## FORM 1 PHYSICS- MEASUREMENT I

FORM 1 PHYSICS- MEASUREMENT I

In order to measure we need to know or define the quantity to be measured and the units for measuring it. In **1971 **a system known as the **International System of Units **(*Systeme’ Internationale*) and seven basic units were agreed upon as follows. Other quantities can be obtained from these basic quantities and are referred to as **derived quantities**.

Basic quantity |
SI units |
Symbols |

Length | Metre | m |

Mass | Kilogram | kg |

Time | Second | s |

Electric current | Ampere | A |

Thermodynamic temperature | Kelvin | K |

Luminous intensity | Candela | Cd |

Amount of substance | Mole | mol |

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**Length**

*This*** is the measure of distance between two points in space. **The SI unit for length is the

**metre (m).**Therefore 1 km = 1000 m

1 Hm = 100 m

1 Dm= 10 m

1 mm = 0.001 m

Length is measured using a **metre rule **(100 cm), **tape measure **(100 m, 300 m, 500 m)

**Area**

** This is the measure of the extent of a surface**. It is a derived quantity of length. Its SI units are square metres (

**m**. Other units are

^{2})**cm**, etc. Formulas are used to determine areas of regular bodies while for irregular bodies an approximation of area is used.

^{2}, km^{2}**Volume**

*This is the amount of space occupied *** by matter. **The SI units for volume is cubic metre

**(m**). Other sub-multiples are

^{3}**cm**,

^{3}**mm**and

^{3}**Hence**

*l*.**1 m**.

^{3}= 1,000,000 cm^{3}and 1*l*= 1,000 cm^{3}Volume can be measured using a measuring cylinder, eureka can, pipette, burette, volumetric flask, beaker, etc.

**Mass**

** This is the quantity of matter contained in a substance**. Matter is anything that occupies space and has weight. The SI unit for mass is the Kilogram

**(kg**). Other sub-multiples used are grams (

**g**), milligrams (

**mg**) and tonnes (

**t**).

**1 kg = 1,000 g = 1,000,000 mg=100 tonnes**. A beam balance is used to measure mass.

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FORM 1 PHYSICS- MEASUREMENT I

**Density**

** This is mass per unit volume of a substance**. It is symbolized by rho (

**ρ**) and its SI units are

#### kg/m^{3}. Density = mass / volume.

##### Examples

*A block of glass of mass 187.5 g is 5.0 cm long, 0 cm thick and 7.5 cm high. Calculate the density of the glass in kgm*^{-3}.

*Solution*

Density = mass / volume = (187.5 /1000) /(2.0 × 7.5 × 5.0 /1,000,000) = 2,500 kgm^{-3}.

*The density of concentrated**sulphuric acid is 1.8 g/cm*^{3}. Calculate the volume of 3.1 kg of the

*Solution*

Volume = mass / density = 3,100 / 1.8 = 1,722 cm^{3} or 0.001722 m^{3}.

The following is a list of densities of some common substances

Substance |
Density (g/cm^{3}) |
Density (kg/m^{3}) |

Platinum | 21.4 |
21,400 |

Gold | 19.3 |
19,300 |

Lead | 11.3 |
11,300 |

Silver | 10.5 |
10,500 |

Copper | 8.93 |
8,930 |

Iron | 7.86 |
7,860 |

Aluminium | 2.7 |
2,700 |

Glass | 2.5 |
2,500 |

Ice | 0.92 |
920 |

Mercury | 13.6 |
13,600 |

Sea water | 1.03 |
1,030 |

Water | 1.0 |
1,000 |

Kerosene | 0.80 |
800 |

Alcohol | 0.79 |
790 |

Carbon (iv) oxide | 0.00197 |
1.97 |

Air | 0.00131 |
1.31 |

Hydrogen | 0.000089 |
0.089 |

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##### Example

*The* *mass* *of* *an* *empty* *density* *bottle* *is* *20* *g.* *Its* *mass when filled with water is 40.0 g and*

*50.0* *g* *when* *filled* *with* *liquid* *X.* *Calculate* *the* *density* *of* *liquid* *X** if the density of water is 1,000 kgm ^{-3}.*

Solution

Mass of water = 40 – 20 = 20 g = 0.02 kg.

Volume of water = 0.02 / 1,000 = 0.00002 m^{3}. Volume of liquid = volume of bottle Mass of liquid = 50 – 20 = 30 g = 0.03 kg

Therefore density of liquid = 0.03 / 0.00002 = 1,500 kgm^{-3}

**Relative density**

##### This is the density of a substance compared to the density of water.

It is symbolized by **(d) **and has no units since it’s a ratio. **Relative density (d) = density of substance / density of water. **It is measured using a relative density bottle

##### Example

*The* *relative* *density* *of* *some* *type* *of* *wood* *is* *0.8.* *Find* *the* *density* *of* *the* *wood* *in* *kg/m* ^{3}*.*

Solution

Density of substance = d × density of water Density of substance = 0.8 × 1,000 = 800 kgm^{-3}

**Densities of mixtures**

We use the following formula to calculate densities of mixtures

#### Density of the mixture = mass of the mixture / volume of the mixture

##### Example

*100* *cm ^{3}*

*of*

*fresh*

*water*

*of*

*density 1,000 kgm*

^{-3}is mixed with 100 cm^{3}of sea water of density 1030 kgm^{-3}. Calculate the density of the mixture.*Solution*

Mass = density × volume

Mass of fresh water = 1,000 × 0.0001 = 0.1 kg Mass of sea water = *1030 *× 0.0001 = *0.103 *kg Mass of mixture = 0.1 + *0.103 *= *0.203 *kg

Volume of mixture = 100 + 100 = 200 cm^{3} = 0.0002 m^{3}

Therefore density = mass / volume = *0.203 */ 0.0002 =*1,015* kg/m^{3}.

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FORM 1 PHYSICS- MEASUREMENT I

**Time**

** This is a measure of duration of an event**. The SI unit for time is the second

**(s).**Sub- multiples of the second are milliseconds, microseconds, minute, hour, day, week and year. It is measured using clocks, stop watches, wrist watches, and digital watches.

**Accuracy and errors**

*Accuracy is the closeness*** of a measurement to the correct value of the quantity being measured. **It is expressed as an error.

**. The smaller the error the accurate the measurement.**

*An error is therefore the deviation of measurement to the correct value being measured***% error = (sensitivity / size measured) × 100.**