Next skip Introduction This sixth edition of Physics for the IB Diploma is fully updated to cover the content of the IB Physics Diploma syllabus that will be examined in the years — Both share a common core, which is covered in Topics 1—8. At HL the core is extended to include Topics 9— In addition, at both levels, students then choose one Option to complete their studies. Each option consists of common core and additional Higher Level material. The four Options are included in the free online material that is accessible using education.

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In adding and subtracting, the number of decimal digits in the answer must be equal to the least number of decimal places in the numbers added or subtracted. Thus: 3. Use the rules for rounding when writing values to the correct number of decimal places or significant figures. For example, the number There is a special rule for rounding when the last digit to be dropped is 5 and it is followed only by zeros, or not followed by any other digit.

For example, consider the number 3. How does this number round to 2 s. Because the digit before the 5 is even we do not round up, so 3. But 3. Nature of science Early work on electricity and magnetism was hampered by the use of different systems of units in different parts of the world. Following an international review of units that began in , the SI system was introduced in At that time there were six base units.

In the mole was added, bringing the number of base units to the seven in use today. As the instruments used to measure quantities have developed, the definitions of standard units have been refined to reflect the greater precision possible. Using the transition of the caesium atom to measure time has meant that smaller intervals of time can be measured accurately.

The SI system continues to evolve to meet the demands of scientists across the world. Increasing precision in measurement allows scientists to notice smaller differences between results, but there is always uncertainty in any experimental result. Test yourself 1 How long does light take to travel across a proton? How many molecules of water are there in a glass of water mass of water g?

An electron has a kinetic energy of 2. Give an order-of-magnitude estimate of the density of a white dwarf. Calculate the power mgh delivered. Then compare your estimate with the exact value found using a calculator. Physics is an experimental science and often the experimenter will perform an experiment to test the prediction of a given theory.

No measurement will ever be completely accurate, however, and so the result of the experiment will be presented with an experimental error. Work with absolute, fractional and percentage uncertainties. Use error bars in graphs. Calculate the uncertainty in a gradient or an intercept.

There are two main types of uncertainty or error in a measurement. They can be grouped into systematic and random, although in many cases it is not possible to distinguish clearly between the two. We may say that random uncertainties are almost always the fault of the observer, whereas systematic errors are due to both the observer and the instrument being used. In practice, all uncertainties are a combination of the two. Systematic errors A systematic error biases measurements in the same direction; the measurements are always too large or too small.

If you use a metal ruler to measure length on a very hot day, all your length measurements will be too small because the metre ruler expanded in the hot weather. If you use an ammeter that shows a current of 0. Almost certainly there is a frictional force f between the cart and the table surface.

The graph of the acceleration versus m would be a straight line through the origin, as shown by the red line in Figure 1. If you actually do the experiment, you will find that you do get a straight line, but not through the origin blue line in Figure 1.

There is a negative intercept on the vertical axis. Systematic errors can result from the technique used to make a measurement.

There will be a systematic error in measuring the volume of a liquid inside a graduated cylinder if the tube is not exactly vertical. The measured values will always be larger or smaller than the true value, depending on which side of the cylinder you look at Figure 1.

There will also be a systematic error if your eyes are not aligned with the liquid level in the cylinder Figure 1.

Similarly, a systematic error will arise if you do not look at an analogue meter directly from above Figure 1. Systematic errors are hard to detect and take into account.

Random uncertainties The presence of random uncertainty is revealed when repeated measurements of the same quantity show a spread of values, some too large some too small. Unlike systematic errors, which are always biased to be in the same direction, random uncertainties are unbiased. Suppose you ask ten people to use stopwatches to measure the time it takes an athlete to run a distance of m.

They stand by the finish line and start their stopwatches when the starting pistol fires. You will most likely get ten different values for the time. You would expect that if you took an average of the ten times you would get a better estimate for the time than any of the individual measurements: the measurements fluctuate about some value.

Averaging a large number of measurements gives a more accurate estimate of the result. See the section on accuracy and precision, overleaf. We include within random uncertainties, reading uncertainties which really is a different type of error altogether.

These have to do with the precision with which we can read an instrument. Suppose we use a ruler to record the position of the right end of an object, Figure 1. The first ruler has graduations separated by 0.

We are confident that the position of the right end is greater than The true value is somewhere between these bounds. The average of the lower and upper bounds is This is the conservative way of doing things and not everyone agrees with this.

What if you scanned the diagram in Figure 1. Others might claim that they can do this even without a computer or a scanner! They might say that the right end is definitely short of the We will not discuss this any further — it is an endless discussion and, at this level, pointless. Now let us use a ruler with a finer scale.

We are again confident that the position of the right end is greater than The average of the bounds is Notice

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