Moments

邊玩邊學

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課程筆記

What is a Moment?

A moment is a turning force.
Moment = Force × Perpendicular distance to the pivot.
Force is measured in Newtons (N), distance in metres (m), so moment is in Newton-metres (Nm).
A spanner is a force-multiplier: applying a force at a greater distance reduces the force needed to turn a bolt.

Principle of Moments

An object is balanced when the sum of clockwise moments equals the sum of anticlockwise moments about a pivot.
If moments are unequal, the object will rotate in the direction of the larger moment.
This principle applies to seesaws, levers, and any object that can turn about a pivot.

Calculating Moments

Use the equation: Moment = Force × Distance.
Distance must be the perpendicular distance from the line of action of the force to the pivot.
For a seesaw, calculate clockwise and anticlockwise moments separately.
If clockwise moment = anticlockwise moment, the seesaw is balanced.

Example: Balanced Seesaw

Clockwise moment: 10 N × 0.6 m = 6 Nm.
Anticlockwise moment: 12 N × 0.5 m = 6 Nm.
Since both moments are equal, the seesaw is balanced.

Example: Unbalanced Seesaw

If clockwise moment ≠ anticlockwise moment, the seesaw is unbalanced.
The side with the larger moment will move downwards.
For example, 8 N × 0.4 m = 3.2 Nm clockwise, 6 N × 0.5 m = 3.0 Nm anticlockwise → unbalanced, clockwise side drops.

Key Points

Moments are turning effects; they depend on force size and distance from pivot.
Increasing distance from pivot increases the moment for the same force.
The principle of moments is used to solve problems about balance and rotation.

A simple series circuit (for reference, not directly related to moments).

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練習題

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1.What is the correct equation for calculating a moment?
Easy
- AMoment = Force × Distance
- BMoment = Force ÷ Distance
- CMoment = Distance ÷ Force
- DMoment = Force + Distance
2.What are the correct units for a moment?
Easy
- ANewton metres (Nm)
- BNewtons (N)
- CMetres (m)
- DJoules (J)
3.What is the principle of moments?
Easy
- AAn object is balanced when the sum of clockwise moments equals the sum of anticlockwise moments about a point.
- BAn object is balanced when the sum of clockwise moments is greater than anticlockwise moments.
- CAn object is balanced when the sum of clockwise moments is less than anticlockwise moments.
- DAn object is balanced when the force equals the distance.
4.A force of 20 N is applied at a perpendicular distance of 0.5 m from a pivot. What is the moment?
Medium
- A10 Nm
- B40 Nm
- C20.5 Nm
- D0.025 Nm
5.A seesaw has a 10 N weight 0.6 m from the pivot on the left (anticlockwise) and a 12 N weight 0.5 m from the pivot on the right (clockwise). Is the seesaw balanced?
Medium
- AYes, because clockwise moment = anticlockwise moment = 6 Nm
- BNo, because clockwise moment = 6 Nm and anticlockwise moment = 6 Nm, but forces are different
- CNo, because clockwise moment = 5 Nm and anticlockwise moment = 6 Nm
- DYes, because the forces are different so it must be balanced
6.A spanner is used to turn a bolt. A force of 30 N is applied at a distance of 0.2 m from the pivot. What force would be needed if the distance is increased to 0.6 m to produce the same moment?
Medium
- A10 N
- B90 N
- C15 N
- D60 N
7.What is a turning force called?
Easy
- AA moment
- BA newton
- CA lever
- DA pivot
8.In the equation Moment = Force × Distance, what does 'distance' refer to?
Easy
- AThe perpendicular distance from the force to the pivot
- BThe length of the lever
- CThe distance from the force to the ground
- DThe total distance moved by the force

