mass, weight and density

Mass and weightGravitational fields

Density

MASS, WEIGHT & DENSITY

Mass, Weight & Density 1

The mass of an object is a measure of the amount substance in the object.

All bodies with mass posses a property known as inertia.

The inertia of an object is the reluctant of the object to change either its state of rest, or if it is moving, its motion in a straight line.

Inertia depends on mass and not weight.The greater the mass of a body the greater

will be its inertia.


Mass & Inertia

Gravitational field is a region in which the mass of an object experiences a force due to gravitational attraction.

Gravitational field strength, g, is defined as gravitational force per unit mass.


Gravitational Field and Field Strength

Any object placed around the Earth experiences a force pulling it towards the Earth.

The force is stronger on the surface of the Earth and gets weaker as we go farther away.

Gravitational field strength (Nkg-1) is the same as the acceleration due to gravity, g, (ms-2).

The weight of an object is the force of gravity acting upon the object.

The greater the mass of an object, the greater is its weight.

Weight = Mass × Acceleration due to gravityW = mg

Weight


Measuring Mass & Weight


triple beam balance

electronic balance

Spring balance

1. A hammer has a mass of 1 kg. What is its weight (i) on Earth (ii) on the Moon (iii) in outer space.

2. The weight of an object on Earth is 55 N. The gravitational field strength on Earth is 10 N/kg. What is the mass of the object.

3. A man has a mass of 70 kg. What is his weight on Jupiter where the field strength is 26 N/kg.


Example

4. A spacecraft travels from Earth to Mars, where the gravitational field strength near the surface is 3.7 N/kg. The spacecraft is carrying a probe which has a mass of 100 kg when measured on Earth. Assuming that g = 10 N/kg on Earth

a) What is the probe’s weight on Earth?b) What is the probe’s mass in space?c) What is the probe’s mass in Mars?d) What is the probe’s weight on Mars?e) When the probe is falling, near the surface of

Mars, what is its acceleration?Mass, Weight & Density 7

5. What is the acceleration of the rocket on the right?


weight

3000 N force from rocket enginemass

200 kg

Mass Weight1 is the amount of

substance in the bodyis the force of gravity acting on the body

2 is constant at any location

depends on acceleration due to gravity at the location

3 is a scalar quantity is a vector quantity

4 is measured in kilograms

is measured in newtons

5 is measured using a beam balance or electronic balance (pan balance)

is measured using a spring balance

6 can never be zero can be zeroMass, Weight & Density 9

1. The mass of a full bottle of cooking oil is 1.30 kg.

2. When exactly half of the oil has been used, the mass of the bottle plus the remaining oil is 0.90 kg.


1. What is the mass of the empty bottle?A. 0.40 kg B. 0.50 kg C. 0.65 kg D. 0.80 kg


2. What is the meaning of the weight of an object?

A. the density of the material from which it is made

B. the force exerted on it by gravityC. the mass of the matter it containsD. the pressure it exerts on the floor


3. What is the gravitational force that the Earth exerts on an object?

A. the density of the objectB. the mass of the objectC. the volume of the objectD. the weight of the object


4. Which relationship defines gravitational field strength?

A. mass x 10B. mass x weightC. mass / weightD. weight / mass


5. On the Earth, the gravitational field strength is 10 N/kg. On the Moon, the gravitational field strength is 1.6 N/kg.

If an object has a weight of 50 N on Earth, what is its weight on the Moon?

A. 1.6 N B. 5.0 N C. 8.0 N D. 80 N


6. At a point on the surface of the Earth, the gravitational field strength is 9.8 N / kg.

Which pair of values for mass and weight are correct for an object placed at this point?


C

7. A body of mass 10 kg falling freely in the gravitational field close to the Moon’s surface has an acceleration of 1.6 m / s2.

What is the gravitational field strength on the Moon?

A. 0 N / kgB. 1.6 N / kgC. 10 N / kgD. 16 N / kg


8. An object that has a mass of 15 kg on the Earth is taken to the Moon.

The gravitational field strength on the Earth is 10 N / kg and on the Moon is 1.6 N / kg.

What are the mass and the weight of the object on the Moon?

Mass, Weight & Density 18A

9. The table shows the weight of a 10 kg mass on each of five planets.


1. On which planets would an astronaut have a smaller weight than on Earth?

A. Mercury, Mars and JupiterB. Mercury, Venus and MarsC. Mercury, Venus and JupiterD. Venus, Mars and Jupiter


10. Which statement is correct?A. Mass is a force, measured in kilograms.B. Mass is a force, measured in newtons.C. Weight is a force, measured in kilograms.D. Weight is a force, measured in newtons.


