1.5.3 Centre of gravity (3)
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1.
Question 2
A small, rigid block is placed on top of a larger, stable block. Describe, qualitatively, how the stability of the combined system is affected by the position of the centre of gravity of the smaller block relative to the larger block.
The stability of the combined system depends on the combined centre of gravity (CG) of the two blocks and its position relative to the base of support, which is the larger block.
If the CG of the smaller block is directly above the larger block, the combined CG will be very close to the edge of the larger block. This configuration is relatively stable. Any slight movement of the smaller block will have a minimal effect on the overall stability.
However, if the CG of the smaller block is significantly to the side of the larger block, the combined CG will be further away from the edge of the larger block. This makes the system less stable. Even a small nudge to the smaller block could cause the combined CG to move outside the base of support, leading to a loss of stability and potential toppling. The greater the distance of the CG from the base, the less stable the system.
2.
A student carried out an experiment to determine the centre of gravity of an irregularly shaped piece of metal. They suspended the metal from a plumb line and drew a vertical line along the thread. They then made a 45° angle with the vertical line and drew another line along the metal's surface. They repeated this process at two other points on the metal. Explain why this method is not ideal for finding the centre of gravity and suggest an improvement.
Why the method is not ideal:
This method is not ideal because the lines drawn at 45° to the vertical will not necessarily intersect at the true centre of gravity. The vertical line of gravity passes through the centre of gravity, but the 45° lines are influenced by the shape of the metal and may not accurately reflect the vertical line of gravity at the centre of gravity. The lines are likely to intersect at a point that is off-centre.
Suggested Improvement:
The student should suspend the metal from a plumb line and repeat the process at more than two points. Ideally, at least three or four different points should be chosen, ensuring they are well-spaced across the metal's surface. The intersection of the vertical lines drawn at these points will give a more accurate determination of the centre of gravity. Using a larger lamina would also improve accuracy.
3.
Explain, in terms of forces, what is meant by the term 'centre of gravity'. How does the position of the centre of gravity affect the stability of an object?
Centre of Gravity - Definition:
The centre of gravity (CG) is the point at which the entire weight of an object can be considered to be concentrated. It is the point where the vertical line of gravity (the line of action of the weight of the object) passes through. Essentially, it's the average position of all the mass in the object.
Stability and Centre of Gravity:
The position of the centre of gravity significantly affects the stability of an object. An object is more stable if its centre of gravity is low. This is because a lower CG means that a greater torque (turning force) is required to tip the object over. Conversely, an object with a high centre of gravity is less stable and more likely to topple. Consider a simple example: a wide, flat object is more stable than a narrow, tall object, even if they have the same mass. This is because the wide object has a lower centre of gravity.
The stability of an object is also related to the base of support. A wider base of support raises the centre of gravity, which can reduce stability. Therefore, a combination of a low centre of gravity and a wide base of support provides the greatest stability.