更多題目

9.A seesaw is balanced with a 15 N weight 0.4 m from the pivot on one side. On the other side, a weight of 10 N is placed. How far from the pivot must the 10 N weight be to balance the seesaw?
Medium
- A0.6 m
- B0.4 m
- C0.27 m
- D1.0 m
10.A 50 N force is applied at a distance of 0.3 m from a pivot, producing a moment. If the force is reduced to 25 N, what distance is needed to produce the same moment?
Medium
- A0.6 m
- B0.15 m
- C0.3 m
- D1.2 m
11.Which of the following statements about moments is true?
Medium
- AA longer lever allows a smaller force to produce the same moment.
- BA longer lever requires a larger force to produce the same moment.
- CThe distance from the pivot does not affect the moment.
- DMoments are measured in Newtons.
12.What is the unit of force used in the moment equation?
Easy
- ANewtons (N)
- BMetres (m)
- CNewton metres (Nm)
- DKilograms (kg)
13.A force of 40 N is applied at a perpendicular distance of 0.25 m from a pivot. What is the moment?
Medium
- A10 Nm
- B160 Nm
- C0.625 Nm
- D40.25 Nm
14.A spanner is used to turn a nut. The force applied is 50 N at a distance of 0.4 m from the nut. What is the moment?
Medium
- A20 Nm
- B125 Nm
- C0.008 Nm
- D50.4 Nm
15.A 30 N weight is placed 0.6 m from the pivot on the left side of a seesaw. On the right side, a 20 N weight is placed 0.9 m from the pivot. Is the seesaw balanced?
Medium
- AYes, because clockwise moment equals anticlockwise moment
- BNo, because clockwise moment is greater
- CNo, because anticlockwise moment is greater
- DYes, because forces are equal
16.A seesaw has a 25 N weight 0.8 m from the pivot on the left. On the right, a 40 N weight is placed. How far from the pivot must the 40 N weight be for the seesaw to balance?
Medium
- A0.5 m
- B0.8 m
- C1.28 m
- D0.2 m
17.What is the turning effect of a force called?
Easy
- AMoment
- BWork
- CPower
- DEnergy
18.A force of 12 N is applied at a distance of 0.5 m from a pivot. What is the moment?
Medium
- A6 Nm
- B24 Nm
- C0.042 Nm
- D12.5 Nm
19.A mechanic uses a spanner of length 0.3 m to apply a force of 60 N to a bolt. What is the moment?
Medium
- A18 Nm
- B200 Nm
- C0.005 Nm
- D60.3 Nm
20.A seesaw is balanced with a 50 N weight 0.4 m from the pivot on one side. On the other side, a 20 N weight is placed. How far from the pivot must the 20 N weight be to balance?
Medium
- A1.0 m
- B0.16 m
- C0.4 m
- D2.5 m
21.A force of 100 N produces a moment of 25 Nm. What is the perpendicular distance from the pivot?
Medium
- A0.25 m
- B4 m
- C2500 m
- D0.4 m
22.A 15 N weight is 0.8 m from the pivot on the left of a seesaw. A 12 N weight is 1.0 m from the pivot on the right. Which statement is correct?
Medium
- AThe seesaw is balanced
- BThe seesaw tilts left
- CThe seesaw tilts right
- DNot enough information
23.What is the unit of moment?
Easy
- ANewton metre (Nm)
- BNewton (N)
- CMetre (m)
- DJoule (J)
24.A force of 8 N is applied at a distance of 0.75 m from a pivot. What is the moment?
Medium
- A6 Nm
- B10.67 Nm
- C0.094 Nm
- D8.75 Nm
25.A student uses a spring balance to measure the force needed to lift a load using a lever. The load of 5 N is placed 0.2 m from the pivot, and the spring balance is attached 0.5 m from the pivot on the other side. What is the reading on the spring balance when the lever is balanced?
Medium
- A2 N
- B5 N
- C12.5 N
- D0.5 N
26.In an experiment to verify the principle of moments, a student places a metre rule on a pivot at its centre. She hangs a 1.0 N weight at the 10 cm mark and a 2.0 N weight at the 40 cm mark on the same side of the pivot. To balance the rule, she hangs a 3.0 N weight on the other side. At what mark should the 3.0 N weight be placed?
Medium
- A60 cm mark
- B70 cm mark
- C80 cm mark
- D90 cm mark
27.Which of the following is the correct definition of a moment?
Easy
- AThe turning effect of a force
- BThe speed of a turning object
- CThe energy stored in a rotating object
- DThe distance from the pivot to the force
28.What is the moment when a force of 10 N is applied at a perpendicular distance of 0.5 m from the pivot?
Easy
- A5 Nm
- B20 Nm
- C0.5 Nm
- D10.5 Nm
29.A see-saw is balanced with a 30 N child sitting 1.5 m from the pivot on one side. On the other side, a 20 N child sits at a distance of 2.0 m from the pivot. Which child produces the larger moment?
Medium
- AThe 30 N child
- BThe 20 N child
- CBoth produce equal moments
- DCannot be determined without more information
30.A student investigates the relationship between force and distance for a lever. She applies a force of 5 N at a distance of 0.4 m from the pivot and measures the moment. She then applies a force of 10 N at a distance of 0.2 m from the pivot. What is the ratio of the first moment to the second moment?
