Force and Equilibrium of Objects
Senior 1 · Physics
Force and Equilibrium of Objects
Lesson 5 of 5
25 min
On the roads of Rwanda you often see people carrying heavy loads on their heads, a basket of bananas or a sack of charcoal, walking up steep hills without using their hands. Yet a minibus with bags piled high on its roof is more likely to roll over on a sharp bend than the same bus with the bags stowed low. Both puzzles are answered by one idea: the point where an object's weight acts, its centre of gravity.
Definition
The centre of mass of an object is the point where all its mass can be thought of as concentrated.
The centre of gravity (G) is the point through which the whole weight of the object appears to act. Near the Earth's surface it is at the same place as the centre of mass.
A lamina is a thin, flat sheet, such as a piece of card.
For a uniform object with a regular shape, the centre of gravity is at its geometric centre, where its lines of symmetry meet.
Figure 5.1: The centre of gravity G of uniform regular laminas. For a ring, G is at the centre, where there is no material at all.
Worked example 1: a rectangular sheet
Where is the centre of gravity of a uniform rectangular sheet of metal 40 cm long and 30 cm wide?
The diagonals cross at the middle, so G is 20 cm from the short edges and 15 cm from the long edges:
Figure 5.2: The plumb-line method. The card hangs with G directly below the pin, so G lies on the plumb line. Two plumb lines cross at G.
Why it works: a freely hanging object comes to rest with its centre of gravity directly below the point of suspension. Then its weight passes through the pin and has no moment about it.
Important
Safety. Take care with pins and scissors, and hand them to others handle first. Make sure the stand is steady before hanging anything from it.
Worked example 2: weighing a metre rule with moments
A uniform metre rule balances on a knife edge at its 30 cm mark when a 2.0 N weight hangs at its 10 cm mark. Find the weight of the rule.
The rule is uniform, so its weight acts at G, the 50 cm mark, which is 0.20 m from the pivot. The 2.0 N weight is also 0.20 m from the pivot, on the other side. Principle of moments about the pivot:
Definition
An object in equilibrium can be in one of three states:
Figure 5.3: The three states of equilibrium of a cone. The red arrow is the weight acting at G.
An object topples when the vertical line through its centre of gravity (the line of its weight) falls outside its base. Then the weight has a moment about the edge it is tipping over, and that moment turns it further over. While the line stays inside the base, the moment of the weight turns the object back.
Figure 5.4: Both blocks are tilted by the same angle. The line of the weight of the wide, low block still falls inside its base; that of the tall, narrow block falls outside, so it topples.
So an object is more stable if it has:
Warning
Common mistakes. (1) Thinking the centre of gravity must be inside the material: for a ring, a horseshoe or a boomerang it is in the empty space. (2) Thinking G is where the object is "heaviest": it is the balance point of the whole weight. (3) Thinking a heavy object is always more stable: stability depends on how HIGH G is and how WIDE the base is.
Tip
Low and wide stays upright. Picture the line of the weight dropping straight down from G: inside the base, safe; outside the base, it tips.
Centre of gravity of regular and irregular laminas: a Senior 1 lesson recorded by Rwanda Education Board (REB elearning), about 27 minutes. Watch the plumb-line method and compare it with the steps above.
Practice
Key points
Further reading
Sources and credits
The worked examples, diagrams, Rwandan applications and practice exercises are written by Ganzaa.
