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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
GO TO: GO TO: http://teacherweb.com/MA/KeithMiddleSchool/PachecoScience7/wqr5.aspx
Begin your virtual lab activities with:Begin your virtual lab activities with:
Forces and FluidsForces and Fluids
WHAT’S NEXT………WHAT’S NEXT………