Moments, balance and structural design

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Notas de aula

Big idea: moments, balance and structural design

Key concept: Systems. Moment equals force times perpendicular distance from the pivot. Rotational equilibrium requires total clockwise moment to equal total anticlockwise moment.
Related concepts: Models and evidence. Use a scientific explanation to make predictions, then test it against observations.
Global context: Scientific and technical innovation. Moment calculations help design balanced structures and lifting systems.

Moments

A moment is the turning effect of a force about a pivot.
Examples: see-saw, spanner, door, crane, screwdriver, tap, wheelbarrow, scissors.
Rotation can be clockwise or anticlockwise (use clock hands as reference).
Equation: moment = force × perpendicular distance from pivot (M = F × d).
Units: newton metre (N m) or newton centimetre (N cm).
Increasing distance from pivot reduces the force needed for the same moment.

Illustration of a pivot and a force acting on a lever, demonstrating a moment.

Principle of Moments

Principle of moments: For a balanced object, total clockwise moment equals total anticlockwise moment.
Clockwise moment = anticlockwise moment.
Used to solve for unknown forces or distances when the system is in equilibrium.
Always convert distances to metres unless question specifies N cm.

Principle of moments: a beam balanced on a pivot, with the clockwise and anticlockwise turning directions labelled on each side.

Principle of Moments

Extended tier: multiple forces on each side of the pivot.
Sum of clockwise moments = sum of anticlockwise moments.
Example: F2 × d2 = (F1 × d1) + (F3 × d3).
Ensure all distances are in the same units and directions are correctly identified.

Three forces on a beam about a pivot, with each force's perpendicular distance from the pivot labelled (d1, d2, d3).

Equilibrium

Equilibrium means a state of balance or stability – no resultant force and no resultant moment.
Conditions: (1) forces balanced (resultant force = 0), (2) clockwise moments = anticlockwise moments (resultant moment = 0).
If either condition fails, the object will accelerate or rotate.

Centre of Gravity

Centre of gravity is the point through which the weight of an object acts.
For symmetrical objects of uniform density, it lies at the centre of symmetry.
The centre of gravity can lie inside or outside the object.
In force diagrams, always draw weight from the centre of gravity.

Stability

An object is stable when its centre of gravity lies above its base.
If the line of action of weight falls outside the base, the object topples.
Stability increases with a low centre of gravity and a wide base.
Tall, narrow objects (e.g., buses) are less stable and topple more easily.

Investigating Centre of Gravity (Suspension Method)

Aim: find the centre of gravity of an irregularly shaped plane lamina.
Method: punch 3 holes near edges, hang lamina from a clamp, use a plumb line to mark vertical line of weight.
Repeat for each hole – the intersection of the three lines is the centre of gravity.
When suspended, the object settles with its centre of gravity directly below the point of suspension.
Avoid parallax error by viewing plumb line straight on; allow lamina to settle before marking.

Demonstrating Equilibrium (Extended Experiment)

Aim: show no resultant moment for an object in equilibrium.
Use a metre ruler pivoted at its centre, hang unequal masses on cotton loops at different distances.
Adjust distances until ruler is horizontal and balanced.
Calculate anticlockwise moment (m1 × g × d1) and clockwise moment (m2 × g × d2).
Results should show anticlockwise moment = clockwise moment for equilibrium.
Control variables: equal cotton loop lengths, no friction at pivot.

Think like a scientist

Balance a ruler on a pivot using small known masses placed at different perpendicular distances.
Comparison: the distance of one force from the pivot. Outcome: the balancing force required on the other side.
Control: keep the other force's distance and pivot position constant. Explain why this makes the comparison fairer.
Evidence: Use a consistent method, repeated observations where appropriate and a table with labelled quantities and units. Keep unexpected results and investigate their cause.
Safety: Practical activities need teacher supervision and an appropriate risk assessment. Use the provided data or simulation where the investigation specifies it.
Inquiry task: State a testable question, predict the outcome using the science, then explain how your observations would support or challenge the prediction.

