CIE iGCSE Co-ordinated Sciences-P1.5.2 Turning effect of forces- Study Notes- New Syllabus
CIE iGCSE Co-ordinated Sciences-P1.5.2 Turning effect of forces – Study Notes
CIE iGCSE Co-ordinated Sciences-P1.5.2 Turning effect of forces – Study Notes -CIE iGCSE Co-ordinated Sciences – per latest Syllabus.
Key Concepts:
Core:
- Describe the moment of a force as a measure of its turning effect and give everyday examples
- Define the moment of a force as moment = force × perpendicular distance from the pivot; recall and use this equation
- State that, when there is no resultant force and no resultant moment, an object is in equilibrium
Supplement
- Apply the principle of moments to situations with one force each side of the pivot, including balancing of a beam
CIE iGCSE Co-Ordinated Sciences-Concise Summary Notes- All Topics
Moment of a Force
The moment of a force is a measure of its turning effect about a pivot (or axis of rotation).
- When a force is applied at some distance from a pivot, it tends to rotate the object around that pivot.
- The size of the turning effect depends on:
- The magnitude of the force applied.
- The perpendicular distance from the pivot to the line of action of the force.
Everyday Examples of Moments:
- Pushing a door open – the further from the hinge (pivot) you push, the easier it opens.
- Using a spanner to tighten a bolt – a longer spanner gives a larger turning effect with the same force.
- Seesaws in playgrounds – children of different weights balance by sitting at different distances from the pivot.
- Rowing a boat – oars act as levers, with the water providing the pivot.
Moment of a Force Eqaution
The moment of a force is the measure of its turning effect about a pivot (or axis of rotation). It depends on both the size of the force and the perpendicular distance of the line of action of the force from the pivot.
Equation:
$\text{Moment} = \text{Force} \times \text{Perpendicular distance from pivot} $
- SI Unit: Newton-metre (N·m).
Example:
A force of \( 20~\text{N} \) is applied at a distance of \( 0.5~\text{m} \) from a pivot. What is the moment?
▶️ Answer/Explanation
$ \text{Moment} = \text{Force} \times \text{Distance} $
$ = 20 \times 0.5 = 10~\text{N·m} $
Final Answer: The moment is \( \boxed{10~\text{N·m}} \).
Example:
A 600 N child sits at one end of a seesaw, 2 m from the pivot. To balance, another child sits on the opposite side, 1.5 m from the pivot. What must be the weight of the second child?
▶️ Answer/Explanation
Step 1: Condition for balance:
Clockwise moment = Anticlockwise moment
Step 2: Write equation:
$ 600 \times 2 = W \times 1.5 $
Step 3: Solve:
$ W = \dfrac{600 \times 2}{1.5} = 800~\text{N} $
Final Answer: The second child must weigh \( \boxed{800~\text{N}} \).
Example:
A person pushes a door with a force of \( 50~\text{N} \) at a distance of \( 0.8~\text{m} \) from the hinges (pivot). What is the moment of the force?
▶️ Answer/Explanation
$ \text{Moment} = \text{Force} \times \text{Distance} $
$ = 50 \times 0.8 = 40~\text{N·m} $
Final Answer: The moment of the force is \( \boxed{40~\text{N·m}} \).
Equilibrium of an Object
An object is said to be in equilibrium when two conditions are satisfied:
- There is no resultant force acting on the object, i.e. all the forces balance each other.
- There is no resultant moment acting on the object, i.e. the turning effects of forces are balanced.
In equilibrium, the object will either:
- Remain at rest (if it was initially stationary), or
- Continue to move in a straight line with constant speed (if it was already in motion).
Everyday Examples:
- A book resting on a table – the weight of the book is balanced by the upward force from the table, and there is no turning effect.
- A balanced seesaw – forces and moments on either side of the pivot are equal.
- A picture hanging straight on a nail – forces pulling it down and the support force are balanced, and no rotation occurs.
Principle of Moments
The principle of moments states that:
For an object in equilibrium about a pivot, the sum of the clockwise moments is equal to the sum of the anticlockwise moments.
Mathematically:
\( \text{Clockwise moments} = \text{Anticlockwise moments} \)
This principle is often applied to beams, levers, and seesaws where forces act on both sides of a pivot.
Example:
A uniform beam is pivoted at its centre. A force of \( 40~\text{N} \) is applied 2 m from the pivot on the left side. On the right side, a force is applied at a distance of 1 m from the pivot. Find the force required on the right to balance the beam.
▶️ Answer/Explanation
Anticlockwise moment = \( 40 \times 2 = 80~\text{N·m} \).
For equilibrium, clockwise moment must equal anticlockwise moment, so clockwise moment = \( 80~\text{N·m} \).
If the force on the right is \( F \) applied at \( 1~\text{m} \): \( F \times 1 = 80 \) ⟹ \( F = 80~\text{N} \).
Therefore, a force of \( 80~\text{N} \) is needed to balance the beam.
Example:
The beam is pivoted at its centre. One child of weight \( 300~\text{N} \) sits at the left end (3 m from the pivot). Another child sits 3 m from the pivot on the right end. What is the weight of the second child for equilibrium?
▶️ Answer/Explanation
Anticlockwise moment = \( 300 \times 3 = 900~\text{Nm} \).
For equilibrium: Clockwise moment = Anticlockwise moment = \( 900~\text{Nm} \).
If the second child’s weight is \( W \): \( W \times 3 = 900 \).
So, \( W = \dfrac{900}{3} = 300~\text{N} \).
Therefore, the second child must weigh \( 300~\text{N} \) to balance the beam.