Medium
- A1:1
- B2:1
- C1:2
- D4:1
31.In a practical activity, students use a metre rule and a pivot to find the weight of an unknown object. They balance the rule with a known 2 N weight at 30 cm from the pivot, and the unknown weight at 15 cm from the pivot on the other side. What is the unknown weight?
Medium
- A1 N
- B4 N
- C0.5 N
- D2 N
32.What is the unit of a moment?
Easy
- ANewton metre (Nm)
- BNewton (N)
- CMetre (m)
- DJoule (J)
33.A spanner is used to turn a nut. The force applied is 40 N at a perpendicular distance of 0.15 m from the nut. What is the moment?
Easy
- A6 Nm
- B60 Nm
- C0.6 Nm
- D600 Nm
34.A uniform metre rule is balanced on a pivot at its centre. A 0.5 N weight is hung at the 10 cm mark. A 1.0 N weight is hung at the 70 cm mark. Is the rule balanced? If not, which side will drop?
Medium
- ABalanced
- BNot balanced, left side drops
- CNot balanced, right side drops
- DCannot be determined
35.What is a moment?
Easy
- AA turning force
- BA pushing force
- CA pulling force
- DA stretching force
36.What does the 'distance' in the equation Moment = Force × Distance represent?
Easy
- AThe perpendicular distance from the force to the pivot
- BThe distance from the force to the ground
- CThe length of the object being turned
- DThe distance from the pivot to the centre of mass
37.A spanner is used as a force-multiplier. What does this mean?
Easy
- ABy applying a force at a greater distance, a smaller force is needed to turn the bolt
- BBy applying a force at a smaller distance, a larger force is produced
- CThe spanner multiplies the force applied by the user
- DThe spanner reduces the force needed by using a longer handle
38.A force of 30 N is applied at a distance of 0.2 m from a pivot. What force would be needed if the distance is increased to 0.6 m to produce the same moment?
Medium
- A10 N
- B90 N
- C15 N
- D60 N
39.The distance in the moment equation is the perpendicular distance from the pivot to the line of action of the force.
Easy
True or false?
40.Which of the following are units used in the moment equation? (Select all that apply)
Easy
- AN
- Bm
- CNm
- Dkg
41.A spanner acts as a force-multiplier because applying a force at a greater distance from the pivot reduces the force needed to turn the bolt.
Easy
True or false?
42.Match each quantity to its correct unit.
Easy
- Force
- Distance
- Moment
- metre (m)
- newton (N)
- newton metre (Nm)
43.Arrange the following steps in the correct order to determine if a seesaw is balanced.
Easy
- Calculate the anticlockwise moment.
- Calculate the clockwise moment.
- Compare the two moments.
44.If the clockwise moment is 8 Nm and the anticlockwise moment is 7 Nm, the seesaw is balanced.
Easy
True or false?
45.A force of 5 N is applied at a perpendicular distance of 0.3 m from a pivot. What is the moment?
Easy
- A1.5 Nm
- B15 Nm
- C0.15 Nm
- D1.5 N
46.Which of the following are correct about a spanner being used as a force-multiplier? (Select all that apply)
Medium
- AA longer spanner reduces the force needed to turn a bolt.
- BA longer spanner increases the moment for the same force.
- CThe spanner multiplies the force applied.
- DThe distance from the pivot is the length of the spanner.
47.A student uses a spanner to turn a bolt. She applies a force of 40 N at a distance of 0.15 m from the centre of the bolt. What is the moment applied to the bolt?
Easy
- A6 Nm
- B60 Nm
- C0.6 Nm
- D600 Nm
48.Complete the sentence.
Easy
The unit of moment is the ____ (abbreviation).
49.State the principle of moments.
Easy
An object is balanced when the sum of the ____ moments about a point equals the sum of the ____ moments about that point.
50.A spanner applies a moment of 12 Nm to a bolt. The force applied is 40 N. What is the perpendicular distance from the pivot?
Medium
51.A seesaw is balanced. On the left side, a 30 N weight is placed 0.8 m from the pivot. On the right side, a 20 N weight is placed. How far from the pivot must the 20 N weight be for the seesaw to balance?
Medium
52.Explain why a longer spanner makes it easier to turn a bolt.
Medium
53.A spanner applies a moment of 12 Nm to a bolt. The force applied is 40 N. What is the perpendicular distance from the pivot?
Medium
- A-0.7 m
- B1.3 m
- C0.3 m
- D2.3 m
54.A seesaw is balanced. On the left side, a 30 N weight is placed 0.8 m from the pivot. On the right side, a 20 N weight is placed. How far from the pivot must the 20 N weight be for the seesaw to balance?
Medium
- A1.2 m
- B0.2 m
- C3.2 m
- D2.2 m

