Unit 5: Turning Effect of Forces

1. Unit 5: Turning Effect of Forces Discover PHYSICS for GCE ‘O’ Level Background: Walking the tightrope pg 82

2. Unit 5.1 Moments Learning Outcomes: In this section, you’ll be able to: • describe the moment of a force and relate this to everyday examples • define and apply moment of a force = force x perpendicular distance from the pivot

3. Unit 5.1: Moments Fig 5.1 Why does the boy require more effort to pull the doorknob when the doorknob is near the hinge than when it is near the edge of the door?

4. Unit 5.1: Moments Definition: The moment of a force (or torque) is the product of the force and the perpendicular distance from the pivot to the line of action of the force. Fig 5.2 A simple diagram that show the effect of pulling a door open.

5. Unit 5.1: Moments • The SI unit of the moment is the newton metre (N m) • It is a vector and thus has both magnitude and direction. • Its direction is either clockwise or anti-clockwise. Moment of a force = F x d where F = force (in N) d = perpendicular distance from pivot (in m)

6. Unit 5.1: Moments Fig 5.4 The moment of a force can be clockwise or anticlockwise.

7. Unit 5.1 Moments Worked Example 5.1

8. Unit 5.1 Moments Key Ideas

9. Unit 5.2 Principle of Moments Learning Outcome In this section, you’ll be able to: • state and apply the principle of moments for a body in equilibrium

10. Unit 5.2: Principle of Moments • Why does a beam balance measure mass? (Recall Unit 4) Fig 5.6 A simple diagram showing the forces acting on an equal-arm beam balance.

11. 5.2 Principle of Moments Fig 5.6 A simple diagram showing the forces acting on an equal-arm beam balance. Anticlockwise moment = mg x d Clockwise moment = Sg x d For the beam to balance, the turning effects of these two forces must be equal. Hence, mg x d = Sg x d Therefore m = S Thus, the mass of apple m can be measured by the standard masses S.

12. Unit 5.2: Principle of Moments What is the Principle of Moments? The Principle of Moments states: When a body is in equilibrium, the sum of clockwise moments about a pivot is equal to the sum of anticlockwise moments about the same pivot.

13. 5.2 Principle of Moments

14. 5.2 Principle of Moments Experiment 5.1 (continued)

15. 5.2 Principle of Moment What is the conditions for equilibrium? For an object to be in equilibrium: • All forces acting on it are balanced. i.e. the resultant force is zero. • The resultant moment about the pivot is zero. i.e. The Principle of Moment must apply.

16. 5.2 Principle of Moments Worked Example 5.3 Figure 5.9

17. 5.2 Principle of Moments Levers Levers are simple machines that make use of the principle of moments. When apply a force at one end of the lever, a load may be lifted at the other end. Fig 5.14 Simple levers.

18. 5.2 Principle of Moments Key Ideas

19. 5.2: Principle of Moments Test Yourself 5.2 • State the Principle of Moments. Discuss how this principle may be used to balance a see-saw by two persons of different weight. Answer: When a body is in equilibrium, the sum of clockwise moments about a pivot is equal to the sum of anticlockwise moments about the same pivot. The heavier person has to sit nearer to the pivot, while the lighter person has to sit further away from the pivot. In this way, the moments of the two persons can be equal and the see-saw can be balanced.

20. 5.3 Centre of Gravity Learning Outcome In this section, you’ll be able to: • Understand the centre of gravity of a body as the point through which its weight appears to act.

21. 5.2 Centre of Gravity Try balancing a meter rule with your index finger. At which mark did you observe the ruler does the ruler balance?

22. 5.3 Centre of Gravity Why does a uniform metre rule balance only at the 50 cm mark? W W When the pivot is not at the 50 cm mark, the moment of the weight W is not zero. This causes the ruler to turn clockwise about the pivot. When the pivot is at the 50 cm mark, the ruler is balanced. The moment of the weight is zero.

23. 5.3 Centre of Gravity What is centre of gravity? The centre of gravity of an object is defined as the point through which its whole weight appears to act for any orientation of the object.

24. 5.3 Centre of Gravity Centre of Gravity of some regular shaped objects. Fig 5.18 Centre of gravity of regular-shaped objects.

25. 5.3 Centre of Gravity How to find the centre of gravity of an object? Fig 5.19 A piece of thin lamina that is suspended at various positions will come to rest with its weight acting directly downward as indicated by a plumb line. Where do you think the centre of gravity is?

26. Unit 5.3: Centre of Gravity How to find the centre of gravity of an object? Fig 5.20. Locating the centre of gravity of a lamina by the plumb line method. Note that two lines are sufficient. The third line serves as a check.

27. 5.2 Centre of Gravity Experiment 5.2 Fig 5.22 Fig 5.23

28. 5.4 Stability Learning Outcome In this section, you’ll be able to: • Describe the stability of an object in terms of the position of its centre of gravity

29. Unit 5.4: Stability Definition: Stability refers to the ability of an object to return to its original position after it has been tilted slightly.

30. 5.4 Stability Stable Equilibrium • The centre of gravity rises and then falls back again. • The line of action of its weight W lies inside the base area of the cone. • The anticlockwise moment of its weight W about the point of contact C cause the cone to return to its original position. Fig 5.27(a). Stable Equilibrium.

31. 5.4 Stability Unstable Equilibrium • The centre of gravity falls and continues to fall further. • The line of action of its weight W lies outside the base area of the cone. • The clockwise moment of its weight W about the point of contact C causes the toppling. Fig 5.27(b). Unstable Equilibrium.

32. 5.4 Stability Neutral Equilibrium • The centre of gravity neither rises nor falls; it remains at the same level above the surface supporting it. • The lines of action of the two forces always coincide. • There is no moment provided but its weight W about the point of contact C to turn the paper cone. Fig 5.27(c). Neutral Equilibrium.

33. 5.4 Stability Hence, to increase stability of object, • Centre of gravity is as low as possible. • The area of its base is as wide as possible. Fig 5.28. The more stable a car, the faster it can go round turns without overturning. Hence, all racing cars have a very low wide base and a low centre of gravity.

34. Worked Example 5.5

35. Worked Example 5.7

36. 5.3 – 5.4 Centre of Gravity and Stability

37. 5.3-5.4 Centre of Gravity and Stability Test Yourself 5.3-5.4 • Flat-dwellers in Singapore usually hang their laundry out on bamboo poles. These bamboo poles have to be lifted out of the window and stuck into specially build holes. With wet laundry on it, a lot of effort may be needed to lift the pole up at one end. What advice can you give to reduce the required effort? You may wish to consider a) The turning effects of the weight of the pole and the wet laundry. b) How the distribution of the weight of the wet garments affects the position of the centre of gravity of the pole and wet laundry system. Answer: Some possible advices: • Use a light bamboo pole. • Use shorter bamboo poles. • Place the heavier clothes nearer the end of the pole where the hand is.