Putting it together
The whole chapter comes down to one question: how many forces are acting, and how are they arranged?
| Arrangement | What equilibrium needs | Example |
|---|---|---|
| Two forces | Equal, opposite, collinear | A book on a table |
| Three parallel forces | Coplanar; the sum of two equals the third | A child on a swing |
| Three non-parallel forces | Coplanar; lines meet at a point; the resultant of two equals the third | A picture on a wall |
| More than three forces | The resultant must be zero | A plank hung by four ropes |
Mixed exercise (1)
The problem
(i) A body on a horizontal surface is pulled in one direction by a force of 20 N. What force must be applied in the direction opposite to the 20 N force to bring the body to rest?
(ii) With the 20 N force still applied to that body, what happens if a force of 25 N is applied in the opposite direction?
Solution
(i) For equilibrium under two forces they must be equal. So the force to apply is 20 N.
(ii) The resultant is 25 N − 20 N = 5 N in the direction of the 25 N force. So the body moves in the direction of the 25 N force.
Equilibrium breaks not because a force was added, but because the two forces are no longer equal.
Mixed exercise (2)
The problem
If several people together push a vehicle whose engine has stopped, in order to move it a short distance, in what manner must each person apply force to that vehicle?
Solution
Everyone must push in the same direction.
The sum of the individual forces is then the resultant force, and the vehicle moves once that exceeds the frictional force holding it still.
If one person pushes in a different direction, part of their force cancels the others' — that is a step towards equilibrium, not away from it.
Mixed exercise (3)
The problem
Two forces inclined to each other are applied to a ring by two spring balances, B and C. Given the resultant of those two forces, what must be done to bring the ring to rest?
Solution
A third spring balance must apply a force equal in magnitude and opposite in direction to that resultant.
Its line of action must also pass coplanar through the point where the lines of the other two forces meet.
Mixed exercise (4) and (5)
The problem
(4) A box is placed on a table. Although the gravitational force acts downward on this box, for what reason does it stay still instead of falling?
(5) If a body on a horizontal table is pulled in opposite directions by two ropes applying forces unequal to each other, what can you say about the state of motion of that body?
Solution
(4) Because the table applies an upward normal reaction equal to the weight of the box, opposite to it and along the same line. Under those two forces the box is in equilibrium.
(5) The two forces being unequal, the resultant is not zero. So the body moves in the direction of the larger force — it is not in equilibrium.
A case of three forces in balance
Consider the example given in the summary: a body has two forces of 10 N applied to one side and a force of 20 N applied to the opposite side. The sum of the two forces in the same direction is 10 N + 10 N = 20 N, equal to the force in the opposite direction. The resultant is therefore zero and the body is in equilibrium.
Glossary
| Force | බලය |
| Equilibrium of forces | බල සමතුලිතතාව |
| Equilibrium of co-planer forces | ඒකතල බල සමතුලිතතාව |
| Equilibrium of two forces | බල දෙකක සමතුලිතතාව |
| Equilibrium of three forces | බල තුනක සමතුලිතතාව |
| Equilibrium of three parallel forces | සමාන්තර බල තුනක සමතුලිතතාව |
| Tension | ආතතිය |
| Normal reaction | අභිලම්බ ප්රතික්රියාව |
| Centre of gravity | ගුරුත්ව කේන්ද්රය |
Chapter summary
- A body is in equilibrium if two coplanar forces applied to it are equal in magnitude and opposite in direction.
- A body is in equilibrium under three parallel forces when a force equal to the resultant of two of them acts in the opposite direction.
- A body is in equilibrium under three coplanar non-parallel forces when, for any two of those three forces, the remaining force is equal in magnitude and opposite in direction to their resultant.
- Even under more than three forces a system can be kept in equilibrium by applying forces as required.