11. Which of the following statements is correct?

A. Mass and weight are different names for the same thing.

B. The mass of an object is different if the object is taken to the Moon.

C. The weight of a car is one of the forces acting on the car.

D. The weight of a chocolate bar is measured in kilograms.


12. Which statement is correct?A. The mass of a bottle of water at the North

Pole is different from its mass at the Equator.B. The mass of a bottle of water is measured in

newtons.C. The weight of a bottle of water and its mass

are the same thing.D. The weight of a bottle of water is one of the

forces acting on it.


13. A brick is placed on a newton balance X and then on a beam balance Y.

What is measured by each balance?

Mass, Weight & Density 24C

14. In a laboratory on Earth, balances show that an object has a mass of 2 kg and a weight of 20 N.

The same balances and object are then taken to the Moon, where the gravitational field strength is less than on the Earth.

Are the mass and weight of the object the same, or less, than before?

Mass, Weight & Density 25C

15. A stone is weighed using a newtonmeter (spring balance) and a pair of scales (pan balance).

This experiment is repeated on the Moon. Are the readings for each balance the same or

different when taken on Earth and on the Moon?

Mass, Weight & Density 26B

16. When two blocks X and Y are placed on a uniform beam, the beam balances on a pivot at its centre as shown.


1. What does this show about X and Y?A. They have the same mass and the same

density.B. They have the same mass and the same

weight.C. They have the same volume and the same

density.D. They have the same volume and the same

weight.


17. The weight of an object is to be found using the beam balance shown in the diagram.


1. The object is put in the left-hand pan and various standard weights are put in the right-hand pan, with the following results.


1. What is the best estimate of the weight of the object?

A. 0.27 NB. 0.29 NC. 0.31 ND. 0.58 N


The density of a substance is defined as its mass per unit volume.

The SI unit for density is kilogram per cubic metre (kgm-3) but other units like gram per cubic centimeter (gcm-3) is also commonly used.

1 gcm-3 = 1000 kgm-3


Density

Volume

Mass Density

1. A cylinder has a base of area 100 cm2 and contains water to a height of 10 cm. A piece of rock mass 600 g is lowered into the water and the water level rises to a height of 12 cm.

a. What is the volume of the piece of rock?b. Calculate the density of the rock.

2. The density of a solid is 4 g/cm3. What is the volume of 200 g of the solid.

3. An empty measuring cylinder has a mass of 200 g. A liquid is poured into the measuring cylinder until the liquid is at the 80 cm3 mark. The total mass is now 272 g. What is the density of the liquid in g/cm3? Mass, Weight & Density 33

Example

4. A sample of ethanol has a volume of 240 cm3. Its mass is found to be 190.0 g. What is the density of ethanol.

5. Calculate the density of mercury if 500 cm3 has a mass of 6.60 kg. Give your answer in g/cm3.

6. A steel block has a mass of 40 g. It is in the form of a cube. Each edge of the cube is 1.74 cm long. Calculate the density of the steel.

7. What is the volume of a storage tank which will hold 3200 kg of petrol? Density of petrol = 800 kg/m3.

8. What mass of lead has the same volume of 1600 kg of petrol? Density of petrol = 800 kg/m3 & Density of lead = 11400 kg/m3.


1. TO DETERMINE THE DENSITY OF WATERApparatusProcedureCalculation Precautionary Measure

EXPERIMENTAL PROCEDURE


Apparatus electronic balanceMeasuring cylinder


ProcedureMeasure the mass of the empty measuring

cylinder. Take the average readingFill the measuring cylinder with waterMeasure the mass of the water inside the

measuring cylinder. Take average readingRead the volume of water on the measuring

cylinder


CalculationMass of the water = mass of measuring

cylinder & water – mass of the empty measuring cylinder

Density of water = mass of water / volume of water


Precautionary measureAvoid parallax error when reading the

measuring cylinderTo reduce wind interferenceAlways re-zero the electronic balanceTake average reading of the mass


2. TO DETERMINE THE DENSITY OF SOLID CUBE

Apparatus Procedure Calculation Precautionary Measure



Apparatus electronic balance30 cm rule


Procedure measure the mass of the cube using

electronic. Take average readingUsing the rule measure all the length of the

side (length, breadth & height)


CalculationVolume of cube = length x breadth x heightDensity = mass / volume


Precautionary measureAvoid parallax errorCheck zero errorReduce wind interferenceTake average reading of mass and length


3. TO DETERMINE THE DENSITY OF PLASTICINE

Apparatus Procedure Calculation Precautionary Measure



ApparatusElectronic balanceMeasuring cylinder


ProcedureMeasuring the mass of the plasticine using the

electronic balance. Take average readingFill the measuring cylinder with water. Take

the initial reading of the meniscus, V1Submerged the palsticine into the cylinder.