Evaluate the science

Moment calculations help design balanced structures and lifting systems.
Balanced moments alone do not guarantee complete equilibrium; resultant force must also be zero.
Evaluation task: Link your conclusion to evidence, identify a limitation and suggest a specific improvement. Distinguish a measured result from an explanation of its cause.

Slides

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Questões de prática

Prévia grátis — 8 de 50 perguntas. Cadastre-se para ver todas.

1.What is the moment of a force?
Easy
- AThe turning effect of a force about a pivot
- BThe speed at which a force is applied
- CThe energy transferred by a force
- DThe power output of a force
2.Which of the following is an example of the turning effect of a force?
Easy
- AA child sitting on a see-saw
- BA book rests on a desk
- CA ball rolling down a hill
- DA magnet attracting a nail
3.What is the unit of a moment?
Easy
- Anewton metre (N m)
- Bnewton (N)
- Cmetre (m)
- Djoule (J)
4.A force of 10 N acts at a perpendicular distance of 0.5 m from a pivot. What is the moment?
Easy
- A5 N m
- B20 N m
- C0.5 N m
- D10.5 N m
5.A uniform metre rule is balanced at its midpoint. A 2.0 N weight is placed 30 cm from the pivot on the left. Where must a 3.0 N weight be placed on the right to balance the rule?
Medium
- A20 cm from the pivot
- B30 cm from the pivot
- C45 cm from the pivot
- D15 cm from the pivot
6.The principle of moments states that for an object in equilibrium:
Medium
- Atotal clockwise moment = total anticlockwise moment
- Btotal clockwise moment > total anticlockwise moment
- Ctotal clockwise moment < total anticlockwise moment
- Dthe sum of forces is zero
7.An object will topple over when:
Medium
- Aits centre of gravity lies outside its base
- Bits centre of gravity is directly above its base
- Cits base is very wide
- Dits centre of gravity is low
8.Which of the following increases the stability of an object?
Medium
- ALowering its centre of gravity
- BRaising its centre of gravity
- CMaking its base narrower
- DMaking it taller