複習筆記

## Moments A **moment** is a turning force. It is calculated using: **Moment = Force × Distance** - **Force** is measured in Newtons (N). - **Distance** is the perpendicular distance from the pivot, measured in metres (m). - **Moment** is measured in Newton metres (Nm). A spanner is a **force-multiplier**: applying a force at a greater distance reduces the force needed to turn a bolt. ### Principle of Moments An object is **balanced** when the sum of the clockwise moments equals the sum of the anticlockwise moments about a point. #### Example: Seesaw - Clockwise moment = 10 N × 0.6 m = 6 Nm - Anticlockwise moment = 12 N × 0.5 m = 6 Nm - Since moments are equal, the seesaw is balanced. If moments are not equal, the seesaw is unbalanced and will rotate.

Moment: A turning force; calculated as Force × perpendicular distance from pivot.
Force: A push or pull measured in Newtons (N).
Perpendicular distance: The shortest distance from the pivot to the line of action of the force, measured in metres.
Newton metre (Nm): The unit of a moment.
Principle of moments: An object is balanced when the sum of clockwise moments equals the sum of anticlockwise moments about a point.
Force-multiplier: A tool (e.g., spanner) that allows a smaller force to produce a larger moment by increasing the distance from the pivot.

字卡

What is a moment?

A moment is a turning force.

What is the equation to calculate a moment?

Moment = Force × Distance

What is the distance in the moment equation?

The perpendicular distance to the pivot.

What are the units of force?

Newtons (N).

What are the units of moment?

Newton metres (Nm).

What is a spanner an example of?

A force-multiplier.

How does a spanner act as a force-multiplier?

By applying a force at a greater distance, we only need to apply a smaller force to turn the bolt.

State the principle of moments.

An object is balanced when the sum of the clockwise moments about a point are equal to the sum of the anticlockwise moments about the point.

When is an object balanced according to the principle of moments?

When the sum of clockwise moments equals the sum of anticlockwise moments about a point.

Calculate the moment when a force of 10 N is applied at a perpendicular distance of 0.6 m from the pivot.

Moment = 10 × 0.6 = 6 Nm.

Calculate the moment when a force of 12 N is applied at a perpendicular distance of 0.5 m from the pivot.

Moment = 12 × 0.5 = 6 Nm.

If clockwise moment is 6 Nm and anticlockwise moment is 6 Nm, is the seesaw balanced?

Yes, the seesaw is balanced because the moments are equal.

What is the equation linking moment, force, and perpendicular distance?

Moment = Force × Distance (perpendicular to pivot).

What are the units of distance in the moment equation?

Metres (m).

What does the principle of moments apply to?

Objects being balanced or unbalanced on a seesaw.

If clockwise moment is 8 Nm and anticlockwise moment is 6 Nm, is the seesaw balanced?

No, it is unbalanced because the moments are not equal.

What is the moment when a force of 5 N is applied at 0.2 m from the pivot?

Moment = 5 × 0.2 = 1 Nm.

What is the moment when a force of 20 N is applied at 0.3 m from the pivot?

Moment = 20 × 0.3 = 6 Nm.

What is the moment when a force of 15 N is applied at 0.4 m from the pivot?

Moment = 15 × 0.4 = 6 Nm.

What does 'perpendicular distance' mean?

The shortest distance from the pivot to the line of action of the force, measured at a right angle.

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