1. Mass and weight Gravitational fields Density
MASS, WEIGHT & DENSITY
Mass and weight
Gravitational fields
Density
Mass, Weight & Density

2. Mass & Inertia
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, Weight & Density

3. Gravitational Field and Field Strength
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.
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).
Mass, Weight & Density

4. Weight = Mass × Acceleration due to gravity
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 gravity
W = mg
Mass, Weight & Density

5. Measuring Mass & Weight
triple beam balance
Spring balance
electronic balance
Mass, Weight & Density

6. Example
A hammer has a mass of 1 kg. What is its weight (i) on Earth (ii) on the Moon (iii) in outer space.
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.
A man has a mass of 70 kg. What is his weight on Jupiter where the field strength is 26 N/kg.
Mass, Weight & Density

7. 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
What is the probe’s weight on Earth?
What is the probe’s mass in space?
What is the probe’s mass in Mars?
What is the probe’s weight on Mars?
When the probe is falling, near the surface of Mars, what is its acceleration?
Mass, Weight & Density

8. What is the acceleration of the rocket on the right?
weight
3000 N force from rocket engine
mass 200 kg
Mass, Weight & Density

9. is the amount of substance in the body
Mass
Weight 1
is the amount of substance in the body
is 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 zero
Mass, Weight & Density

10. The mass of a full bottle of cooking oil is 1.30 kg.
When exactly half of the oil has been used, the mass of the bottle plus the remaining oil is 0.90 kg.
Mass, Weight & Density

11. What is the mass of the empty bottle?
0.40 kg
0.50 kg
0.65 kg
0.80 kg
Mass, Weight & Density

12. What is the meaning of the weight of an object?
the density of the material from which it is made
the force exerted on it by gravity
the mass of the matter it contains
the pressure it exerts on the floor
Mass, Weight & Density

13. What is the gravitational force that the Earth exerts on an object?
the density of the object
the mass of the object
the volume of the object
the weight of the object
Mass, Weight & Density

14. Which relationship defines gravitational field strength?
mass x 10
mass x weight
mass / weight
weight / mass
Mass, Weight & Density

15. On the Earth, the gravitational field strength is 10 N/kg
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?
1.6 N
5.0 N
8.0 N
80 N
Mass, Weight & Density

16. 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
Mass, Weight & Density

17. What is the gravitational field strength on the Moon?
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?
0 N / kg
1.6 N / kg
10 N / kg
16 N / kg
Mass, Weight & Density

18. 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? A
Mass, Weight & Density

19. The table shows the weight of a 10 kg mass on each of five planets.
Mass, Weight & Density

20. On which planets would an astronaut have a smaller weight than on Earth?
Mercury, Mars and Jupiter
Mercury, Venus and Mars
Mercury, Venus and Jupiter
Venus, Mars and Jupiter
Mass, Weight & Density

21. Which statement is correct?
Mass is a force, measured in kilograms.
Mass is a force, measured in newtons.
Weight is a force, measured in kilograms.
Weight is a force, measured in newtons.
Mass, Weight & Density

22. Which of the following statements is correct?
Mass and weight are different names for the same thing.
The mass of an object is different if the object is taken to the Moon.
The weight of a car is one of the forces acting on the car.
The weight of a chocolate bar is measured in kilograms.
Mass, Weight & Density

23. Which statement is correct?
The mass of a bottle of water at the North Pole is different from its mass at the Equator.
The mass of a bottle of water is measured in newtons.
The weight of a bottle of water and its mass are the same thing.
The weight of a bottle of water is one of the forces acting on it.
Mass, Weight & Density

24. A brick is placed on a newton balance X and then on a beam balance Y.
What is measured by each balance? C
Mass, Weight & Density

25. Are the mass and weight of the object the same, or less, than before?
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? C
Mass, Weight & Density

26. This experiment is repeated on the Moon.
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? B
Mass, Weight & Density

27. When two blocks X and Y are placed on a uniform beam, the beam balances on a pivot at its centre as shown.
Mass, Weight & Density

28. What does this show about X and Y?
They have the same mass and the same density.
They have the same mass and the same weight.
They have the same volume and the same density.
They have the same volume and the same weight.
Mass, Weight & Density

29. The weight of an object is to be found using the beam balance shown in the diagram.
Mass, Weight & Density

30. The object is put in the left-hand pan and various standard weights are put in the right-hand pan, with the following results.
Mass, Weight & Density

31. What is the best estimate of the weight of the object?
0.27 N
0.29 N
0.31 N
0.58 N
Mass, Weight & Density

32. Density
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
Mass, Weight & Density

33. Example
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.
What is the volume of the piece of rock?
Calculate the density of the rock.
The density of a solid is 4 g/cm3. What is the volume of 200 g of the solid.
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

