Chapter 5: Turning Effects of Forces

Transcription

1 Chapter 5: Turning Effects of Forces Brief Recap [Centre of Gravity] 1. 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. 2. Identify the positions of the centre of gravity of regular as well as irregular objects

2 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

3 Regular and uniform objects The geometrical centre of some common shapes- This is also where the centre of gravity and the object s weight, W, can be considered to act

4 For a triangle The centre of gravity (and geometrical centre) is found by drawing a line from the corner to the opposite line s midpoint

5 External CoG For some objects the CoG is not located on the actual object - Stool Ring 2 uniform perpendicular planks

6 CoG of an irregular shape Find the CoG of an irregular shaped lamina Pin held by clamp a b c b c c a a b hole plumb line

7 Balancing Act! Now, try to balance the object at that point c a b Question- explain in terms of moments why the object can be balanced at this point? Answer- on one side of the point of CoG, the object s weight is causing a turning effect. This is counter balanced on the other side where the weight is causing a turning effect in the opposite direction.

8 Let s Watch A Short Clip

9 A Simple Experiment

10 Stability Stability refers to the ability of an object to return to its original position after it has been tilted slightly.

11 Case A: Base of cone in contact with ground Anticlockwise moment When the cone is tilted slightly, 1) Its centre of gravity rises and then falls back again 2) the line of action of its weight W lies insides the base area of the cone 3) the anticlockwise moment of its weight W about the point of contact C causes the cone to return to its original position Hence, the cone is in stable equilibrium because when it is tilted slightly, it returns to its original position without toppling.

12 Case B: Tip of cone in contact with ground Clockwise moment When the cone is tilted slightly, 1) its centre of gravity falls and continues to fall further 2) the line of action of its weight W lies outside the base area of the cone 3) the clockwise moment of its weight W about the point of contact C causes toppling Hence, the cone is in unstable equilibrium because when it is tilted slightly, it topples over.

13 Case C: Slant surface of cone in contact with ground No moment When the cone is tilted slightly, 1) its centre of gravity neither rises nor falls; it remains at the same level above the surface supporting it 2) the lines of action of the two forces W and R always coincide 3) there is no moment provided by its weight W about the point of contact C to turn the cone Hence, the cone is in neutral equilibrium because when it is slightly displaced or rolled, it will stay in its new position.

14 Stability For an object to start rotating it needs to have an unbalanced moment acting on it- Rotates Clockwise Rotates Anti-Clockwise W Stable Pivot W Stable W Pivot Unstable

15 An object becomes unstable when its Centre of Gravity falls outside of the object s base. Why? All of the object s weight can be considered as acting through the CoG. If this acts outside the base then it will cause a turning effect or a moment

16 Factors affecting stability of objects 1. The base area of an object (As wide as possible) 2. The height of the centre of gravity above the base of an object (As low as possible) To increase the stability of an object: 1. Broaden/widen the base area of the object 2. Add weights to the base of the object such that the CG becomes lower

17 The Traffic Cone A great example of a VERY stable object. What features of the cone make it so stable? -Low Centre of Gravity -Wide base

18 Balance and Sport

19 Balance and Sport

20 The Double Decker Bus Each of the diagrams on the right represent a Double Decker bus with passengers inside. Draw out and label the one which shows all passengers on - the lower level - the upper level - both levels

21 Delete a word to complete the sentences If more people sit upstairs on the bus the CoG will rise/fall. This will make the bus more stable/unstable and it can be tilted by a greater/lesser angle The bus will fall over when the CoG acts inside/outside of the bus base A stable object has a low/high CoG and a narrow/wide base

22 Formula One Racing Car The more stable a car, the faster it can go round sharp turns without overturning. Hence, all racing cars have a very wide base and a low centre of gravity)

23 Tightrope Walker The tightrope walker has to position his centre of gravity directly above the metal wire in order to maintain his balance and not fall. If his centre of gravity is not aligned vertically with the wire, it will give rise to a moment that will rotate him about the wire. If the tightrope walker does not quickly realign his centre of gravity, he will fall. The long balancing rope helps to lower his CG. By using a long drooping pole with weighted ends, his CG may actually lie below the wire. In this case, the tightrope walker will be more stable and will find it easier to balance on the rope.)

24 We have learnt 1) State that stability refers to the ability of an object to return to its original position after it has been tilted slightly 2) Describe qualitatively the effect of the position of the centre of gravity on the stability of objects 3) Identify and describe three different cases of equilibrium namely stable equilibrium, unstable equilibrium and neutral equilibrium in terms of centre of gravity and moments of its weight about the point of contact 4) Identify that in order to increase the stability of an object, 1. The object s centre of gravity should be as low as possible 2. The area of the object s base should be as wide as possible 5) Relate and use the concept of stability to explain daily activities happening in real-life context