Unit 4: Mass, Weight and Density

1. Unit 4: Mass, Weight and Density PHYSICS Matters for GCE ‘O’ Level

2. Unit 4.1 Mass and Weight Learning Outcomes In this section, you’ll be able to: • define mass, gravitational field and gravitational field strength g • differentiate between mass and weight • recall and apply weight W = m x g to solve problems

3. Video Links Use the links below to have a good idea of what is Mass and Weight: Mass http://www.youtube.com/watch?v=uvy4nWh0KwE&NR=1 Weight http://www.youtube.com/watch#v=grWG_U4sgS8

4. Unit 4.1: Mass and Weight What is mass? • Mass is a measure of the amount of matter or substance in a body. • The SI unit of mass is the kilogram (kg) Fig 4.1 The number and composition of atoms and molecules make up the mass of a body.

5. Unit 4.1: Mass and Weight What is weight? • Weight is a force and has direction pointing towards the centre of the earth (downwards). • Its SI unit is the Newton (N). • This force is called gravitational force (pull) or gravity.

6. Unit 4.1: Mass and Weight What is gravitational field? • The Earth’s gravity is experienced by any object near it. • The region surrounding the Earth where gravity is experienced is called the gravitational field. • The force experienced is strongest on the surface of the earth and gets weaker further away. Fig 4.3 Earth is surrounded by a gravitational field. Field lines are drawn to represent the gravitation field.

7. Unit 4.1: Mass and Weight What is gravitational field strength? • Gravitational field strength (g) is defined as the gravitational force acting per unit mass on an object. • On Earth, the gravitational field strength is about 10 N kg-1 • A mass of 1 kg will weight 10 N on Earth. • On Moon, the gravitational field strength is about 1.6 N kg-1 • A mass of 1 kg will weight 1.6 N on Moon.

8. Unit 4.1: Mass and Weight • On Earth, acceleration of free fall • g = 9.81 m s−2 • For a 1 kg mass, • W = mg • = 1 kg × 9.81 m s−2 • = 9.81 N • Every 1 kg mass has a weight of 9.81 N.

9. 4.1 Mass and Weight Differences between mass and weight

10. Unit 4.1: Mass and Weight How are mass and weight related? • The weight or amount of gravitational force acting on an object is dependent on its mass. • The weight W can be found by where m = mass of object (in kg) g = gravitational field strength in (N kg-1) W = m g

11. Unit 4.1: Mass and Weight How are mass and weight related? • Common weighing instruments such as electronic balance, spring balance and bathroom scales actually measure the weight and not the mass of an object. • Using the scale on Moon will give different readings. Fig 4.7 The fastest way to lose weight.

12. Unit 4.1: Mass and Weight How is mass measured? • Mass of an object does not depend on the gravitational field strength. • It can be measured using the beam balance. • The beam balance compares the gravitational force acting on an object with standard masses. (Unit 5)

13. Unit 4.1 Mass and Weight

14. Unit 4.1 Mass and Weight

15. Unit 4.1 Mass and Weight Key Ideas • Mass measures the amount of matter or substance in a body. The SI unit is kilograms (kg) • Weight is the gravitational force acting on a body. The SI unit is newtons (N). • The weight of a body is related to its mass by the equation: W = mg • Gravitational field strength, in N kg-1 is the same as the acceleration of free fall in m s-2. • The weight of an object varies according to the gravitational field strength. The mass of an object is a physical property of the object that does not change.

16. Unit 4.1: Mass and Weight Differences between mass and weight Table 4.1 Differences between mass and weight.

17. Unit 4.1 Mass and Weight Test Yourself 4.1 • Why is the mass of a body not affected by changes in the physical environment such as location? Answer: Mass is the amount of matter in the object. It does not change with physical environment.