34. A sample of ethanol has a volume of 240 cm3
A sample of ethanol has a volume of 240 cm3. Its mass is found to be g. What is the density of ethanol.
Calculate the density of mercury if 500 cm3 has a mass of kg. Give your answer in g/cm3.
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.
What is the volume of a storage tank which will hold kg of petrol? Density of petrol = 800 kg/m3.
What mass of lead has the same volume of 1600 kg of petrol? Density of petrol = 800 kg/m3 & Density of lead = kg/m3.
Mass, Weight & Density

35. EXPERIMENTAL PROCEDURE
TO DETERMINE THE DENSITY OF WATER
Apparatus
Procedure
Calculation
Precautionary Measure
Mass, Weight & Density

36. Apparatus
electronic balance
Measuring cylinder
Mass, Weight & Density

37. Procedure
Measure the mass of the empty measuring cylinder. Take the average reading
Fill the measuring cylinder with water
Measure the mass of the water inside the measuring cylinder. Take average reading
Read the volume of water on the measuring cylinder
Mass, Weight & Density

38. Calculation
Mass of the water = mass of measuring cylinder & water – mass of the empty measuring cylinder
Density of water = mass of water / volume of water
Mass, Weight & Density

39. Precautionary measure
Avoid parallax error when reading the measuring cylinder
To reduce wind interference
Always re-zero the electronic balance
Take average reading of the mass
Mass, Weight & Density

40. EXPERIMENTAL PROCEDURE
TO DETERMINE THE DENSITY OF SOLID CUBE
Apparatus
Procedure
Calculation
Precautionary Measure
Mass, Weight & Density

41. Apparatus
electronic balance
30 cm rule
Mass, Weight & Density

42. Procedure
measure the mass of the cube using electronic. Take average reading
Using the rule measure all the length of the side (length, breadth & height)
Mass, Weight & Density

43. Calculation Volume of cube = length x breadth x height
Density = mass / volume
Mass, Weight & Density

44. Precautionary measure
Avoid parallax error
Check zero error
Reduce wind interference
Take average reading of mass and length
Mass, Weight & Density

45. EXPERIMENTAL PROCEDURE
TO DETERMINE THE DENSITY OF PLASTICINE
Apparatus
Procedure
Calculation
Precautionary Measure
Mass, Weight & Density

46. Apparatus
Electronic balance
Measuring cylinder
Mass, Weight & Density

47. Procedure
Measuring the mass of the plasticine using the electronic balance. Take average reading
Fill the measuring cylinder with water. Take the initial reading of the meniscus, V1
Submerged the palsticine into the cylinder. Take the new reading of the meniscus, V2
Mass, Weight & Density

48. Calculation Volume of plasticine = V2 – V1
Density of plasticine = mass / volume
Mass, Weight & Density

49. Precautionary measure
All plasticine must submerge
Take average reading of mass
Mass, Weight & Density

50. EXPERIMENTAL PROCEDURE
TO DETERMINE THE DENSITY OF CORK
Apparatus
Procedure
Calculation
Precautionary Measure
Mass, Weight & Density

51. Apparatus Electronic balance Eureka can Beaker Measuring cylinder
Sinker
Mass, Weight & Density

52. Procedure
Measuring the mass of the cork using the electronic balance. Take average reading
Tied the cork to a sinker with known volume V
Submerged the cork and sinker into the eureka can
Measure the volume Vm of the excess water using the measuring cylinder
Mass, Weight & Density

53. Calculation Volume of cork = Vm - V Density of cork = mass / volume
Mass, Weight & Density

54. Which graph shows their results?
Some students measure the masses and the volumes of different sized samples of a type of wood.
Which graph shows their results? B
Mass, Weight & Density

55. Which of the following is a unit of density?
cm3/ g
g/cm2
g/cm3
kg /m2
Mass, Weight & Density

56. What apparatus is needed to determine the density of a regularly-shaped block?
a balance and a ruler
a balance and a forcemeter (spring balance)
a measuring cylinder and a ruler
a measuring cylinder and a beaker
Mass, Weight & Density

57. Which items of equipment are needed?
A student does an experiment to estimate the density of an irregularly-shaped stone.
Which items of equipment are needed?
a balance and a measuring cylinder containing water
a balance and a ruler
a ruler and a measuring cylinder containing water
only a measuring cylinder containing water
Mass, Weight & Density

58. Which apparatus is needed to find the density of both?
A student is trying to find the density of water and of a large, regularly-shaped solid.
Which apparatus is needed to find the density of both?
balance, clock, ruler
balance, measuring cylinder, ruler
balance, measuring cylinder, string
clock, ruler, string
Mass, Weight & Density

59. A student needs to find the density of a cubic block of wood.
Which two pieces of apparatus should she use?
balance and metre rule
balance and thermometer
measuring cylinder and metre rule
measuring cylinder and thermometer
Mass, Weight & Density

