2. 1© Manhattan Press (H.K.) Ltd. 1.7 Stability

3. 2 © Manhattan Press (H.K.) Ltd. Stability 1.7 Stability (SB p. 75) What makes objects more stable than others? Unstable equilibrium - CG outside its base It falls over

4. 3 © Manhattan Press (H.K.) Ltd. Stability 1.7 Stability (SB p. 75) Stable equilibrium - CG within its base It falls back to its initial position

5. 4 © Manhattan Press (H.K.) Ltd. Stability 1.7 Stability (SB p. 75) Neutral equilibrium - CG is raised or lowered when displaced horizontally It will not roll further or roll back to its initial position

6. 5 © Manhattan Press (H.K.) Ltd. Stability 1.7 Stability (SB p. 76) Which one topples over? A – topples over (the line of action of its weight acts outside the corner of its base) Hence, an object is more stable if: (a) it has a larger base (e.g. B), and (b) its CG if lower (e.g. C). Go to More to Know 9 More to Know 9

7. 6 © Manhattan Press (H.K.) Ltd. Stability 1.7 Stability (SB p. 76) Use in design - double decker bus engine mounted as low as possible, passengers not stand on upper deck - racing car wide base Go to Example 16 Example 16

8. 7 © Manhattan Press (H.K.) Ltd. 1.1 Force 1. There are four types of forces in nature: gravitational force, electromagnetic force, weak nuclear force and strong nuclear force. 1.7 Stability (SB p. 78)

9. 8 © Manhattan Press (H.K.) Ltd. 1.2 Different types of forces 2. Weight – the gravitational attractive force acting on a body by the earth. 3. Normal reaction – force exerting vertically upwards on a body by the ground. 4. Tension – force acting along an inextensible string when a body connected to it is being pulled. 1.7 Stability (SB p. 78)

10. 9 © Manhattan Press (H.K.) Ltd. 1.2 Different types of forces 5. (a) Elastic force – force setting up along an elastic body when it is stretched or compressed. (b) According to Hooke’s Law, the elastic force is directly proportional to the extension or compression of the elastic body, i.e. F e = ke where k is the force constant and e is the extension / compression of the body. 1.7 Stability (SB p. 78)

11. 10 © Manhattan Press (H.K.) Ltd. 1.2 Different types of forces 6. (a) Friction – force acting between two rough contact surfaces to oppose any relative motion. (b) Static friction occurs between the surfaces which are both at rest. (c) Limiting friction (f L ) is the maximum friction for a body to stay rest. f L = μ s R where μ s is the coefficient of static friction and R is the normal reaction. 1.7 Stability (SB p. 78)

12. 11 © Manhattan Press (H.K.) Ltd. 1.2 Different types of forces 6. (d) Kinetic friction (f k ) is the frictional force acting on a constantly moving object. f k = μ k R where μ k is the coefficient of kinetic friction and R is the normal reaction. 1.7 Stability (SB p. 78)

13. 12 © Manhattan Press (H.K.) Ltd. 1.3 Vectors and resolution of forces 7. (a) A scalar is described by its magnitude only. (b) A vector is described by both its magnitude and direction. 8. The resultant of two forces can be found by using the methods: (a) Parallelogram of vectors; and (b) Triangle of vectors. 1.7 Stability (SB p. 78)

14. 13 © Manhattan Press (H.K.) Ltd. 1.3 Vectors and resolution of forces 9. A force can be resolved into its components. 10. When the forces in a system are in equilibrium, the algebraic sum of the components of the forces in any direction must be zero. 11. When more than three coplanar forces act on a point, the resultant can be found by drawing a polygon of forces. 1.7 Stability (SB p. 78)

15. 14 © Manhattan Press (H.K.) Ltd. 1.4 Moment of a force 12. The turning effect of a force about an axis is called the torque or moment of a force about that axis. Torque = F ×r where F is the rotating force and r is the perpendicular distance of F from the axis. 13. A couple consists of two forces of the same magnitude but acting in opposite directions and not along the same line. 1.7 Stability (SB p. 78)

16. 15 © Manhattan Press (H.K.) Ltd. 1.5 Static equilibrium of a rigid body 14. A rigid body is in static equilibrium if (a) the resultant force is zero, and (b) the algebraic sum of the moments of the forces about any axis is zero. 1.7 Stability (SB p. 78)

17. 16 © Manhattan Press (H.K.) Ltd. 1.6 Centre of gravity 1.7 Stability (SB p. 79) 15. (a) The centre of gravity (CG) of an object is the point where the line of action of the weight of the object passes. (b) The co-ordinates of CG of a lamina is given by: 16. The centre of mass of an object is the point where the whole mass of the object is assumed to be concentrated.

18. 17 © Manhattan Press (H.K.) Ltd. 1.7 Stability 17. An object is in unstable equilibrium if any displacement lowers its centre of gravity. 18. An object is in stable equilibrium if it returns to its initial position when slightly displaced. 19. An object is in neutral equilibrium if it rolls to a new position and stops there after being displaced. 20. An object is more stable if it has a larger base and lower CG. 1.7 Stability (SB p. 79)

19. 18 © Manhattan Press (H.K.) Ltd. 1.7 Stability (SB p. 80)

20. 19 © Manhattan Press (H.K.) Ltd. End

21. 20 © Manhattan Press (H.K.) Ltd. Boxing By keeping his feet apart, a boxer lowers his CG and makes his “base” as wide as possible so that he is less likely to be hit down by his opponent. Return to Text 1.7 Stability (SB p. 76)

22. 21 © Manhattan Press (H.K.) Ltd. Q: Q:A uniform rectangular block shown in the figure is of height 40 cm and 20 cm wide. It is prevented from sliding. If the angle θ is slowly increased, at what value of θ will the block topple over? Solution 1.7 Stability (SB p. 77)

23. 22 © Manhattan Press (H.K.) Ltd. Solution: Return to Text The block will topple over when the line of action of the weight W passes through the corner A. Using the figure, θ= ∠ ABC = tan −1 (20/40) = 26.6° 1.7 Stability (SB p. 77)