Take the new reading of the meniscus, V2


CalculationVolume of plasticine = V2 – V1Density of plasticine = mass / volume


Precautionary measureAll plasticine must submergeTake average reading of mass


4. TO DETERMINE THE DENSITY OF CORK Apparatus Procedure Calculation Precautionary Measure



ApparatusElectronic balanceEureka canBeakerMeasuring cylinderSinker


ProcedureMeasuring the mass of the cork using the

electronic balance. Take average readingTied the cork to a sinker with known volume VSubmerged the cork and sinker into the eureka

canMeasure the volume Vm of the excess water

using the measuring cylinder


CalculationVolume of cork = Vm - VDensity of cork = mass / volume


1. Some students measure the masses and the volumes of different sized samples of a type of wood.

Which graph shows their results?


B

2. Which of the following is a unit of density?A. cm3/ gB. g/cm2

C. g/cm3

D. kg /m2


3. What apparatus is needed to determine the density of a regularly-shaped block?

A. a balance and a rulerB. a balance and a forcemeter (spring balance)C. a measuring cylinder and a rulerD. a measuring cylinder and a beaker


4. A student does an experiment to estimate the density of an irregularly-shaped stone.

5. Which items of equipment are needed?A. a balance and a measuring cylinder

containing waterB. a balance and a rulerC. a ruler and a measuring cylinder containing

waterD. only a measuring cylinder containing water


5. A student is trying to find the density of water and of a large, regularly-shaped solid.

6. Which apparatus is needed to find the density of both?

A. balance, clock, rulerB. balance, measuring cylinder, rulerC. balance, measuring cylinder, stringD. clock, ruler, string


6. A student needs to find the density of a cubic block of wood.

7. Which two pieces of apparatus should she use?

A. balance and metre ruleB. balance and thermometerC. measuring cylinder and metre ruleD. measuring cylinder and thermometer


7. A student is trying to find the density of a stone, but he has mixed up the instruction cards.


What order should the cards be in?A. 5 → 3 → 6 → 2 → 1 → 4→ 7B. 1 → 5 → 3 → 6 → 2 → 7 → 4C. 5 → 6 → 3 → 2 → 1 → 7 → 4D. 1 → 4 → 5 → 3 → 6 → 2 → 7


8. A person measures the length, width, height and mass of a rectangular metal block.

Which of these measurements are needed in order to calculate the density of the metal?

A. mass onlyB. height and mass onlyC. length, width and height onlyD. length, width, height and mass


9. A student pours liquid into a measuring cylinder.

10. The student records the volume of the liquid from the scale on the measuring cylinder. He then puts the measuring cylinder containing the liquid on a balance and records the mass.

11. What else needs to be measured before the density of the liquid can be calculated?

A. the depth of the liquid in the measuring cylinderB. the mass of the empty measuring cylinderC. the temperature of the liquid in the measuring cylinderD. the volume of the empty measuring cylinder


10. A student tries to find the density of a metal block. First he measures the weight with a forcemeter (spring balance). Next he measures the sides of the block using a rule, in order to calculate the volume of the block. Finally he divides the weight by the volume to find the density.

The student has made a mistake. Why does his method not give the density?

A. Density is volume divided by weight.B. He should have measured the surface area, not the

volume.C. He should have used the mass in his calculation, not the

weight.D. Weight is not measured with a forcemeter (spring

balance).Mass, Weight & Density 64

11. Ten identical steel balls, each of mass 27 g, are immersed in a measuring cylinder containing 20 cm3 of water.

The reading of the water level rises to 50 cm3.

What is the density of the steel?A. 0.90 g/cm3 B. 8.1 g/cm3

C. 9.0 g/cm3

D. 13.5 g/cm3


12. A measuring cylinder containing some water stands on a scale pan. A solid ball is lowered into the water.

The water level rises from the 30 cm3 mark to the 40 cm3 mark. The scale reading increases from 100 g to 180 g. What is the density of the material of the ball?

