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.