6.2.3Chemical Change: Rate and Extent
Equilibrium — AQA GCSE Combined Science Trilogy 8464 - Chemistry Revision Notes & Topical Questions
5 min read 9 parts Lesson 12 of 16
Part 1 of 7Conditions for equilibrium
Equilibrium
Equilibrium the state in which an object is not changing its motion and is not starting to turn.
It is at rest or moving at constant velocity.
Condition 1
- Condition 1 the resultant force is zero, so there is no acceleration.
- Forces up equal forces down and forces left equal forces right.
Condition 2
- Condition 2 the resultant moment about any point is zero, so the object does not turn.
Both conditions must be stated; giving only balanced forces is incomplete.
Examples
- Examples a bridge, a shelf, a crane holding a load and a person standing still.
Part 2 of 7The principle of moments
Principle of moments
Principle of moments for a body in equilibrium, the sum of the clockwise moments about any pivot equals the sum of the anticlockwise moments about the same pivot.
Symbols
- Σ = Σ(anticlockwise moments), or F1d1 = F2d2 for two forces.
- (clockwise moments)
It works about any point you choose.
Choosing the point where an unknown force acts makes that force drop out, because its distance is zero.
Part 3 of 7A balanced beam or see-saw
A uniform plank has its weight acting at its centre.
Pivot at the centre
- Pivot at the centre the weight of the plank has no moment and can be ignored.
Pivot not at the centre
- Pivot not at the centre the weight of the plank acts at its middle and gives a moment that must be included.
A heavier load must sit closer to the pivot to balance a lighter load.
- Children of weight 300 N and 450 N balance when the heavier child sits at two-thirds of the distance of the lighter one.
Support force
- Support force the pivot pushes upwards with a force equal to the total downward force.
Part 4 of 7Method for solving problems
1
Draw a clear diagram and label all forces and distances.
2
Choose a pivot, often the point where an unknown force acts.
3
Identify which forces turn clockwise and which turn anticlockwise about it.
4
Write total clockwise moment = total anticlockwise moment.
5
Solve for the unknown, then use upward forces = downward forces for any support force.
Method for solving problems
Use distances from the pivot in metres and weights in newtons.
Convert a mass to weight with W
Convert a mass to weight with W mg.
State the point about which moments are taken.
Part 5 of 7Demonstrating equilibrium
1
Mount a metre rule on a pin pivot at its centre so that it sits horizontal before loading.
2
Hang unequal masses on cotton loops on either side of the pivot.
3
Adjust the distances until the beam balances horizontally.
4
Record the masses and their distances from the pivot.
5
Calculate F = mg and M = Fd for each side, converting g to kg and cm to m.
Result
- Result the clockwise moment equals the anticlockwise moment for every set of loads.
The pivot sits at the centre of the ruler, so the ruler's own weight gives no moment.
Part 6 of 7Stable and unstable equilibrium
Stable equilibrium
- Stable equilibrium a slightly tilted object returns to its original position, as with an object on a flat base.
Unstable equilibrium
- Unstable equilibrium a small push makes the object fall, as with a cone balanced on its point.
Stability depends on the position of the centre of gravity.
Moments apply to levers, cranes with counterweights and laboratory balances.
Part 7 of 7More from the specification
More from the specification
Moment of a Force and Principle of Moments
- The turning effect or moment of a force is defined as the force multiplied by the perpendicular distance from the pivot to the line of action of the force (Moment = F * d);
- for an object in rotational equilibrium, total clockwise moments equal total anticlockwise moments.
Centre of Gravity Experiment for an Irregular Lamina
- In a laboratory experiment using a retort stand and clamp, an irregular flat plane lamina is suspended freely from three spaced pinholes alongside a weighted plumb line;
- the intersection of vertical plumb lines locates the centre of gravity.
Stability and Conditions for Toppling
- An object will remain stable and will not topple as long as the vertical line of action of its weight acting through its centre of gravity falls within its base of support.
Conditions for Complete Mechanical Equilibrium
- For a body to be in complete mechanical equilibrium, two conditions must be satisfied: the resultant force in any direction must be zero,
- and the resultant turning moment about any pivot point must be zero.
Lamina
- A thin flat sheet.
Topple
- Tip over because the weight acts outside the base.
Perpendicular
- At right angles.
Perpendicular distance
- Distance from the axis to the line of motion, r⊥ = r sinθ.
Turning effect
- Moment that rotates the coil.
Key terms
| Term | Meaning |
|---|---|
| Equilibrium | State in which resultant force and resultant moment are both zero. |
| Principle of moments | In equilibrium, total clockwise moment equals total anticlockwise moment about any point. |
| Uniform | Same density throughout, so the weight acts at the centre. |
| Reaction force | Force from a support pushing up on an object. |
| Stable equilibrium | Object returns to its position after a small tilt. |
| Resultant force | Single force with the same effect as all forces acting on the body. |
Avoid these mistakes
1
Using distances from the end of the beam instead of from the pivot.
2
Forgetting the weight of the plank when the pivot is not at its centre.
3
Adding all moments together without separating clockwise and anticlockwise.
4
Mixing masses in kg with weights in N — convert with W = mg first.
5
Thinking equilibrium means the object must be at rest — constant velocity with no turning is also equilibrium.
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