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| Equilibrium and Stability |
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| What makes a body stable? An object is said to be stable if it is steady and well balanced so that when it is pushed slightly it does not topple or fall off easily. Let us try to do a simple experiment or derive the conditions for stability. |
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| Stick three pins close together to the bottom of a cork and make the cork stand on the pins (figure (b) shown below). Now try to push or tilt the cork and see what happens. Remove the pins and fix on the cork as shown in figure (b) below. You will notice that in the new arrangement, the base has become broader. Now place the cork resting on the pins as legs and give it a slight tilt. Watch what happens. You will notice that in the first case, the cork topples down while in the second case, the cork comes back to the original position. |
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| Objects with small base are less stable than objects with large base. |
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| We can conclude that the object with a broad base as in figure (b) is more stable than with a narrow base as in figure (a). |
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| Take a narrow hollow light cylinder and place it on the table. Give it a slight push and see what happens. Repeat the experiment by sticking some lead shots at the base of the cylinder with the help of plasticine. Now give the push. You will notice that in the first case, the cylinder falls off easily, while in the second case, it comes back to the resting position. |
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| The jar (b) is more stable because its C.G. is lower. |
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| From this experiment, we can conclude that when the
center of gravity is nearer the base of support as in figure (b) above, the body is in the stable equilibrium. In figure (a) in previous experiment and figure (a) above, the body is said to be in unstable equilibrium. The body is said to be in neutral equilibrium when the
center of gravity of a body neither goes up nor goes down when it is displaced from its position. Take the example of a ball or a cylinder rolling on the ground. Even though the body is moving, the height of
center of gravity from the ground level remains unchanged. |
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| Three States of Equilibrium |
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 Stable equilibrium |
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| Place a Bunsen burner on its broad base (figure below). Push the top to one side and see what happens. You will notice that the burner does not fall off unless it is given a hard push. This is because the body is in stable equilibrium, it has a broad base, a heavy bottom, thus lowering its
center of gravity. When the burner is tilted more and more, the C.G. gets raised and the burner falls back to make the C.G. as low as possible [Figure (a) below)]. |
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Unstable equilibrium |
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| Place the burner upside down as shown in figure below. A slight push causes the C.G. to be lowered and the burner begins to fall to make the C.G. as low as possible [Figure (b) below)]. |
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Neutral equilibrium |
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| Let the burner lie on its side as in figure below. Push it slightly and see what happens. On further pushing, the C.G. neither gets raised nor lowered. The burner just rolls maintaining its
center of gravity at the same level. Objects like cylinders and cones lying on their side roll because they are in neutral equilibrium [Figure (c) below)]. |
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| Equilibrium of a Bunsen burner |
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| Center of Gravity and Stability |
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| (a) Center of gravity in loading a ship |
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| When a ship floats in the water the forces of buoyancy and gravity balance each other because they are equal. |
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| The following three diagrams show how loads affect the
center of gravity and stability of a ship. A fully loaded ship [figure (a)] brings the
center of gravity and the center of buoyant force close together making the ship stable. |
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| When the ship is unloaded [figure (b) above] the
center of the gravity and the center of buoyancy have moved far apart, then the ship will be unstable. |
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| In the figure (c) above, weight of the flooded ballast tanks restore balance. |
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| (b) As the C.G. of a body is raised the body becomes more unstable. This is because when the body is tilted the vertical line drawn from the C.G. falls outside the base. |
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| For the same reason extra passengers are not allowed on the upper deck of a bus. If they are allowed to stand in the upper deck the C.G will be raised and the bus will be more unstable when it takes a sharp turn. |
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| For the same reason even the height of a sports car is reduced to the minimum. |
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| (c) Manufacturers make toys which appear to be unstable but are in fact very stable. For example, the rocking doll will come back to right position even if you tilt it completely on one side. This is because of its heavy base (low C.G). |
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The body should have a broad base. |
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Center of gravity of the body should be as low as possible. |
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Vertical line drawn from the
center of gravity should fall within the base of |
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| You must have seen that: |
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 A tight rope walker in a circus carries a weighted pole or an umbrella. |
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| Tight rope walker |
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Rocking Toys: These are the toys called 'mobiles' which look unstable and yet do not fall (figure shown below). The weights of these toys are so adjusted that their
center of gravity is very much near the base. As a result, any push to the toy tends to raise the
center of gravity. When the force is removed, the mobiles swing back and forth about its stable rest position. |
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| To increase stability C.G. of the toy is lowered. |
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| A uniform meter rod of weight 100 N carries a weight of 40 N and 60 N suspended from 20 cm and 90 cm mark respectively. Where will you provide a knife edge to balance the meter scale? |
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| If we assume the fulcrum to be at 50 cm mark, then the moment due to the force at 90 cm mark is greater than the one at 20 cm mark. Therefore, the knife edge should be supported at a distance of 'X' cm away from 50 cm mark. |
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| Taking moments about X, |
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| 40(30 + X) + 100 + X = 60 (40 - X) |
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 120 + 4X + 10X = 240 - 6X (dividing by 10) |
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 14X + 6X = 240 - 120 |
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| 20X = 120 |
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| The knife edge should be provided at 56 cm mark. |
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| A see-saw of 4m is provided with a wedge at the
center.
Susan and Jason of weights 500 N and 300 N respectively are sitting on the same side of the fulcrum at 2 m and 1.5 m from
center respectively. If
Karl weighing 600 N is sitting on the opposite side at a distance of 2 m from the
center where must
Peter weighing 200 N sit to balance the see-saw? |
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| Let Peter be at a distance of 'd' m away from
center nearer to
Karl as the moment on the opposite side is greater. |
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| By the principle of moments, |
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| (600 x 2) + (200 x d) = (500 x 2) + (300 x 1.5) |
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 12 + 2d = 10 + 4.5 (dividing both sides by 100) |
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 2d = 14.5 - 12 |
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  from the
center near
Karl. |
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| Two ropes are attached to points P and Q on a wheel of radius 0.5 m which can turn about O. Equal forces of 10 N are applied on the ropes at P and Q. State whether the wheel will turn, if at all whether clockwise or anticlockwise. Support your answer with a scientific reason. |
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| Moment due to force at P |
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| = 10 x 0.5 = 5 N m (clockwise) |
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| Moment due to force at Q. |
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| = 10 x 0.4 = 4 N m (anticlockwise) |
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| The force P is tangential perpendicular distance from O = 0.5 m while the perpendicular distance OR from Q = 0.4 m. Hence, the clockwise moment being greater the wheel will turn in that direction. |
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