Moments and levers

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Big idea: forces can turn things

Big idea. Key concept: Systems. A lever, a door or a seesaw is a system that turns about one fixed point.
Related concept: Balance. An object stays balanced when the turning effects on it cancel out.
Global context: Scientific and technical innovation. Spanners, scissors, cranes, wheelbarrows and bottle openers were all designed by understanding turning forces.
A force can make an object turn as well as move. The fixed point it turns about is called the pivot (or fulcrum). A door turns about its hinge.
The turning effect of a force is called its moment.
Opening a door by pushing near the hinge is very hard. Pushing at the handle, far from the hinge, is easy. The same turning effect needs a smaller force when the force is further from the pivot.

A door turning about its hinge

Calculating a moment

moment = force × perpendicular distance from the pivot.
The force is in newtons (N), the distance in metres (m), and the moment in newton metres (N m).
Worked example: a 20 N force acts 0.5 m from a pivot. Moment = 20 N × 0.5 m = 10 N m.
Change centimetres to metres first. A 30 N force at 40 cm is at 0.4 m, so the moment is 30 N × 0.4 m = 12 N m.
Rearranged: force = moment ÷ distance and distance = moment ÷ force.
A nut needs a moment of 24 N m to loosen it. With a spanner you grip 0.30 m from the nut, the force needed is 24 N m ÷ 0.30 m = 80 N. A longer spanner gripped 0.60 m away needs only 40 N.
The door at the hinge: a 15 N push at the handle, 0.8 m from the hinge, gives 12 N m. Pushing at 0.1 m from the hinge, you would need 12 N m ÷ 0.1 m = 120 N to get the same moment.

A spanner turning a bolt

Clockwise and anticlockwise moments

A moment can turn an object in one of two directions. Clockwise is the way the hands of a clock turn. Anticlockwise is the opposite way.
Think of a beam with a pivot in the middle. A downward force on the right of the pivot pushes the right side down, so it turns the beam clockwise.
A downward force on the left pushes the left side down, so it turns the beam anticlockwise.
An upward force reverses the direction. An upward force on the left lifts the left side, so it turns the beam clockwise. An upward force on the right turns it anticlockwise.
A force that acts through the pivot has a distance of zero, so its moment is 0 N m. The upward push of the pivot itself has no turning effect about the pivot.
A uniform beam has its weight acting at its middle. If the beam is pivoted at its middle, its own weight has no moment either.

Which way a force turns a beam about its pivot

The principle of moments

An object is balanced (in equilibrium) when it is not turning. The turning effects cancel out.
The principle of moments says: for a balanced object, the sum of the clockwise moments = the sum of the anticlockwise moments, taken about the same pivot.
Example: a beam has 30 N at 0.8 m on the left and 20 N at 1.2 m on the right. Anticlockwise moment = 30 × 0.8 = 24 N m. Clockwise moment = 20 × 1.2 = 24 N m. They are equal, so the beam is balanced.
If the moments are not equal, the beam turns in the direction of the bigger moment. With 50 N at 0.6 m on the left (30 N m) and 40 N at 0.9 m on the right (36 N m), the bigger moment is clockwise, so the right side goes down.
Use it to find a missing value. A 300 N adult sits 2.0 m from the pivot of a seesaw. A 400 N person on the other side balances it. Anticlockwise moment = 300 × 2.0 = 600 N m, so 400 N × d = 600 N m and d = 1.5 m. The heavier person sits closer to the pivot.
With several forces on a side, add their moments. On the left, 10 N at 0.5 m and 20 N at 0.25 m give 5 + 5 = 10 N m. A 25 N force on the right balances this at d = 10 ÷ 25 = 0.4 m.

Levers in everyday life

A lever is a rigid bar that turns about a pivot. You apply an effort to overcome a load.
Because moment = force × distance, a long distance from the pivot lets a small effort balance a large load.
A crowbar: an effort of 100 N acts 0.6 m from the pivot and the load is 0.1 m from the pivot. Effort moment = 60 N m, so the load force = 60 ÷ 0.1 = 600 N.
A wheelbarrow: the wheel axle is the pivot. A 400 N load is 0.5 m from the axle and your hands are 1.0 m away. Effort = 400 × 0.5 ÷ 1.0 = 200 N.
Other levers: scissors (pivot at the screw), bottle openers, spanners, seesaws and the claw of a hammer.
Tweezers do the opposite. Your fingers press closer to the pivot than the tips are, so the tips push with a smaller force, which helps with delicate jobs.
A lever does not give you free energy. The effort moves a longer distance than the load, so a smaller force acts over a larger distance.

