Define centre of gravity.
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The centre of gravity is the point through which the entire weight of an object acts.
Centre Of Gravity
A student says “the centre of gravity of every object is inside the object.” Explain why this statement is incorrect.
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The centre of gravity is the point through which the weight acts; it does not have to be inside the material of the object. For example, the centre of gravity of a ring-shaped object lies at the centre of the ring, where there is no material. Therefore the statement is incorrect because the distribution of mass can place the centre of gravity outside the physical body of the object.
Describe how you would determine the position of the centre of gravity of an irregularly shaped piece of cardboard.
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Make a small hole near the edge of the cardboard; suspend the cardboard from a pin through the hole so it hangs freely; hang a plumb line from the same pin and wait for it to come to rest; draw a line on the cardboard along the plumb line. Repeat the procedure using a second hole at a different position on the edge. The centre of gravity is the point where the two lines cross. A third hole can be used as a check — the third line should pass through the same point.
Explain why the lamina must be able to swing freely on the pin for the experiment to give an accurate result.
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When the lamina swings freely, it comes to rest with its centre of gravity directly below the pivot point; the plumb line then marks a true vertical line through the centre of gravity. If the lamina cannot swing freely (because friction at the pin prevents rotation), it may stop in a position where the centre of gravity is not directly below the pivot; therefore the line drawn would not pass through the true centre of gravity, and the result would be inaccurate.
State two features of an object that make it more stable.
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A lower centre of gravity; a wider base.
A tall bookshelf is more likely to topple over than a short, wide chest of drawers. Explain why, in terms of centre of gravity and base area.
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The tall bookshelf has a high centre of gravity and a narrow base. When it is tilted slightly, the vertical line through its centre of gravity quickly falls outside the narrow base area, so an overturning moment acts and the bookshelf topples. The short, wide chest of drawers has a lower centre of gravity and a wider base. The object must be tilted through a much larger angle before the line of action of the weight moves outside the base area, so it is more stable and resists toppling.
Explain why the holes used for suspension must be near the edge of the lamina and spaced well apart.
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The holes must be near the edge so the lamina can hang freely and rotate about the pin without the pin being too close to the centre of gravity, which would reduce the accuracy of the hanging position. The holes must be spaced well apart so the lines drawn on the lamina cross at a large angle; if the holes are close together, the lines are nearly parallel and their intersection point is difficult to determine accurately.
A student finds that the three lines drawn on the lamina do not all pass through exactly the same point. Suggest two possible reasons for this error.
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The lamina may not have been hanging completely still when the pencil lines were drawn, so the plumb line was not truly vertical; the pin hole may have been too tight, causing friction that prevented the lamina from rotating freely to its equilibrium position. Either error causes the pencil line to deviate from the true vertical through the centre of gravity.