Pulley power
This is a level 4 number activity from the Figure It Out series. It is focused on applying linear proportions. A PDF of the student activity is included.
About this resource
Figure It Out is a series of 80 books published between 1999 and 2009 to support teaching and learning in New Zealand classrooms.
This resource provides the teachers' notes and answers for one activity from the Figure It Out series. A printable PDF of the student activity can be downloaded from the materials that come with this resource.
Specific learning outcomes:
- Apply linear proportions.
Pulley power
Achievement objectives
NA4-4: Apply simple linear proportions, including ordering fractions.
Required materials
- Figure It Out, Level 4+, Number, Book Six, "Pulley power", page 23
See Materials that come with this resource to download:
- Pulley power activity (.pdf)
Activity
The pedals, chain, and sprockets on a bike are a form of pulley system. The big sprocket with pedals is equivalent to the motor, the chain is the same as the belt, and the small sprockets on the back wheel are equivalent to the pulley. (See "Gearing up", pages 22–23, in Figure It Out, Level 3–4, Sport.) It may therefore be useful to first link this activity to the action of pedalling a bike. The students probably haven’t previously considered the physics of pedalling, so this activity could provide them with some interesting insights.
This activity requires not only some maths calculations but also some spatial visualisation. To determine which way the pulley will turn in each problem, the students will have to mentally trace the path of the belt from the motor wheel to the pulley wheel. If this proves to be a challenge for some students, they could physically trace the path with their finger. After they have tried one or two examples, the students may come to see that when there is:
- a direct pathway (as with a bike chain, and as in question 2b ii), the pulley turns in the same direction as the motor wheel
- one loop in the belt (as in question 2b i), the pulley turns in the opposite direction to the motor wheel.
The next task is to determine the speed of the pulley wheel in each case. Here, you can help the students to see that the speed is in inverse proportion to the size of the motor and pulley wheels. Thus, when the motor wheel is, say, 50 centimetres in diameter and the pulley wheel is 25 centimetres wide (that is, the motor wheel is twice the diameter of the pulley), the speed of the pulley will be twice that of the motor wheel. To illustrate further, if the motor wheel was twice as large again (100 centimetres in diameter) and the pulley wheel remained at 25 centimetres, the motor wheel would now be four times the diameter of the pulley wheel and so the speed of the pulley wheel would be four times as great as the speed of the motor wheel. Perhaps the students could summarise this relationship as follows:
Circumference of motor wheel compared with pulley wheel |
Speed of pulley wheel compared with motor wheel |
|---|---|
Same |
Same |
Twice the size |
2 times |
3 times the size |
3 times |
4 times the size |
4 times |
1.
The pulley wheel will turn twice in the opposite (anticlockwise) direction.
2.
a.–b.
- i. Three turns anticlockwise
- ii. Four turns anticlockwise
- iii. Eight turns clockwise
- iv. The 16 pulley wheel will make three turns clockwise. The 12 pulley wheel will make four turns anticlockwise.
3.
a. Wheel a should have a circumference of 25.
Wheel b should have a circumference of 20.
b. Drawings will vary. They should be similar to this one:
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