18. Unit 4.1: Mass and Weight Test Yourself 4.1 • The gravitational field strength of Jupiter is 22.9 N kg-1. An astronaut weighs 1200 N on Earth. What will his weight on Jupiter be? Answer: First, we deduce the mass of the astronaut. Wearth = m gearth 1200 = m x 10  m = 1200 / 10 = 120 kg Hence his weight on Jupiter (if he managed to reach Jupiter) is WJupiter = m gjupiter = 120 x 22.9 = 2750 N

19. Unit 4.1: Mass and Weight Test Yourself 4.1 • What is the difference between gravitational field strength and gravitational pull? Answer: Gravitation field strength g is the gravitational force acting per unit mass on an object. g has SI units N kg-1. Gravitational pull is the gravitational force acting on the object and this is equivalent to its weight. The weight is given by W = m g Weight has SI units of N.

20. Pg 32 Q2

21. Unit 4.2: Inertia Lesson Outcomes In this section, you’ll be able to: • understand and define inertia.

22. Video Use the following links to watch videos on Inertia! • http://www.youtube.com/watch#v=by-7kkAu2Pg&feature=related • http://www.youtube.com/watch#playnext=1&playnext_from=TL&videos=SfsODLJvrys&v=cuG8sIiV8iQ

23. Unit 4.2: Inertia Fig. 4.13 Driver not wearing the seat belt. Fig. 4.14 Driver wearing the seat belt.

24. Inertia and Mass • Inertia of an object is the • reluctance of the object to change either its state of rest, or if it is moving, its motion in a straight line. • Newton’s first law of motion states that • a body continues in its state of rest or uniform motion in a straight line unless compelled by a force to do otherwise.

25. Inertia and Mass • A force is needed to overcome inertia • Inertia depends on mass and not weight • The greater the mass of an object, the more difficult it is to start it moving or to stop it • The greater the mass of a body the greater will be its inertia

26. Pg 32 Q3

27. Unit 4.3 Density Lesson Outcome In this section, you’ll be able to: • recall and apply density = mass/volume to solve problems

28. Unit 4.3: Density • Density of a substance is defined as its mass per unit volume where  = density (in kg m-3) m = mass of object (in kg) V = volume of object (in m3) The SI unit of density is kilogram per cubic metre (kg m-3)

29. Unit 4.3: Density Table. 4.2 Densities of common substances.

30. Pg 35 Q1

31. Unit 4.3 Density Floating • Substances that float on water have lower densities than water. eg. Ice (ice = 917 kg m-3) has a lower density than water (water = 1000 kg m-3). Hence we can observe that ice floats on water. Do you know what would happen if we place the ice in turpentine (turpentine = 870 kg m-3). ? Fig 4.16

32. Unit 4.3: Density Pg 77 Fig 4.18

33. Unit 4.3: Density Pg 77 Fig 4.19

34. Figure 4.20 (pg 78) Unit 4.3: Density

35. Unit 4.3: Density

36. Workbook pg 36 Q3 Unit 4.3: Density

37. Pg 36 Q3

38. Unit 4.3 Density Key Ideas • The density of a substance is defined as its mass per unit volume. • The SI units for density is kg m-3. • The density of a substance is a fixed physical property. • Substances that are less dense than water will float on water. • To measure density of a substance, we measure its: • Mass, eg. With a beam balance, and • Volume, eg. Using mathematical formulae of volume (for regular objects) or measuring the volume of water it displaces (for irregular objects).

39. Unit 4.2,4.3: Inertia & Density Test Yourself 4.2-4.3 1. Two groups of people get into two identical cars. One group consists of five Sumo wrestlers while the other group consists of five marathon runners. Assuming both drivers step on the accelerator with equal force, state and explain a) which car takes off faster from rest, and b) which car will need a longer braking distance, once in motion. Answer: (a) The car with marathon runners has smaller mass. It is said to have smaller inertia. Hence it will take off faster. We can also see that by Newton’s 2nd Law, a = F/m Hence the car with smaller mass will have a larger acceleration. (b) The car with the Sumo wrestlers will have a larger breaking distance since they have a larger inertia and hence greater reluctance to come to a stop.

40. Unit 4.3: Density Test Yourself 4.3 3. The density of water is 1000 kg m-3. What is the mass of 1 cm3 of water in grams? Answer: Density of water water Hence 1 cm3 of water has a mass of 1 g.

41. Unit 4: Mass, Weight and Density