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ational as and a Level Physics Revision Guide Cambridge Education Cambridge Uni Samples

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Physical Quantities and Units Revision Objectives

This chapter will explain the SI system of units used for measuring physical quantities and will distinguish ­between vector and scalar quantities

You are already familiar with much of this chapter but it does contain a great deal of detail that you must use accurately

In examinations many candidates are sloppy in their use of SI units and consequently can lose marks unnecessarily

Even a few lost marks can result in a lower grade

Physical quantities All measurements of physical quantities require both a numerical value and a unit in which the measurement is made

For example,

The number and the unit in which it is measured need to be kept together because it is meaningless to state ‘height = 1

The numerical value is called the magnitude of the quantity and the magnitude only has meaning once the unit is attached

In this particular case it would be equally correct to state ‘height = 173 centimetres’,

since there are 100 centimetres in a metre

Many careless mistakes are made with this type of conversion and all of them can be eliminated by this simple method

Write the conversion as an equation

73 m = 1

In public examinations a large number of nonsensical mistakes are made because candidates have not thought about the meaning of what they

Physics_Chapter 01_Sample

In this simple example,

Other conversions are not necessarily so obvious

Another matter of convention with units concerns the way they are written on graph axes and in tables of values

You will often use or see a statement such as ‘energy/joule’ or in its abbreviated form ‘E/J’

This does mean energy divided by joule

For example energy 780 joule = = 780 joule joule The figure 780 is now just a number with no unit

That is what will appear in a table of values or on a graph so there is no need to add the unit in tables or graphs ­provided the convention is used on the heading or axis

In order to answer the questions given you will have had to use the prefixes on multiples and submultiples of units

The following table shows the meaning of each term you may have to use

Abbreviation

Multiplying factor

Abbreviation

Multiplying factor

light of wavelength 456 nm is a wavelength of 456 × 10-9 m

This will equate to 4

Always be careful with any of these prefixes and double check to see that you are not using them the wrong way round

It is amazing how often candidates will,

find the speed of a car as an unrealistic 0

The reason for the difference being that at some stage in the calculation the candidate has divided by 100 when he ought to have multiplied

 I units (système S international d’unités) All the units you use during your AS course are called the SI units

They are derived from five base units

These are,

together with the abbreviation used for each,

the kilogram (kg) as the unit of mass,

the metre (m) as the unit of length,

the second (s) as the unit of time,

the ampere (A) as the unit of electric current and ✓✓ the kelvin (K) as the unit of temperature

The definition of these five units is amazingly complicated and you are not required to know the definitions

Each definition is very precise and enables national laboratories to measure physical quantities with a high degree of accuracy

To express other units in terms of the base units requires that the definitions of the corresponding definitions are known

All the definitions and their corresponding units are given in this book when required in appropriate chapters but there is also a summary of the mechanics and matter definitions on pages *** and ***,

and of the electricity and magnetism definitions on pages *** and ***

Knowledge of the details in these summaries is absolutely necessary since every

Physics_Chapter 01_Sample

numerical question you may have to answer will be dependent upon using units included in the tables

To find the expression of a unit in base units it is necessary to use the definition of the quantity

For ­example the newton,

is defined by using the equation force = mass × acceleration

So  1 N = 1 kg × 1 m s-2  or  1 N = 1 kg m s-2

Estimating physical quantities In making estimates of physical quantities it is essential that you do not just guess a value and write it down

Most of the marks for your answer will be for the method you use and not for the numerical ­values

Answers you write may have numerical values stretching from 10-30 to 1040

You do need to know some key values,

The following list is by no means complete but is a starting point

1000 kg

30 m s-1

300 m s-1

300 m s-1

energy requirement for a person for one day

100 000 Pa

A few astronomical values are useful too

400 000 km

6000 km

Physical Quantities and Units   3

Do not forget that various atomic sizes and masses are given in the exam paper data Once you have some basic data you can incorporate it to find an approximate value for all sorts of unlikely quantities

For example,

a question may ask you to estimate a value for the kinetic energy of a cruise liner