A force turning a beam about its pivot

Think like a scientist: testing the principle of moments

In a safe school investigation, balance a metre ruler on a pin or knife-edge at its 50 cm mark. Hang a small mass on one side and balance it with a different mass on the other.
Keep your feet clear of the falling masses and use small masses of 500 g or less.
The independent variable is the distance of one mass from the pivot. The dependent variable is the distance of the second mass that gives balance. Control variables include the two masses, the pivot position and the ruler.
Weights come from mass × 10 N/kg. A 200 g mass is 0.2 kg, so its weight is 2 N.
Calculate the clockwise and anticlockwise moments for each balance. If the principle of moments holds, they should be close to equal. Small differences come from measuring errors, so repeat and take a mean.
Inquiry task: plan an investigation to test whether the principle of moments still works when two masses hang on the left and one on the right. State your variables, how you will measure distance accurately, and how you will decide whether the moments are equal enough.

A metre ruler balanced on a pin

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Soal latihan

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1.Which unit is used for the size of a moment?
Easy
- ANewton metre (N m)
- BNewton (N)
- CNewton per square metre (N/m²)
- DMetre per second (m/s)
2.Which equation gives the moment of a force?
Easy
- Amoment = force ÷ perpendicular distance from the pivot
- Bmoment = force + distance from the pivot
- Cmoment = mass × perpendicular distance from the pivot
- Dmoment = force × perpendicular distance from the pivot
3.What is a pivot?
Easy
- AThe force that makes an object turn
- BThe fixed point that an object turns about
- CThe distance between two forces
- DThe heaviest part of a lever
4.Which way of pushing a door needs the smallest force to open it?
Easy
- APushing close to the hinge
- BPushing in the middle of the door
- CPushing at the handle, far from the hinge
- DPushing at the top of the door, near the hinge
5.Which direction is clockwise?
Easy
- AThe same way the hands of a clock turn
- BThe opposite way to the hands of a clock
- CAlways upwards
- DAlways towards the pivot
6.Which of these tools works as a lever?
Easy
- AA thermometer
- BA pair of scissors
- CA magnifying glass
- DA battery
7.A seesaw is balanced. How does the total clockwise moment compare with the total anticlockwise moment?
Easy
- AThe clockwise moment is bigger
- BThe anticlockwise moment is bigger
- CThey are both zero
- DThey are equal
8.Why is it easier to loosen a tight nut with a long spanner?
Easy
- AA longer spanner makes the nut weigh less
- BA longer spanner reduces the moment needed
- CFor the same force, a longer spanner gives a bigger moment
- DA longer spanner has a smaller pivot