Mais perguntas

9.In an experiment to find the centre of gravity of an irregular lamina, the lamina is suspended from a pin. It comes to rest with its centre of gravity:
Hard
- Adirectly below the point of suspension
- Bdirectly above the point of suspension
- Cat the point of suspension
- Dat the geometric centre of the lamina
10.A man uses a spanner to turn a nut. He applies a force of 40 N at a distance of 0.25 m from the pivot. What is the moment?
Hard
- A10 N m
- B160 N m
- C0.25 N m
- D40.25 N m
11.A beam is in equilibrium with three forces: F1 = 10 N at 0.2 m left of pivot (anticlockwise), F2 = 15 N at 0.3 m right of pivot (clockwise), and F3 at 0.1 m left of pivot (anticlockwise). What is the magnitude of F3?
Hard
- A25 N
- B35 N
- C5 N
- D45 N
12.A truck has a pivot near the front wheel. The load (weight) is 2.0 m from the pivot and the counterweight is 4.0 m from the pivot on the other side. If the counterweight is 5000 N, what is the maximum load that can be lifted without toppling?
Hard
- A10000 N
- B2500 N
- C5000 N
- D2000 N
13.A uniform metre rule is balanced horizontally on a pivot at its centre. A 4.0 N weight is placed 20 cm from the pivot on the left side. A 2.0 N weight is placed 30 cm from the pivot on the right side. What is the resultant moment about the pivot?
Medium
- A0.2 N m clockwise
- B0.2 N m anticlockwise
- C1.4 N m clockwise
- D1.4 N m anticlockwise
14.In an experiment to find the centre of gravity of an irregular lamina, the lamina is suspended from a pin through a hole near its edge. It comes to rest. Where is its centre of gravity relative to the point of suspension?
Medium
- Adirectly below the point of suspension
- Bdirectly above the point of suspension
- Cat the same height as the point of suspension
- Dat the centre of the lamina
15.A student uses the suspension method to find the centre of gravity of an irregular plane lamina. After suspending the lamina from a hole and drawing the line of action of the weight, the student repeats the process with two more holes. The three lines intersect at a point. What does this point represent?
Hard
- Athe centre of gravity of the lamina
- Bthe point of suspension
- Cthe centre of mass of the lamina
- Dthe centre of the lamina
16.In the experiment to demonstrate equilibrium using a metre ruler and masses, which of the following is a control variable?
Medium
- Athe length of the cotton loops on each side of the pivot
- Bthe mass added to the hangers
- Cthe distance of the masses from the pivot
- Dthe moment calculated
17.In the equilibrium experiment using a metre ruler, the ruler is balanced on a pin. One student suggests that friction between the ruler and the pin might affect the results. Which of the following is the best way to reduce this systematic error?
Hard
- Aensure the ruler is perfectly horizontal before adding masses
- Buse a spirit level to check the ruler's angle
- Ccheck that the ruler is free to rotate with no friction
- Duse a G clamp to secure the clamp stand
18.Which of the following is the correct definition of the centre of gravity of an object?
Easy
- Athe point through which the weight of the object acts
- Bthe point at which the object is balanced
- Cthe geometric centre of the object
- Dthe point where the object's mass is concentrated
19.A uniform metre rule is balanced on a pivot at its centre. A 2.0 N weight is placed at the 20 cm mark on the left side. Where should a 3.0 N weight be placed on the right side to balance the rule?
Medium
- A20 cm
- B30 cm
- C40 cm
- D50 cm
20.A truck has a pivot near the front wheel. The load (weight) is 2.0 m from the pivot and the counterweight is 4.0 m from the pivot on the other side. The counterweight has a weight of 5000 N. What is the maximum load that can be lifted without the truck toppling?
Hard
- A2500 N
- B5000 N
- C10000 N
- D20000 N
21.Which of the following is a unit of moment?
Easy
- Anewton metre
- Bnewton per metre
- Cjoule
- Dwatt
22.In the experiment to find the centre of gravity of an irregular lamina, why is it important to punch the holes before drawing the lines?
Hard
- Ato ensure the holes are at the correct positions
- Bbecause punching holes after can affect the position of the centre of gravity
- Cto make the lamina easier to hang
- Dto avoid parallax error
23.An object will topple over when its centre of gravity:
Easy
- Alies above its base
- Blies outside its base
- Cis at its lowest possible point
- Dis directly above the pivot
24.The centre of gravity of an object is defined as:
Easy
- Athe point through which the weight of the object acts
- Bthe geometric centre of the object
- Cthe point where all the mass is concentrated
- Dthe point where the object balances when suspended
25.A uniform metre rule is balanced at its centre. Where is its centre of gravity?
Easy
- AAt the 50 cm mark
- BAt the 0 cm mark
- CAt the 100 cm mark
- DAt the point of suspension
26.A force of 5 N is applied at a perpendicular distance of 20 cm from a pivot. What is the moment in N m?
Medium
- A1.0 N m
- B100 N m
- C0.25 N m
- D25 N m
27.Which of the following describes a system in equilibrium?
Medium
- AThe sum of clockwise moments equals the sum of anticlockwise moments
- BThe forces are balanced but there is a resultant moment
- CThe object is moving at constant velocity
- DThe object is accelerating
28.A uniform beam is balanced on a pivot. A 10 N weight is placed 0.4 m to the left of the pivot. Where must a 5 N weight be placed on the right to balance the beam?
Medium
- A0.8 m from the pivot
- B0.2 m from the pivot
- C0.4 m from the pivot
- D0.6 m from the pivot
29.An object is more stable when its centre of gravity is:
Medium
- Alow and its base is wide
- Bhigh and its base is narrow
- Clow and its base is narrow
- Dhigh and its base is wide
30.In an experiment to find the centre of gravity of an irregular lamina, the lamina is suspended from a hole near its edge. It comes to rest. Where is its centre of gravity?
Hard
- ADirectly below the point of suspension
- BDirectly above the point of suspension
- CAt the point of suspension
- DAt the geometric centre of the lamina
31.A student uses the suspension method to find the centre of gravity of an irregular plane lamina. After suspending the lamina from a hole and drawing the line of action, what should the student do next?
Hard
- ASuspend the lamina from a different hole and draw another line