Your answer should look like this– Mass of cruise liner taken as 20 000 tonnes = 2 × 107 kg Speed of cruise liner = 15 m s-1 (half the speed of a car) Kinetic energy = ½ mv2 = 0

Always work in SI units

It would be impossible for you to know the unit of an answer,

should you try to do the above question in Imperial units

Vectors and scalars A vector is a quantity that has direction as well as magnitude

a scalar is a quantity with magnitude only

The following lists put quantities in their correct category

Scalars

Vectors

It might seem impossible for a force of 8 N to be added to a force of 6 N and get an answer 2 N,

but it could be correct if the two forces acted in opposite directions on a body

In fact,

any numerical magnitude is possible between a maximum of 14 N and a minimum of 2 N,

depending on the angle that the forces have with one another

In order to find the resultant of these two forces,

use is made of a triangle of forces,

The two vectors are drawn to scale,

The mathematics of finding the resultant can be difficult but if there is a right angle in the triangle things can be much more straightforward

Subtracting vectors also makes use of a vector triangle

Note that you can always do subtraction by addition

If you want to know how much money you can spend if you want to keep $20 out of a starting sum of $37,

then instead of $37 − $20 = $17 you can think ‘what needs to be added to 20 to get 37

To subtract vector B from vector A a triangle of vectors is used in which −vector B is added to vector A

This is shown in Figure 1

Note that A + (−B) is the same as A − B

Resultant 4N

Resultant 10 N

Combining vectors Adding or subtracting scalars is just like adding money so poses no problems

Adding vectors,

Physics_Chapter 01_Sample

6N Resultant 13 N

Figure 1

A + (−B)

Figure 1

Resolution of vectors Not only is it possible to add vectors,

it is often useful to be able to split a single vector into two

This process is called resolution of a vector and almost always resolution is to split one vector into two components at right angles to one another

This is illustrated in Figure 1

In Figure 1

The velocity can be considered equi­valent to the two other velocities

F sin f f (b)

Figure 1

v sin q is its vertical component and v cos q is its horizontal component

In Figure 1

force F is the force the sloping ground exerts on a stationary object resting on it

(This force will be equal and opposite to the weight of the object

) F can be resolved into two components

F sin f is the force along the slope and is the frictional force that prevents the object sliding down the slope

F cos f is the component at right angles to the slope

Questions   1

1 Convert

(e) 6 500 000 seconds into days

2 Convert

(e) a speed of 110 kilometres per hour into metres per second

(a) the joule (b) the pascal (c) the watt

show whether or not the following equations are possible

(a) E = mc2 (b) E = mgh (c) E = mv2

Physics_Chapter 01_Sample

(d) power = force × velocity (e) p = rgh

(a) The energy required for you to go upstairs to bed

(b) The average speed of a winner of a marathon

(c) The power requirement of a bird in a migration flight

(d) The vertical velocity of take-off for a good high jumper

(e) The acceleration of a sports car

(f ) The density of the human body

(g) The pressure on a submarine at a depth of  1000 m

(a) The power of a hot plate on a cooker is 2 W

(b) The speed of a sub-atomic particle is 4 × 108 m s-1

(c) The hot water in a domestic radiator is at a temperature of 28 °C

(d) The pressure of the air in a balloon is 15 000 Pa

(e) The maximum possible acceleration of a racing car is 9

81 m s-2

determine the value of vector B – vector A

Physical Quantities and Units   5 What is the change in velocity of the car

? Give the angle of the change in direction relative to the i­ nitial direction of the car

Its speed is 1020 m s-1

Deduce (a) the time taken for a complete orbit of the Earth,

(b) the angle the Moon moves through in 1

(c) the change in velocity of the Moon in 1

just after the start of a race,

has a force of 780 N exerted on her by the ground and acting at an angle of 35° to the vertical

What is the weight of the athlete and what is the force causing her horizontal acceleration

is being pulled by a force in the string of 6

Physics_Chapter 01_Sample

Force of wind

Figure 1

(a) Resolve the force in the string into ­horizontal and vertical components

(b) Assuming that the kite is flying steadily,

deduce the upward lift on the kite and the horizontal force the wind exerts on the kite