Determine the resultant of two or more forces acting along the same straight line
1.5.1 Effects of Forces
Objective
Determine the resultant of two or more forces acting along the same straight line.
If all forces are on the same line, you can treat them as numbers: add them algebraically, giving positive or negative values depending on direction.
Concept: Resultant of Forces on a Straight Line
When forces act along the same line, their directions can be represented by positive (e.g., to the right) or negative (to the left) signs. The resultant force is simply the algebraic sum:
$F_{\text{R}} = \sum_{i=1}^{n} F_i$
For two forces:
$F_{\text{R}} = F_1 + F_2$
If the forces are in opposite directions, one will be negative:
$F_{\text{R}} = F_{\text{right}} - F_{\text{left}}$
Step‑by‑Step Method
- Choose a positive direction (e.g., to the right).
- Assign a sign to each force: + if it acts in the chosen direction, – if opposite.
- Write the algebraic sum of all forces.
- Calculate the resultant magnitude and determine its direction from the sign of the sum.
Practical Examples
| Force | Direction | Symbol | Resultant |
|---|---|---|---|
| Pulling a cart to the right | Right | $+5\,\text{N}$ | $+5\,\text{N}$ (right) |
| Push from the left | Left | $-3\,\text{N}$ | $+2\,\text{N}$ (right) |
| Two opposing pulls | Right & Left | $+8\,\text{N}$ & $-5\,\text{N}$ | $+3\,\text{N}$ (right) |
Exam Tips
- Always pick a consistent positive direction.
- Write forces with signs before adding.
- Check the sign of the resultant to state the direction.
- Show your work clearly; examiners look for the algebraic process.
Example question style: “Two forces of 7 N and 4 N act along the same line, one to the left and one to the right. Find the resultant force and its direction.”
Revision
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