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## Monday, October 26, 2009

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## Sunday, October 11, 2009

### Simple Machines - The Movable Pulley

This article was first published on 3 Sep 2008.

One of the functions of simple machines is to lighten our workload. A small effort can move a greater load. What is sacrificed is that the distance moved by the effort is greater than the distance moved by the load.

As an example, we will take a look at the movable pulley. So how does a movable pulley help to lighten our work?

Remember that in order to be able to move a load that is greater than the effort, **the distance moved by the effort has to be greater than the distance moved by the load**.

With reference to the diagram above:-**Pulley A** - The distance from the pulley to the ceiling is 2m. This means that the cable attached to the pulley is also 2m.**Pulley B** – The distance moved by the effort is 2 m. However, the load moves only 1 m from the original position of the pulley. This is confirmed by …. 2-m cable divided by 2 = 1m, which means that the distance from the pulley to the ceiling is 1m. Hence, the distance from the pulley now, is 1 m from where it was originally.

Since the effort moved twice the distance moved by the load, only ½ the effort is needed to raise the load. Hence if the load weighs 10 kg, an effort of slightly over 5 kg only is needed to move the load.

### Simple Machines – The Inclined Plane

This article was originally published in Oct 2008.

As with all machines, if we want the force exerted by the effort to be less than the force exerted by the load, the **distance travelled by the effort has to be more than the distance travelled by the load**.

Below are 4 illustrations how the inclined plane works.

The more gradual the slope, the greater the distance travelled by the effort compared to the distance travelled by the load. This means that the more gradual the slope, the less effort is needed to move the load.

Examples of applications of the ramp in real life – wheelchair ramps for the disabled, gradual and winding slopes of a road found in mountainous terrain (e.g. roads to Gentling Highlands or Cameron Highlands).

It can be noted that the ‘sharper’ the wedge, the less the effort is needed because for the same distance travelled by the effort, the distance moved by the load is now less.

Examples of applications of the wedge in real life – axe head, blades of knives, metal wedges for prying open flanges of pipes in heavy industries.**Fig 1** - For every 1 turn the screw makes, the screw is driven down by the distance of ‘1 pitch’. Hence, the more gradual the slope of the thread, the smaller the distance it will be between 2 threads, as shown in Fig 2.**Fig 2 -** the distance travelled by the load is less than in Fig 1, although in both cases, the effort moves by the same one turn. Since the load moves less in Fig 2, less effort is also needed.

In conclusion, for screws, **the more the number of threads there is, OR the smaller the pitch, OR the more gradual the slope of the threads, the less the effort is needed to move the load**.

Again, like the screw, the smaller the pitch, the less the ends of the ‘V’ move towards each other, which also means the less the distance the load moves.

Like the screw, for the screw jack, **the more the number of threads there is, OR the smaller the pitch, OR the more gradual the slope of the threads, the less effort is needed to move the load**.

Take note that for the screw jack, while the mechanism of the inclined plane is used to lift the vehicle off the ground, the handle of the screw jack works on the principle of the wheel and axle. In this case, the handle is the wheel, while the screw of the jack (the part with the threads) is the axle.**Important note to parents and students** – The purpose of the above 4 illustrations is to help students understand the mechanics of the inclined plane. Most schools’ practice papers and science textbooks do not use the terms ‘pitch’ or ‘threads’. Those terms are technical terms used in the heavy and light industries.

In trying to make the illustration as simple as possible, I have found that I cannot avoid using those technical terms. The use of the above terms is to assist the student (or parent) to understand the mechanics of screws and screw jacks.

Take note that markers who will be marking your Science PSLE Paper, in all likelihood have been teachers all their lives and may not have worked in industries before, and would probably not be familiar with the terms ‘pitch’ and ‘threads’.**In other words, it is highly advised that you do not use the terms ‘pitch’ and ‘threads’, unless you are able to draw and label the diagrams as accurately as the above**.

## Saturday, October 10, 2009

### Parents up in arms again over PSLE Mathematics paper

From Channel News Asia

As requested by some students, here is one possible workout for the solution.**QuestionJim bought some chocolates and gave half of it to Ken. Ken bought some sweets and gave half of it to Jim. Jim ate 12 sweets and Ken ate 18 chocolates. The ratio of Jim's sweets to chocolates became 1:7 and the ratio of Ken's sweets to chocolates became 1:4. How many sweets did Ken buy?Solution**

Chocolates ----- C

Sweets ----- S

Jim bought 2 units of chocolates ----- C, C

Ken bought 2 units of sweets ---- S, S

Jim gave 1 unit of chocolates to Ken and Ken gave 1 unit of sweets to Jim.

Jim ----- S, C

Ken ----- S, C

Jim ate 12 sweets and Ken ate 18 chocolates.

Jim ----- S – 12; C

Ken ----- S; C – 18

Jim’s sweet to chocolate ratio 1:7. Therefore for number of sweets to be same as number of chocolates, multiply sweets by 7.

C ----- 7 x (S – 12)

C ----- 7S – 84

Ken’s sweet to chocolate ratio 1:4. Therefore, for number of sweets to be same as number of chocolates, multiply sweets by 4.

4 x S ---- C – 18

4S ---- C – 18

From Jim, (C ----- 7S – 84), replace Ken's C....

(Ken) 4S ----- C - 18

4S ----- (7S – 84) – 18

4S ----- 7S – 102

3S ----- 102

1S ----- 34

Number of sweets Jim had at first

2 units of sweets ----- 2 x 34 = 68

**Answer: 68 sweets.**