- BWeigh the lamina and calculate the centre of gravity
- CMeasure the distance from the hole to the line
- DCut the lamina along the line
32.A beam is acted upon by three forces: F1 = 10 N at 0.2 m left of pivot (anticlockwise), F2 = 15 N at 0.3 m right of pivot (clockwise), and F3 at 0.1 m left of pivot (anticlockwise). The beam is in equilibrium. What is the magnitude of F3?
Hard
- A25 N
- B5 N
- C15 N
- D10 N
33.A truck has a pivot near the front wheel. The load (weight) is 2.0 m from the pivot and the counterweight is 4.0 m from the pivot on the other side. The counterweight is 5000 N. The truck is in equilibrium. What is the load?
Hard
- A10,000 N
- B2500 N
- C5000 N
- D2000 N
34.In the experiment to find the centre of gravity of an irregular lamina, the lamina is suspended from a pin through a hole near its edge. It comes to rest. Where is its centre of gravity located?
Medium
- ADirectly below the point of suspension
- BDirectly above the point of suspension
- CAt the point of suspension
- DAt the geometric centre of the lamina
35.A truck has a pivot near the front wheel. The load (weight) is 2.0 m from the pivot and the counterweight is 4.0 m from the pivot on the other side. The counterweight is 5000 N. What is the maximum load that can be lifted without the truck toppling?
Medium
- A10000 N
- B2500 N
- C2000 N
- D5000 N
36.In an experiment to demonstrate equilibrium, a metre ruler is balanced on a pivot at its centre. A 100 g mass is hung at the 20 cm mark on the left, and a 200 g mass is hung at the 70 cm mark on the right. What is the resultant moment about the pivot? (Take g = 10 N/kg)
Hard
- A0.1 N m clockwise
- B0.1 N m anticlockwise
- C0.3 N m clockwise
- D0.3 N m anticlockwise
37.A student uses the suspension method to find the centre of gravity of an irregular plane lamina. After suspending the lamina from a hole and drawing the line of action of the weight, the process is repeated from two other holes. Why are three lines drawn?
Medium
- ATo ensure accuracy by finding the intersection point
- BTo measure the weight of the lamina
- CTo check if the lamina is uniform
- DTo determine the area of the lamina
38.A uniform beam of weight 120 N and length 6.0 m is supported at its ends. A load of 80 N is placed 2.0 m from the left end. What is the upward force at the left support?
Hard
- A113 N
- B87 N
- C100 N
- D120 N
39.Balance a ruler on a pivot using small known masses placed at different perpendicular distances. What is the independent variable?
Easy
- Athe balancing force required on the other side
- Bthe number of repeated trials
- Cthe distance of one force from the pivot
- Dthe scientific explanation written afterwards
40.Balance a ruler on a pivot using small known masses placed at different perpendicular distances. Which observation or quantity is the dependent variable?
Easy
- Athe distance of one force from the pivot
- Bthe title given to the investigation
- Cthe number of references in the report
- Dthe balancing force required on the other side
41.Balance a ruler on a pivot using small known masses placed at different perpendicular distances. Which decision best controls another factor in this comparison?
Medium
- Akeep the other force's distance and pivot position constant
- Bchange every condition for each trial
- Cuse a different measurement method for every result
- Drecord only results that agree with the prediction
42.Balance a ruler on a pivot using small known masses placed at different perpendicular distances. Why should the class repeat measurements or check multiple comparable observations?
Medium
- ATo guarantee that every systematic error disappears
- BTo assess variation and judge how consistent the evidence is
- CTo make an unsupported prediction become correct
- DTo avoid reporting results that disagree with a model
43.A class is evaluating an application of moments, balance and structural design. Which statement identifies a relevant limitation?
Hard
- AAll scientific models reproduce every feature of the real world
- BOne favourable result proves that a technology has no disadvantages
- CBalanced moments alone do not guarantee complete equilibrium; resultant force must also be zero.
- DA conclusion needs no evidence when a scientific term is used
44.Balance a ruler on a pivot using small known masses placed at different perpendicular distances. Which conclusion is most justified by a controlled comparison?
Hard
- AA claim that the result must hold in all possible conditions
- BA claim that alternative explanations never need testing
- CA claim based only on the most convenient observation
- DA conclusion restricted to the tested conditions, with uncertainty and limitations stated
45.Balance a ruler on a pivot using small known masses placed at different perpendicular distances. Select the two practices that strengthen the validity of this comparison.
Medium
- Akeep the other force's distance and pivot position constant
- Bchange the measurement method whenever a result is unexpected
- Crecord the balancing force required on the other side using the same agreed procedure
- Dreport only observations that confirm the prediction
46.When evaluating evidence about moments, balance and structural design, select the two scientifically defensible statements.
Hard
- AOne result proves the explanation in every situation
- BBalanced moments alone do not guarantee complete equilibrium; resultant force must also be zero.
- CA conclusion should state the conditions and uncertainty of the evidence
- DModels never need revision when new evidence appears
47.Design a fair investigation for this question: Balance a ruler on a pivot using small known masses placed at different perpendicular distances. Identify what to compare, what to record and one control.
Medium
48.Explain one use of the science in moments, balance and structural design and evaluate one limitation of the evidence or application.
Hard
49.A 6.0 N force acts 0.40 m from a pivot. What opposing force at a perpendicular distance of 0.30 m balances its moment?
Hard
- A8.0 N
- B4.5 N
- C2.4 N
- D0.72 N
50.Clockwise and anticlockwise moments balance, but the resultant vertical force is non-zero. Is the object in full equilibrium?
Hard
- AYes; moments are the only condition
- BNo; zero resultant force is also required for translational equilibrium
- CYes; a non-zero force can never cause acceleration
- DNo; balance requires every individual force to be zero

