Putting it together
By the end of the chapter what you should have is not four formulae but one sequence of decisions.
| If the two forces are… | Do this | Direction |
|---|---|---|
| The same direction (one line or two) | Add them | That same direction |
| Opposite, along one line | Subtract them | Direction of the larger |
| Opposite and equal in size | The difference is zero | No direction |
| Inclined to each other | Neither add nor subtract | Between the two |
Example — the two bulls at the plough
The problem
When ploughing with a yoke of two bulls harnessed to a plough, one bull pulled with a force of 100 N and the other with 80 N. With what resultant force is the plough drawn forward?
Solution
The bulls stand side by side, so the two pulls are parallel — but both are in the direction the plough has to go.
resultant = 100 N + 80 N
resultant = 180 N, forward.
Example — the reading on a Newton balance
The problem
When one object was hung from a Newton balance the reading was 80 N. When another object of mass 500 g was hung as well, what is the resultant force pulling the Newton balance down, in newtons? (Take g = 10 m s−2.)
Solution
Find the weight of the second object. 500 g = 0.5 kg.
weight = m g = 0.5 kg × 10 m s−2 = 5 N
Both weights act downwards — the same direction — so add them.
resultant = 80 N + 5 N = 85 N, downwards.
Do not add 500. A mass is not a force; it becomes one only after multiplying by g.
| Resultant force | සම්ප්රයුක්ත බලය |
| Newton balance | නිව්ටන් තුලාව |
| Unbalanced force | අසංතුලිත බලය |
| Opposite direction | විරුද්ධ දිශාව |
Chapter summary
- The single force that acts in place of several forces is called the resultant force.
- The magnitude of the resultant of two forces acting in the same direction is the sum of those two forces. Its direction is the direction of those forces.
- If two collinear forces acting in opposite directions differ in magnitude, the resultant force equals the difference between their magnitudes, and it acts in the direction of the greater force.
- The resultant of two inclined forces acts in a direction lying between those forces.