Mass Weight and Density Lesson Objectives At the

Mass, Weight and Density

Lesson Objectives At the end of this lesson, you should be able to: 1. 2. 3. 4. 5. 6. 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.

Mass n n 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.

Examples of Masses of Objects Object Mass in kilogram (kg) Electron 10 -30 A fine grain of sand 10 -6 A pea 10 -3 An apple 10 -1 A medium-sized car 103 Earth 1024 Sun 1030

Measurement Instruments Mass is measured using a balance such as the beam balance electronic balance Beam Balance Electronic Balance

Newton’s First Law An object at rest tends to stay at rest and an object in motion tends to continue in motion at constant speed in a straight line (uniform velocity) unless an external resultant force acts on it.

Inertia

Inertia The inertia of an object is its reluctance to move when it is at rest or to slow down or stop when it is moving. That is, it is its reluctance to change its state of rest or motion The car and the wall

Inertia is. . . measured by mass The more massive an object, the more inertia it has, hence, the larger the force is required to change its motion Conversely. . .

Gravitational Field Strength n n n The gravitational field is a region in which a mass experiences a force due to gravitational attraction. Gravitational field strength is gravitational force acting per unit mass on an object. On earth, the gravitational field strength is 10 N kg-1 or 10 ms-2.

Weight is. . . gravitational force acting on an object W = mg where m is the mass of the object g is the gravitational field strength. Weight is measured in newtons (N)

Measurement Instruments Weight is measured using a balance such as the spring balance compression balance Spring Balance Compression Balance

Differences between Weight and Mass Weight pull of gravity on the body has both magnitude and direction measured in newtons changes from place to place Mass amount of matter in the body has only magnitude but no direction measured in kilograms is constant regardless of place or location

Weight Planets Sun Mercury Venus Earth Moon Mars Jupiter Saturn Uranus Neptune Pluto Acceleration Due to Gravity Comparison Acceleration Due Mass [kg] Radius [m] g / g-Earth to Gravity, "g" [m/s 2 ] 1. 99 x 1030 3. 18 x 1023 4. 88 x 1024 5. 98 x 1024 7. 36 x 1022 6. 42 x 1023 1. 90 x 1027 5. 68 x 1026 8. 68 x 1025 1. 03 x 1026 1. 40 x 1022 6. 96 x 108 2. 43 x 106 6. 06 x 106 6. 38 x 106 1. 74 x 106 3. 37 x 106 6. 99 x 107 5. 85 x 107 2. 33 x 107 2. 21 x 107 1. 50 x 106 274. 13 3. 59 8. 87 9. 81 1. 62 3. 77 25. 95 11. 08 10. 67 14. 07 0. 42 27. 95 0. 37 0. 90 1. 00 0. 17 0. 38 2. 65 1. 13 1. 09 1. 43 0. 04

Story 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 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.

Density What is density? Density is defined as mass per unit volume Density = mass/volume M Units SI units: kg/m 3 Other units: g/cm 3 The floating orange D V My Dear Valentine

Density A cylindrical steel rod has a diameter of 0. 2 m and length of 3 m. Its mass is 3. 5 kg. Calculate its density. Volume of rod = l = = 0. 094 m 3 Density =

Density Object Mass/g Vol/cm 3 Aluminium sheet 50 18. 52 Gold bracelet 150 Water Density g/cm 3 Sink or Float? 2. 70 Sink 7. 89 19. 0 Sink 500 1 --- Ice 10 10. 87 0. 92 Float Block of pinewood 800 1600 0. 5 Float

Concept Map kg/m 3 Densit y Mass per unit volume defined as related to mass by D = M/V related to density by defined as Mass, m kg related to weight by is a measure of W=mxg related to mass by N Weight where defined as Amount of substance in a body inertia g is the gravitational force per unit mass acting on an object Gravitational force acting on an object