Resumos de revisão

## Big idea: moments, balance and structural design - **Key concept: Systems.** Moment equals force times perpendicular distance from the pivot. Rotational equilibrium requires total clockwise moment to equal total anticlockwise moment. - **Related concepts: Models and evidence.** Use a scientific explanation to make predictions, then test it against observations. - **Global context: Scientific and technical innovation.** Moment calculations help design balanced structures and lifting systems. ## Moments - A **moment** is the turning effect of a force about a pivot. - Examples: see-saw, spanner, door, crane, screwdriver, tap, wheelbarrow, scissors. - Rotation can be **clockwise** or **anticlockwise** (use clock hands as reference). - Equation: **moment = force × perpendicular distance from pivot** (M = F × d). - Units: **newton metre (N m)** or **newton centimetre (N cm)**. - Increasing distance from pivot reduces the force needed for the same moment. ## Principle of Moments - **Principle of moments**: For a balanced object, total clockwise moment equals total anticlockwise moment. - Clockwise moment = anticlockwise moment. - Used to solve for unknown forces or distances when the system is in equilibrium. - Always convert distances to metres unless question specifies N cm. ## Principle of Moments - Extended tier: multiple forces on each side of the pivot. - Sum of clockwise moments = sum of anticlockwise moments. - Example: F2 × d2 = (F1 × d1) + (F3 × d3). - Ensure all distances are in the same units and directions are correctly identified. ## Equilibrium - **Equilibrium** means a state of balance or stability – no resultant force and no resultant moment. - Conditions: (1) forces balanced (resultant force = 0), (2) clockwise moments = anticlockwise moments (resultant moment = 0). - If either condition fails, the object will accelerate or rotate. ## Centre of Gravity - **Centre of gravity** is the point through which the weight of an object acts. - For symmetrical objects of uniform density, it lies at the centre of symmetry. - The centre of gravity can lie inside or outside the object. - In force diagrams, always draw weight from the centre of gravity. ## Stability - An object is **stable** when its centre of gravity lies above its base. - If the line of action of weight falls outside the base, the object **topples**. - Stability increases with a **low centre of gravity** and a **wide base**. - Tall, narrow objects (e.g., buses) are less stable and topple more easily. ## Investigating Centre of Gravity (Suspension Method) - Aim: find the centre of gravity of an irregularly shaped plane lamina. - Method: punch 3 holes near edges, hang lamina from a clamp, use a plumb line to mark vertical line of weight. - Repeat for each hole – the intersection of the three lines is the centre of gravity. - When suspended, the object settles with its centre of gravity directly below the point of suspension. - Avoid parallax error by viewing plumb line straight on; allow lamina to settle before marking. ## Demonstrating Equilibrium (Extended Experiment) - Aim: show no resultant moment for an object in equilibrium. - Use a metre ruler pivoted at its centre, hang unequal masses on cotton loops at different distances. - Adjust distances until ruler is horizontal and balanced. - Calculate anticlockwise moment (m1 × g × d1) and clockwise moment (m2 × g × d2). - Results should show anticlockwise moment = clockwise moment for equilibrium. - Control variables: equal cotton loop lengths, no friction at pivot. ## Think like a scientist - Balance a ruler on a pivot using small known masses placed at different perpendicular distances. - **Comparison:** the distance of one force from the pivot. **Outcome:** the balancing force required on the other side. - **Control:** keep the other force's distance and pivot position constant. Explain why this makes the comparison fairer. - **Evidence:** Use a consistent method, repeated observations where appropriate and a table with labelled quantities and units. Keep unexpected results and investigate their cause. - **Safety:** Practical activities need teacher supervision and an appropriate risk assessment. Use the provided data or simulation where the investigation specifies it. - **Inquiry task:** State a testable question, predict the outcome using the science, then explain how your observations would support or challenge the prediction. ## Evaluate the science - Moment calculations help design balanced structures and lifting systems. - Balanced moments alone do not guarantee complete equilibrium; resultant force must also be zero. - **Evaluation task:** Link your conclusion to evidence, identify a limitation and suggest a specific improvement. Distinguish a measured result from an explanation of its cause.