60. A student is trying to find the density of a stone, but he has mixed up the instruction cards.
Mass, Weight & Density

61. What order should the cards be in?
5 → 3 → 6 → 2 → 1 → 4→ 7
1 → 5 → 3 → 6 → 2 → 7 → 4
5 → 6 → 3 → 2 → 1 → 7 → 4
1 → 4 → 5 → 3 → 6 → 2 → 7
Mass, Weight & Density

62. 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?
mass only
height and mass only
length, width and height only
length, width, height and mass
Mass, Weight & Density

63. A student pours liquid into a measuring cylinder.
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.
What else needs to be measured before the density of the liquid can be calculated?
the depth of the liquid in the measuring cylinder
the mass of the empty measuring cylinder
the temperature of the liquid in the measuring cylinder
the volume of the empty measuring cylinder
Mass, Weight & Density

64. The student has made a mistake.
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?
Density is volume divided by weight.
He should have measured the surface area, not the volume.
He should have used the mass in his calculation, not the weight.
Weight is not measured with a forcemeter (spring balance).
Mass, Weight & Density

65. The reading of the water level rises to 50 cm3.
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?
0.90 g/cm3
8.1 g/cm3
9.0 g/cm3
13.5 g/cm3
Mass, Weight & Density

66. The water level rises from the 30 cm3 mark to the 40 cm3 mark.
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?
2.0 g / cm3
4.5 g / cm3
8.0 g / cm3
18 g / cm3
Mass, Weight & Density

67. What is the density of the liquid?
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
Mass, Weight & Density

68. What is the density of the liquid?
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? B
Mass, Weight & Density

69. The mass of a measuring cylinder is measured before and after pouring a liquid into it.
Mass, Weight & Density

70. What is the density of the liquid?
0.79 g / cm3
1.3 g / cm3
1.4 g / cm3
2.2 g / cm3
Mass, Weight & Density

71. 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?
0.4 g / cm3
0.9 g / cm3
1.1 g / cm3
2.5 g / cm3
Mass, Weight & Density

72. The diagram shows an experiment to find the density of a liquid.
Mass, Weight & Density

73. What is the density of the liquid?
0.5 g / cm3
2.0 g / cm3
8.0 g / cm3
10.0 g / cm3
Mass, Weight & Density

74. What is the density of the liquid?
The diagram shows some liquid in a measuring cylinder. The mass of the liquid is 16 g.
What is the density of the liquid?
320 g / cm3
36 g / cm3
1.25 g / cm3
0.8 g / cm3
Mass, Weight & Density

75. What is the density of the material?
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?
0.40 g / cm3
2.5 g / cm3
5.0 g / cm3
10 g / cm3
Mass, Weight & Density

76. The diagram shows a rectangular metal block measuring 10 cm × 5
The diagram shows a rectangular metal block measuring 10 cm × 5.0 cm × 2.0 cm.
Mass, Weight & Density

77. What is the density of the metal?
Its mass is 250 g.
What is the density of the metal?
0.20 g / cm3
0.40 g / cm3
2.5 g / cm3
5.0 g / cm3
Mass, Weight & Density

78. What is the density of methylated spirit?
A metal drum has a mass of 200 kg when empty and kg when filled with 1.0 m3 of methylated spirit.
What is the density of methylated spirit?
kg / m3
0.11 kg / m3
800 kg / m3
1000 kg / m3
Mass, Weight & Density

79. The level of the water rises from 35 cm3 to 140 cm3.
A lump of metal has a mass of 210 g. It is lowered into a measuring cylinder containing water.
The level of the water rises from 35 cm3 to 140 cm3.
Mass, Weight & Density

80. What is the density of the metal?
0.67 g / cm3
1.5 g / cm3
2.0 g / cm3
6.0 g / cm3
Mass, Weight & Density

81. Which object has the greatest density?
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?
the disc
the L-shape
the square
they all have the same density
Mass, Weight & Density

82. The top of each block has an area of 1 cm2.
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
Mass, Weight & Density

83. B Each of the solids shown in the diagram has the same mass.
Which solid has the greatest density? B
Mass, Weight & Density

84. Which box weighs more and why?
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
Mass, Weight & Density

85. The same mass of four different liquids is placed in some measuring cylinders.
Which measuring cylinder contains the liquid with the greatest density? B
Mass, Weight & Density

86. In which diagram does the block have the greatest density?
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? A
Mass, Weight & Density

87. Two identical measuring cylinders containing different liquids are placed on a simple balance.
They balance as shown.
Mass, Weight & Density

88. A How does the density of X compare with the density of Y?
Mass, Weight & Density

89. MASS, WEIGHT & DENSITY
LEARNING OUTCOMES
Mass, Weight & Density

90. Mass & Weight
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 & Density

91. weight = mass x gravitational field strength.
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.
Mass, Weight & Density

92. Density
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.
Mass, Weight & Density