WJEC Physics for AS Level Student Book 2nd Edition

10 (b) Derived quantities and units Most of the time physicists work with quantities other than the base quantities, e.g. area, volume, pressure, power. They use the base units in combination to express these. In order to derive these units we treat them as algebraic letters and remember some simple algebraic rules. To remind yourself of them see Knowledge check 1.1.1. The easiest way of understanding how to derive a unit is to look at some examples: 1. Unit of area. We start with a defining equation: Area of a rectangle = length × breadth \ Unit of area = unit of length × unit of breadth But length and breadth are both distances so they both have m as their unit. \ Unit of area = m × m = m 2 . 2. Unit of change of speed (or change of velocity). The unit of speed (or velocity) is m s – 1 . If the speed of a car changes from 15 m s – 1 to 33 m s – 1 then change of speed = final speed – initial speed = 33 m s – 1 – 15 m s – 1 = 18 m s – 1 (remember that, in algebra, 33 a – 15 a = 18 a ) So the unit of a change of speed is the same as the unit of speed. 3. Unit of acceleration. Again we start with a defining equation: acceleration = change of velocity time or a = Δ v t \  [ a ] = [ Δ v ] [ t ] = m s – 1 s = m s – 2 Some derived units are used very frequently and it is useful to learn how to express them in terms of the base SI units. Example Express the unit of force, the newton ( N ), in terms of base SI units. Answer Equation: Force ( N ) = mass ( kg ) × acceleration ( m s – 2 ). Or in symbols: F = ma \ [ F ] = [ m ][ a ] so N = kg m s – 2 Using the result of the example and the equations Work = Force × distance and Power = Work time we can express the units of work ( J ) and power ( W ) in terms of base SI units. Study point It is rather tedious to keep writing unit of , so we use square brackets to stand for this: [length] = m [area] = m 2 Study point A useful symbol for a change of something is Δ (delta). So Δ v = change of velocity. Knowledge check Simplify the following: (a) 6 a + 2 a (b) 6 a = 3 a (b) 6 a 8 3 b (d) ( 6 a ) 2 1.1.1 Knowledge check Derive the unit of volume by considering a cube. 1.1.2 Knowledge check The unit of the coefficient of viscosity, Ș , is usually written as ‘ Pa s ’ (pascal second) where Pa is the unit of pressure, defined by pressure = force area . Show that this unit is the same as that derived in the example. 1.1.3 WJEC Physics for AS Level Top tip Learn the expressions for N , J and W in terms of kg , m and s , and how to derive them.