Stability Analysis: Analyze the stability of objects based on the position of the centre of gravity and base area.
Centre of Gravity: **Centre of gravity** is the point through which the weight of an object acts.
Moment Calculation: Calculate the moment of a force using moment = force × perpendicular distance from pivot.
Principle of Moments: Extended tier: multiple forces on each side of the pivot.
Designing scientific inquiries: Plan a fair comparison: Balance a ruler on a pivot using small known masses placed at different perpendicular distances.
Evaluating evidence and impacts: Moment calculations help design balanced structures and lifting systems. Balanced moments alone do not guarantee complete equilibrium; resultant force must also be zero.
Moments: A **moment** is the turning effect of a force about a pivot.
Equilibrium: **Equilibrium** means a state of balance or stability – no resultant force and no resultant moment.
Stability: An object is **stable** when its centre of gravity lies above its base.
Investigating Centre of Gravity (Suspension Method): Aim: find the centre of gravity of an irregularly shaped plane lamina.
Demonstrating Equilibrium (Extended Experiment): Aim: show no resultant moment for an object in equilibrium.
moment: A **moment** is the turning effect of a force about a pivot.
clockwise: Rotation can be **clockwise** or **anticlockwise** (use clock hands as reference).
anticlockwise: Rotation can be **clockwise** or **anticlockwise** (use clock hands as reference).
moment = force × perpendicular distance from pivot: Equation: **moment = force × perpendicular distance from pivot** (M = F × d).
newton metre (N m): Units: **newton metre (N m)** or **newton centimetre (N cm)**.

Flashcards

What is the moment of a force?

The turning effect of a force about a pivot A moment is defined as the turning effect of a force about a pivot.

Which of the following is an example of the turning effect of a force?

A child sitting on a see-saw A child on a see-saw creates a turning effect about the pivot, which is a moment.

What is the unit of a moment?

newton metre (N m) Moment is force × distance, so its unit is the newton metre (N m).

A force of 10 N acts at a perpendicular distance of 0.5 m from a pivot. What is the moment?

