Prefixes

Prefixes are also used to represent very large and small numbers. The following examples show there meaning.

 Graphs

A common way to present results is to draw graphs. Graphs often provide us with extra information and helps our understanding.

When plotting a graph the axes are labelled with the quantities involved, their symbols and the units of the quantities. A convenient scale must be chosen in order for the results to use up most of the graph.

A small cross or a circled dot can be used to plot the points. Results must be plotted as accurately as possible and should not be rounded off.

A line of best fit must be drawn to join the plotted points together. This line goes as close as possible to as many points as possible. The points should also be 'balanced' about the line with equal numbers of points below and above the line.

A the results are arranged in a curve, a smooth curve must be drawn.

 Common Graphs

If the graph is a straight line passing through the origin, it means that the two quantities are proportional to each other.

If the graph is a straight line but not passing through the origin, the quantities are linearly related to each other but not proportional to each other.

 Gradient and intercepts of a graph

Two important quantities of a straight-line graph are its gradient and its intercepts on the axes.

The intercept is the point where the line cuts the axis. The y-intercept is the point where the line cuts the y-axis and the x-intercept is the point where the x-axis. In the example below, the y-intercept is 4 and the x-intercept is -8.

The gradient is found using the formula below:

Newton's Cradle

The video below demonstrates the Principle of Conservation of Linear Momentum. Use your observations to do lab #7.

You can also check the link for the blog post called lab no. 7. There you will be able to carry out the experiment for yourself.

Micrometer and Vernier Callipers

The video below shows how a micrometer and vernier calliper are read. Enjoy!

Hope this helps.

Logic Gates

Logic gates are the building blocks of digital electronics and are used to build telecommunication devices, computers, etc.

AND Gate

The truth table for the AND gate is below:

OR Gate

The truth table for the OR gate is below:

NOT Gate

The truth table for the NOT gate is below:

Combining NOT gate with AND and OR gates

The NOT gate can be combined with the AND and OR gates to produce a different output.

NAND Gate

NAND = NOT AND. The NAND gate corresponds to an AND gate followed by a NOT gate.

The truth table for the NAND gate is below:

NOR Gate

NOR = NOT OR. The NOR gate corresponds to an OR gate followed by a NOT gate.

The truth table for the NOR gate is below: