Mass, Weight and Mass, Weight and DensityDensity

Lesson Objectives:Lesson Objectives:

At the end of this lesson, you should be able to:

•State that mass is a measure of the amount of substance in a body. •State that mass of a body resists a change in the state of rest or motion of the body. •State that a gravitational field is a region in which a mass experiences a force due to gravitational attraction. •Define gravitational field strength as gravitational force per unit mass. •Recall the relationship weight = mass x gravitational field strength. •Recall the relationship density = mass / volume.

Developed by the French in the late 1700’s. Developed by the French in the late 1700’s. Based on powers of ten, so it is very easy Based on powers of ten, so it is very easy

to use.to use. Used by almost every country in the world, Used by almost every country in the world,

with the notable exception of the USA.with the notable exception of the USA. Especially used by scientists.Especially used by scientists. Abbreviated SI, which is French for Systeme Abbreviated SI, which is French for Systeme

International.International.

Metric SystemMetric System

Mass is a measure of the amount of substance in a body.

SI Unit: Kilogram (kg) Mass cannot be changed by the location,

shape and speed of the body. Large masses are measured in tonnes while

small masses are measured in grams.

MASSMASS

We will use a triple beam balance andWe will use a triple beam balance and

digital top-loading scaledigital top-loading scale

to measure mass.to measure mass.

Measuring MassMeasuring Mass

Examples of Masses of ObjectsExamples of Masses of Objects

Object Mass in kilogram

(kg)

ElectronA fine grain of sandA peaAn appleA medium-sized carEarthSun

10-30

10-6

10-3

10-1

103

1024

1030

An object at rest tends to stay at rest and An object at rest tends to stay at rest and an object in motion tends to continue in an object in motion tends to continue in motion at constant speed in a straight motion at constant speed in a straight line (uniform velocity)…….. line (uniform velocity)…….. uunlessnless

an external resultant force acts on it.an external resultant force acts on it.

Newton’s First LawNewton’s First Law

The inertia of an object is its reluctance to The inertia of an object is its reluctance to move when it is at rest or to slow down or move when it is at rest or to slow down or stop when it is moving.stop when it is moving.

That is, it is its reluctance to change its That is, it is its reluctance to change its state of rest or motionstate of rest or motion

INERTIAINERTIA

measured by massmeasured by mass

The more massive an object, the more The more massive an object, the more inertia it has, hence, the larger the force inertia it has, hence, the larger the force is required to change its motionis required to change its motion

Conversely ... Conversely ...

Inertia is ...Inertia is ...

The gravitational field is a region in The gravitational field is a region in which a mass experiences a force due which a mass experiences a force due to gravitational attraction. to gravitational attraction.

Gravitational field strength is Gravitational field strength is gravitational force acting per unit mass gravitational force acting per unit mass on an object. on an object.

On earth, the gravitational field On earth, the gravitational field strength is strength is

10 N kg-1 or 10 ms-2.10 N kg-1 or 10 ms-2.

Gravitational Field StrengthGravitational Field Strength

Volume is the amount of space an Volume is the amount of space an object consumes. object consumes.

The base unit for volume is the liter. The base unit for volume is the liter. There are two methods for finding There are two methods for finding

volume.volume.

VolumeVolume

We can find the volume of box shapes with We can find the volume of box shapes with the formula Volume = length x width x the formula Volume = length x width x height.height.

In this case the units would be cubic In this case the units would be cubic centimeters (cm3).centimeters (cm3).

So a box 2 cm x 3 cm x 5cm would have a So a box 2 cm x 3 cm x 5cm would have a volume of 30 cm3 volume of 30 cm3 2 cm

5 cm

3 cm

Volume of Regular ObjectsVolume of Regular Objects

We measure volume of irregular objects with a graduated cylinder.

This method is called water displacement

Liquids form a curved surface in graduated cylinders.

Take your reading at the low point of the curve or MENISCUS

Water Displacement

Pour 7 ml of water in a graduated cylinder. If a rock causes the level to rise to 9 ml, the rock must have a volume of 2 ml.

Gravitational force acting on an objectGravitational force acting on an object

W = mgW = mg

where m is the mass of the objectwhere m is the mass of the object

g is the gravitational field strength.g is the gravitational field strength.

Weight is measured in newtons (N)Weight is measured in newtons (N)

Weight is . . .Weight is . . .

Weight is measured using a balance Weight is measured using a balance such as thesuch as the

spring balancespring balance compression balancecompression balance

Measurement InstrumentsMeasurement Instruments

Differences between Weight and Differences between Weight and MassMass

Weight Mass

pull of gravity on the body has both magnitude and direction measured in newtons changes from place to place

amount of matter in the body has only magnitude but no direction measured in kilograms is constant regardless of place or location

Story of a naked manStory of a naked man

In the first century BC the Roman architect Vitruvius related a story of how Archimedes uncovered a fraud in the manufacture of a golden crown commissioned by Hiero II, the king of Syracuse. The crown (corona in Vitruvius’s Latin) would have been in the form of a wreath. Hiero would have placed such a wreath on the statue of a god or goddess. Suspecting that the goldsmith might have replaced some of the gold given to him by an equal weight of silver, Hiero asked Archimedes to determine whether the wreath was pure gold. And because the wreath was a holy object dedicated to the gods, he could not disturb the wreath in any way.

Story of a naked manStory of a naked man

The solution which occurred when he stepped into his bath and caused it to overflow was to put a weight of gold equal to the crown, and known to be pure, into a bowl which was filled with water to the brim. Then the gold would be removed and the king’s crown put in, in its place. An alloy of lighter silver would increase the bulk of the crown and cause the bowl to overflow.

DENSITYDENSITY

Q) Which weighs more:-Q) Which weighs more:-A kilogram of feathers or a kilogram of A kilogram of feathers or a kilogram of

iron?iron?

What is Density?What is Density?

Density is the Mass per unit Volume

Wood Water Iron

1 cm3 1 cm3 1 cm3

If you take the same volume of different substances, then they will weigh different

amounts.

0.50 g 1.00 g 8.00 g

Q) Which has the greatest mass and therefore the most dense?

IRON

Density = MassVolume

g or kg

cm3 or kg3

gcm-3 or kgm-3

= m

V

Example:

Q) Liquid water has a density of 1000kgm-3, while ice has density of 920kgm-3.

Calculate the volume occupied by 0.25kg of each.

Density Equation:

m

V

V = m = 0.25 = 0.000250m3

1000V = m = 0.25 = 0.000272m3

920

DENSITY OF A REGULAR SOLIDDENSITY OF A REGULAR SOLID

Find the Mass Find the Mass of the solid on of the solid on a balance.a balance.

Measure the Measure the three lengths three lengths and calculate and calculate the Volume.the Volume.

(ie V = l x w x h )(ie V = l x w x h ) Calculate the Calculate the

Density.Density.4.0 cm

2.0 cm

3.0 cm

= m = 240 =10.0 g/cm3

V 24

m = 240 g

Density Formula Wheel

• Formula wheels make it easy to solve density problems.

• Cover the property you are trying to find, and do what is left over.

• To find density, cover the word density. You have mass over volume remaining. So divide mass by volume to find density

Density Volume

MateriaMateriall

MassMass

in gin gLengthLength

in cmin cmWidthWidth

in cmin cmHeight Height

in cmin cmVolumeVolume

in cmin cm33

DensityDensity

in in g/cmg/cm33

DENSITY OF AN IRREGULAR SOLIDDENSITY OF AN IRREGULAR SOLID

Find the Mass of the Find the Mass of the solid on a balance.solid on a balance.Fill the Measuring Fill the Measuring Cylinder with Water to a Cylinder with Water to a known Volume.known Volume. Add the Object.Add the Object. Work out the Volume Work out the Volume of Water that is of Water that is displaced.displaced. Calculate the Density.Calculate the Density.

50 cm3

80 cm3

m = 360 g = m = 360 =12.0 g/cm3

V 30

DENSITYDENSITY g/cmg/cm33

AluminiumAluminium 2.702.70

BrassBrass 8.508.50

IronIron 7.867.86

WoodWood 0.500.50

SlateSlate 2.802.80

GlassGlass 2.502.50

LeadLead 11.311.3

MarbleMarble 2.702.70

WaxWax 0.890.89

DENSITY OF AN IRREGULAR SOLIDDENSITY OF AN IRREGULAR SOLID

OR use a Eureka Can to find the Volume.OR use a Eureka Can to find the Volume.

Find the mass of the solid Find the mass of the solid on a balance.on a balance.Add water until just Add water until just overflowing.overflowing. Place a Measuring Cylinder Place a Measuring Cylinder under the spout.under the spout. Add the Object.Add the Object. Collect the Water and read Collect the Water and read off the Volume.off the Volume.Calculate DensityCalculate Density

m = 440 g

40.0 cm3

= m = 440 =11.0 g/cm3 V 40

DENSITYDENSITY g/cmg/cm33

AluminiumAluminium 2.702.70

IronIron 7.867.86

BrassBrass 8.508.50

WoodWood 0.500.50

SlateSlate 2.902.90

GlassGlass 2.502.50

DENSITY OF A LIQUIDDENSITY OF A LIQUID

Find the Mass of an empty Find the Mass of an empty Measuring Cylinder.Measuring Cylinder.

Add a certain Volume of Add a certain Volume of Liquid.Liquid.

Find the Mass of the Find the Mass of the Measuring Cylinder and Measuring Cylinder and LiquidLiquid

Calculate the Mass of Liquid.Calculate the Mass of Liquid. How?How? Calculate Density of Liquid.Calculate Density of Liquid.

25.0 g

20.0 cm3

45.0 g

45 – 25 = 20 g = m = 20 =1.00 g/cm3 V 20

Mass of Liquid = Mass of Measuring Cylinder and Liquid – Mass of empty Measuring Cylinder

LiquidLiquid Mass of Mass of empty empty

MeasurinMeasuring g

CylinderCylinder

in gin g

Mass of Mass of MeasurinMeasurin

g g Cylinder Cylinder

and and LiquidLiquid

in gin g

Mass of Mass of LiquidLiquid

in gin g

VolumeVolume

in cmin cm33

DensityDensity

in g/cmin g/cm33

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Forces and FluidsForces and Fluids

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