Soal lainnya

9.A force acts straight through the pivot. What is its moment about the pivot?
Easy
- AZero
- BThe same as the force
- CTwice the force
- DInfinite
10.A force is doubled and its distance from the pivot is halved. What happens to its moment?
Medium
- AIt doubles
- BIt stays the same
- CIt halves
- DIt becomes four times bigger
11.What does "perpendicular distance" mean in the equation for a moment?
Medium
- AThe length of the whole beam
- BThe distance from the force to the nearest wall
- CThe shortest distance from the pivot to the line of the force, at right angles to it
- DThe distance the object moves
12.A force is moved closer to the pivot but its size stays the same. What happens to the moment?
Medium
- AIt gets smaller
- BIt gets bigger
- CIt stays the same
- DIt changes direction
13.A heavy adult and a light child want to balance on a seesaw. Where should they sit?
Medium
- AThe adult further from the pivot and the child closer
- BBoth the same distance from the pivot
- CBoth at the very ends of the seesaw
- DThe adult closer to the pivot and the child further away
14.A beam is pivoted at its middle. A 30 N force acts downwards 0.8 m to the left of the pivot and a 20 N force acts downwards 1.2 m to the right. Which statement is correct?
Medium
- AThe beam is balanced because both moments are 24 N m
- BThe beam turns anticlockwise because 30 N is bigger than 20 N
- CThe beam turns clockwise because 1.2 m is bigger than 0.8 m
- DThe beam is balanced because the forces are equal
15.A beam is pivoted at its middle. A 50 N force acts downwards 0.6 m to the left of the pivot. A 40 N force acts downwards 0.9 m to the right. Which way does the beam turn?
Medium
- AAnticlockwise
- BIt stays balanced
- CClockwise
- DIt does not turn but moves sideways
16.Why is it easier to lift a loaded wheelbarrow by holding the ends of the handles?
Medium
- AThe handles reduce the weight of the load
- BA larger distance from the pivot means a smaller force gives the same moment
- CA larger distance from the pivot means the load moves further down
- DThe handles make gravity weaker on the load
17.A beam has a pivot in its middle. Which force turns the beam clockwise?
Medium
- AA downward force on the left of the pivot
- BAn upward force on the right of the pivot
- CA force acting through the pivot
- DA downward force on the right of the pivot
18.A student hangs a 2 N weight 0.30 m from the pivot of a ruler and moves a second weight until the ruler balances. What is the independent variable?
Medium
- AThe distance of the first weight from the pivot
- BWhether the ruler balances
- CThe ruler used
- DThe mass of the second weight
19.A student investigates balancing a ruler. Which is a sensible control variable?
Medium
- AChanging the pivot position each time
- BUsing the same two masses each time
- CUsing a different ruler for each trial
- DChanging the second mass each time
20.A student says: "A 10 N force always has a moment of 10 N m." What is wrong with this?
Hard
- AThe moment is always bigger than the force
- BForces never have moments
- CThe moment depends on the distance from the pivot as well as the force
- DThe moment depends only on the colour of the lever
21.A uniform metre ruler is pivoted at its 50 cm mark. What is the moment of the ruler's own weight about the pivot?
Hard
- AEqual to its weight in newtons
- BZero, because its weight acts through the pivot
- CAnticlockwise, because the left is heavier
- DClockwise, because the right is heavier
22.
A student pulls on a spanner with a constant force of 10 N at different distances. Her results are in the table.
Distance from the bolt (m) Moment (N m)
0.10 1.0
0.20 2.0
0.40 4.0
Which conclusion is best supported by these results?
Hard
- AWhen the force stays the same, doubling the distance doubles the moment
- BWhen the distance stays the same, doubling the force halves the moment
- CThe moment does not depend on the distance
- DThe moment is always 10 N m
23.Which of these affect the size of a moment? (select all that apply)
Easy
- AThe size of the force
- BThe perpendicular distance from the pivot
- CThe colour of the lever
- DThe temperature of the room
24.Which of these use a lever? (select all that apply)
Medium
- AA crowbar
- BA pair of scissors
- CA wheelbarrow
- DA brick resting on the ground
25.A beam has a pivot in its middle. Which forces turn it clockwise? (select all that apply)
Medium
- AA downward force on the right of the pivot
- BAn upward force on the left of the pivot
- CA downward force on the left of the pivot
- DAn upward force on the right of the pivot
26.Which are sensible safety steps when balancing masses on a ruler? (select all that apply)
Medium
- AUse small masses of 500 g or less
- BKeep feet clear of the masses
- CHang very heavy masses from the ruler to test its strength
- DPlace the stand where nobody will knock it
27.A moment is measured in newtons.
Easy
True or false?
28.A force that acts through the pivot has a moment of zero about that pivot.
Easy
True or false?
29.For a balanced beam, the total clockwise moment equals the total anticlockwise moment.
Easy
True or false?
30.Moving a force closer to the pivot makes its moment bigger.
Medium
True or false?
31.A lever lets you move a heavy load with a smaller effort.
Medium
True or false?
32.A lever can give you more energy out than you put in.
Hard
True or false?
33.Match each quantity to its unit.
Easy
- Force
- Distance from the pivot
- Moment
- Mass
- Newton metre (N m)
- Kilogram (kg)
- Metre (m)
- Newton (N)
34.Match each lever to where its pivot is.
Medium
- Scissors
- Seesaw
- Wheelbarrow
- Door
- The central support
- The wheel axle
- The hinge
- The screw joining the blades
35.Match each term to its meaning.
Medium
- Pivot
- Moment
- Clockwise
- Anticlockwise
- Turning the opposite way to the hands of a clock
- The fixed point an object turns about
- Turning the same way as the hands of a clock
- The turning effect of a force
36.Put these steps for finding a moment in a sensible order.
Medium
- Substitute the force and the distance
- Write the equation: moment = force × distance
- Change the distance to metres if needed
- Calculate and give the answer in N m
37.Put these forces in order of the size of their moment about the pivot, smallest first.
Hard
- 5 N at 0.5 m
- 3 N at 0.4 m
- 2 N at 2.0 m
- 10 N at 0.1 m
38.Complete the equation for a moment in words.
Easy
Moment = force × ____ distance from the pivot
39.Complete the sentence about turning.
Easy
The fixed point that an object turns about is called the ____.
40.Complete the principle of moments.
Medium
For a balanced object, the total clockwise moment equals the total ____ moment.
41.Complete the sentence about units.
Easy
Moments are measured in newton ____.
42.Explain why a door is easier to open by pushing at the handle than by pushing near the hinge.
Medium
43.A heavy adult and a light child balance on a seesaw. Use the principle of moments to explain where they must sit.
Medium
44.Describe how you could test the principle of moments using a metre ruler, a pivot and masses. Name the variable you change, the one you measure and two you keep the same.
Hard
45.A force of 20 N acts at a perpendicular distance of 0.5 m from a pivot. Calculate the moment in newton metres (N m).
Easy
46.A person pulls on a spanner with a force of 45 N at a distance of 0.20 m from the bolt. Calculate the moment in newton metres (N m).
Easy
47.A force of 30 N acts at a perpendicular distance of 40 cm from a pivot. Calculate the moment in newton metres (N m).
Medium
48.A tight nut needs a moment of 24 N m to loosen it. You hold the spanner at a perpendicular distance of 0.30 m from the nut. Calculate the force needed in newtons (N).
Medium
49.A seesaw is balanced. A 300 N adult sits 2.0 m from the pivot on one side. A 400 N person sits on the other side. Calculate the distance of the 400 N person from the pivot in metres (m).
Medium
50.A door handle is 0.8 m from the hinge. A force of 15 N at the handle just opens the door. Calculate the force needed to open the door with a push 0.1 m from the hinge, in newtons (N).
Medium
51.A uniform metre ruler is pivoted at its middle. A 200 g mass hangs 30 cm to the left of the pivot. Take g = 10 N/kg. Calculate the distance, in centimetres (cm), at which a 400 g mass must hang on the right to balance the ruler.
Hard
52.A beam is pivoted at its middle. On the left, a 10 N force acts 0.5 m from the pivot and a 20 N force acts 0.25 m from the pivot, both downwards. A 25 N downward force on the right balances the beam. Calculate its distance from the pivot in metres (m).
Hard
53.A wheelbarrow carries a 400 N load that acts 0.5 m from the wheel axle. The handles are 1.0 m from the axle. Calculate the upward force needed at the handles to hold the barrow level, in newtons (N).
Hard

