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Transcript of SECTION
A body behaves as if its whole mass were concentrated at one point, called its centre of mass or centre of gravity, even though the Earth attracts every part of it. The body's weight can be considered to act at this point. The centre of mass of a uniform ruler is at its centre and when supported there it can be balanced, as in Figure 11.1a. If it is supported at any other point it topples because the moment of its weight W about the point of support in not zero, as in Figure 11.1b.
Your centre of mass is near the centre of your body and the vertical line from it to the floor must be enclosed by your feet or you will fall over. You can test this by standing with one arm and the side of one foot pressed against a wall (Figure 11.2). Now try to raise the other leg sidways.
A tightrope walker has to keep his centre of mass exactly above the rope. Some carry a long pole to help them to balance (Figure 11.3). The combined weight of the walker and pole is then spread out more and if the walker begins to topple to one side, he moves the pole to the other side.
The position of the centre of mass of a body affects whether or not it topples over easily. This is important in the design of such things as tall vehicles (which tend to overturn when rounding a corner), racing cars, reading lamps and even drinking glasses.
A body topples when the vertical line through its centre of mass falls outside its base, as in Figure 11.5a. Otherwise it remains stable, as in Figure 11.5b, where the body will not topple.
Toppleing cann be investigated by placing an empty can on a plank (with a rough surface to prevent slipping) which is slowly tilted. The angle of tilt is noted when the can falls over. This is repeated with a mass of 1Kg in the can. How does this affect the position of the centre of mass? The same procedure is followed with a second can of the same height as the first but of greater width. It will be found that the second can with the mass in it can be tilted through the greater angle.
The stability of a body is therefore increased by
Lowering its centre of mass
Increasing the area of its base
raise this leg
can you do this without falling over?
A tightrope walker using a long pole
The centre of mass of a regularly shaped body that has the same density throughout is at its centre. In other cases it can be found by experiment
centre of mass
b wiil not topple (stable)
In Figure 11.6a the centre of mass of a tractor is being found. it is necessary to do this when testing a new design since tractors are often driven over sloping surfaces and any tendency to overturn must be discovered.
The stability of double-decker buses is being tested in Figure 11.6b. When the top deck only is fully laden with passengers (represented by sand bags in the test), it must not topple if tilted through an angle of 28 .
Racing cars have a low centre of mass and a wide wheelbase for maximum stability.
Figure 11.6a A tractor test to find its centre of mass.
Figure 11.6b A double-decker bus being tilted to test its stability
Three terms are used in connection with
A body is in stable equilirium if when slightly displaced and then released it returns to its previous position. The ball at the bottom of the dish in Figure 11.7a is an example. Its centre of mass rises when it is displaced. It rolls back because its weight has a moment about the point of contact that acts to reduce the displacement.
A body is in
if it moves further away from its previous position when slightly displaced and released. The ball in Figure 11.7b behaves in this way. Its centre of mass falls when it is displaced slightly because there is a moment which increases the displacement. Similarly in Figure 11.1a the balanced ruler is in unstable equilibrium.
A body is in
if it stays in its new position when displaced (Figure 11.7c). Its centre of mass does not rise or fall because there is no moment to increase or decrease the displacement.
Point of contact
centre of mass
Centre of mass
Point of contact
Figure 11.7 States of equilibrium
Done by : Layan Audeh