5 N m Moment = force × perpendicular distance = 10 N × 0.5 m = 5 N m.

A uniform metre rule is balanced at its midpoint. A 2.0 N weight is placed 30 cm from the pivot on the left. Where must a 3.0 N weight be placed on the right to balance the rule?

20 cm from the pivot Clockwise moment = anticlockwise moment: 2.0 N × 0.30 m = 3.0 N × d, so d = 0.20 m = 20 cm.

The principle of moments states that for an object in equilibrium:

total clockwise moment = total anticlockwise moment The principle of moments: for a balanced object, clockwise moment equals anticlockwise moment.

An object will topple over when:

its centre of gravity lies outside its base If the line of action of the weight (through the centre of gravity) falls outside the base, a resultant moment causes toppling.

Which of the following increases the stability of an object?

Lowering its centre of gravity A lower centre of gravity and a wider base increase stability.

In an experiment to find the centre of gravity of an irregular lamina, the lamina is suspended from a pin. It comes to rest with its centre of gravity:

directly below the point of suspension When suspended, the lamina settles with its centre of gravity directly below the point of suspension.

A man uses a spanner to turn a nut. He applies a force of 40 N at a distance of 0.25 m from the pivot. What is the moment?

10 N m Moment = force × perpendicular distance = 40 N × 0.25 m = 10 N m.

A beam is in equilibrium with three forces: F1 = 10 N at 0.2 m left of pivot (anticlockwise), F2 = 15 N at 0.3 m right of pivot (clockwise), and F3 at 0.1 m left of pivot (anticlockwise). What is the magnitude of F3?

25 N Clockwise moment = 15 N × 0.3 m = 4.5 N m. Anticlockwise moments: (10 N × 0.2 m) + (F3 × 0.1 m) = 2.0 + 0.1F3. Set equal: 2.0 + 0.1F3 = 4.5 → 0.1F3 = 2.5 → F3 = 25 N.

A truck has a pivot near the front wheel. The load (weight) is 2.0 m from the pivot and the counterweight is 4.0 m from the pivot on the other side. If the counterweight is 5000 N, what is the maximum load that can be lifted without toppling?

10000 N Principle of moments: load × 2.0 m = 5000 N × 4.0 m → load = (5000 × 4.0) / 2.0 = 10000 N.

A uniform metre rule is balanced horizontally on a pivot at its centre. A 4.0 N weight is placed 20 cm from the pivot on the left side. A 2.0 N weight is placed 30 cm from the pivot on the right side. What is the resultant moment about the pivot?

0.2 N m anticlockwise Anticlockwise moment = 4.0 N × 0.20 m = 0.8 N m. Clockwise moment = 2.0 N × 0.30 m = 0.6 N m. The resultant is 0.8 − 0.6 = 0.2 N m anticlockwise.

In an experiment to find the centre of gravity of an irregular lamina, the lamina is suspended from a pin through a hole near its edge. It comes to rest. Where is its centre of gravity relative to the point of suspension?

directly below the point of suspension When an object is suspended from a point, it will always settle with its centre of gravity directly below the point of suspension.

A student uses the suspension method to find the centre of gravity of an irregular plane lamina. After suspending the lamina from a hole and drawing the line of action of the weight, the student repeats the process with two more holes. The three lines intersect at a point. What does this point represent?

the centre of gravity of the lamina The point where the three lines cross is the position of the centre of gravity (or centre of mass) of the lamina.

In the experiment to demonstrate equilibrium using a metre ruler and masses, which of the following is a control variable?

the length of the cotton loops on each side of the pivot The length of the cotton loops should be equal on each side of the beam to ensure they do not affect the balance; this is a control variable.

How would you design the inquiry for moments, balance and structural design?

Balance a ruler on a pivot using small known masses placed at different perpendicular distances. Compare the distance of one force from the pivot; record the balancing force required on the other side; keep the other force's distance and pivot position constant.

What limitation matters when applying moments, balance and structural design?

Balanced moments alone do not guarantee complete equilibrium; resultant force must also be zero.

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