Moments, Equilibrium and Centre of Gravity: Question 5
Syllabus 1.5.2
A wooden plank rests horizontally across two supports and stays completely at rest. Which pair of conditions must both be satisfied for the plank to be in equilibrium?
Show worked solution Hide worked solution
Worked solution
Step 1: Consider what “zero resultant force” guarantees
If the resultant force on the plank is zero, the plank will not accelerate. It will not start moving up, down, or sideways. However, this alone does not stop it from rotating: two forces of equal size acting in opposite directions, but along different lines, can have a zero resultant force while still producing a turning effect.
Step 2: Consider what “zero resultant moment” guarantees
If the resultant moment about a point is zero, the plank will not start rotating about that point. However, this alone does not stop the plank from accelerating in a straight line if there is some unbalanced force acting on it.
Step 3: Combine both conditions
For the plank to be genuinely in equilibrium (no rotation and no acceleration), both conditions must hold at the same time:
- the resultant force on the plank is zero, and
- the resultant moment about any point is zero.
This matches option A.
Why the other options are wrong
| Option | What it misses |
|---|---|
| B (force only) | Ignores the possibility of a resultant turning effect (moment) even when forces balance |
| C (moment only) | Ignores the possibility of the plank accelerating in a straight line even when moments balance |
| D (symmetry) | Describes a shape property, not the physical conditions (force and moment) required for equilibrium |
Final answers
- Both the resultant force and the resultant moment must be zero, option A