Catatan ulasan

## Moments - A **moment** is the turning effect of a force about a **pivot**. - **moment = force × perpendicular distance from the pivot**, in **newton metres (N m)**. - Distance must be in **metres**. Rearrange: **force = moment ÷ distance**. - A force through the pivot has a moment of **0 N m**. ## Direction and balance - **Clockwise** matches the hands of a clock; **anticlockwise** is the opposite. - **Principle of moments:** for a balanced object, total clockwise moment = total anticlockwise moment. - A heavier load sits closer to the pivot to balance a lighter one. ## Levers - A long distance from the pivot lets a small effort move a large load. - Examples: crowbar, wheelbarrow, scissors, spanner. The effort moves further, so no extra energy is made. ## Inquiry - Change one distance, measure the other, keep masses and pivot the same, repeat and calculate both moments.

Moment: The turning effect of a force about a pivot.
Pivot: The fixed point that an object turns about; also called the fulcrum.
Newton metre (N m): The unit of a moment: a force in newtons multiplied by a distance in metres.
Perpendicular distance: The distance from the pivot to the line of the force, measured at right angles to it.
Clockwise: Turning the same way as the hands of a clock.
Anticlockwise: Turning the opposite way to the hands of a clock.
Principle of moments: For a balanced object, the total clockwise moment equals the total anticlockwise moment about the same pivot.
Balanced (equilibrium): Not turning, because the clockwise and anticlockwise moments are equal.
Lever: A rigid bar that turns about a pivot and is used to move a load with an effort.
Effort: The force you apply to a lever.
Load: The force a lever works against.
Independent variable: The variable you change in an investigation.
Dependent variable: The variable you measure in an investigation.

Kartu flash

What is a moment?

The turning effect of a force about a pivot.

What is the equation for a moment?

moment = force × perpendicular distance from the pivot.

What is the unit of a moment?

The newton metre (N m).

What is a pivot?

The fixed point an object turns about, also called the fulcrum.

What units must the distance be in?

Metres, so change centimetres to metres first.

What is the moment of a force that acts through the pivot?

Zero, because the distance is zero.

What does perpendicular mean here?

At right angles to the line of the force.

What does clockwise mean?

Turning the same way as the hands of a clock.

Which force turns a beam clockwise?

A downward force on the right of the pivot, or an upward force on the left.

What is the principle of moments?

For a balanced object, total clockwise moment = total anticlockwise moment.

How do you find a force from a moment?

force = moment ÷ distance.

Why is a door easier to open at the handle?

The handle is further from the hinge, so the same force gives a bigger moment.

A 20 N force acts 0.5 m from a pivot. What is the moment?

20 × 0.5 = 10 N m.

Where does a heavy person sit to balance a lighter person on a seesaw?

Closer to the pivot.

How does a lever make a job easier?

A long distance from the pivot lets a small effort balance a large load.

Does a lever give you extra energy?

No. The effort moves further than the load, so a smaller force acts over a larger distance.

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Distance from the bolt (m)	Moment (N m)
0.10	1.0
0.20	2.0
0.40	4.0