A. 2.0 g / cm3 B. 4.5 g / cm3

C. 8.0 g / cm3

D. 18 g / cm3 Mass, Weight & Density 66

13. The masses of a measuring cylinder before and after pouring some liquid are shown in the diagram.

What is the density of the liquid?


D

14. The masses of a measuring cylinder before and after pouring some liquid into it are shown in the diagram.

What is the density of the liquid?

Mass, Weight & Density 68B

15. The mass of a measuring cylinder is measured before and after pouring a liquid into it.


1. What is the density of the liquid?A. 0.79 g / cm3

B. 1.3 g / cm3

C. 1.4 g / cm3 D. 2.2 g / cm3


16. An object of mass 100 g is immersed in water as shown in the diagram.

What is the density of the material from which the object is made?

A. 0.4 g / cm3

B. 0.9 g / cm3

C. 1.1 g / cm3

D. 2.5 g / cm3


17. The diagram shows an experiment to find the density of a liquid.


1. What is the density of the liquid?A. 0.5 g / cm3

B. 2.0 g / cm3

C. 8.0 g / cm3

D. 10.0 g / cm3


18. The diagram shows some liquid in a measuring cylinder. The mass of the liquid is 16 g.

What is the density of the liquid?A. 320 g / cm3 B. 36 g / cm3 C. 1.25 g / cm3 D. 0.8 g / cm3


19. The diagram shows a material with dimensions 5 cm × 4cm × 2 cm. It has a mass of 100 g.

What is the density of the material?A. 0.40 g / cm3

B. 2.5 g / cm3

C. 5.0 g / cm3

D. 10 g / cm3


20. The diagram shows a rectangular metal block measuring 10 cm × 5.0 cm × 2.0 cm.


1. Its mass is 250 g.2. What is the density of the metal?

A. 0.20 g / cm3

B. 0.40 g / cm3

C. 2.5 g / cm3

D. 5.0 g / cm3


21. A metal drum has a mass of 200 kg when empty and 1000 kg when filled with 1.0 m3 of methylated spirit.

22. What is the density of methylated spirit?A. 0.0050 kg / m3

B. 0.11 kg / m3

C. 800 kg / m3

D. 1000 kg / m3


22. A lump of metal has a mass of 210 g. It is lowered into a measuring cylinder containing water.

23. The level of the water rises from 35 cm3 to 140 cm3.


1. What is the density of the metal?A. 0.67 g / cm3

B. 1.5 g / cm3

C. 2.0 g / cm3

D. 6.0 g / cm3


23. Three objects are cut from the same sheet of steel. They are different shapes but they all have the same mass.

Which object has the greatest density?A. the discB. the L-shapeC. the squareD. they all have the same density


24. The diagram shows four blocks, each made of glass of density 2.6 g / cm3.

The top of each block has an area of 1 cm2. Which block has a mass of 13 g?


C

25. Each of the solids shown in the diagram has the same mass.

26. Which solid has the greatest density?


B

26. A box X full of large granite rocks is weighed. An identical box Y full of small granite chippings is then weighed.

Which box weighs more and why?


C

27. The same mass of four different liquids is placed in some measuring cylinders.

Which measuring cylinder contains the liquid with the greatest density?


B

28. Four blocks, each made from a different material, are placed on scales and balanced as shown in the diagrams below.

In which diagram does the block have the greatest density?

Mass, Weight & Density 86A

29. Two identical measuring cylinders containing different liquids are placed on a simple balance.

30. They balance as shown.


1. How does the density of X compare with the density of Y?


A

LEARNING OUTCOMES

MASS, WEIGHT & DENSITY


State that mass is a measure of the amount of substance in a body.

State that mass of a body resists change from its state of rest or motion.

Mass & Weight


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

Calculate weight from the equation weight = mass x gravitational field strength.

Explain that weights, and therefore masses, may be compared using a balance.

Describe how to measure mass and weight by using appropriate balances.

Gravitational Fields


Describe how to use a measuring cylinder to measure the volume of a liquid or solid.

Describe how to determine the density of a liquid, of a regularly shaped solid and of an irregularly shaped solid which sinks in water (volume by displacement).

Make calculations using the formula density = mass/volume.

Density


mass, weight and density

Education

weight mass mass

mass weight

object mass

weight density

mass x weight

n mass

mass acceleration

jupiter mass