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Mesin Ringkas - TAKAL (‘PULLEY’)
Takal ialah mesin ringkas yang terdiri daripada roda yang mempunyai alur, mengelilingi bulatannya di antara bibir roda tersebut.(‘A pulley is a simple machine which consists of a wheel with a groove, running along its circumference between the rims of the wheel.’)
Tali (atau kabel, rantai) menempati alur tersebut yang mana ia disambungkan kepada beban pada satu hujung dan daya dikenakan untuk melakukan kerja pada hujung yang satu lagi. (‘A rope (or cable, chain) passes through the groove which is attached to the load on one end and effort is applied to do the 'work', on the other end.’)
Dalam kata yang lebih mudah, takal adalah mesin ringkas yang terdiri daripada satu roda yang berputar pada gandar. Tali akan melilit mengelilingi roda. Tali digunakan untuk menyambungkan beban dengan daya. (‘In simple words, a pulley is a simple machine which consist of a wheel that turns around an axle. A rope goes over or wrapped around the wheel. The rope is used to connect the load with the effort.’)
Takal mengubah arah daya, membuatkan ia lebih mudah untuk mengangkat objek ke paras yang lebih tinggi. (‘A pulley changes the direction of the force, making it easier to lift things to high-rise areas.’)
Takal membantu kita mengangkat beban yang berat, takal boleh memudahkan kerja yang dilakukan. Dalam kegunaan harian, sistem takal membantu untuk mengangkat sesuatu beban ke tempat yang lebih tinggi.(‘Pulleys help us to lift a heavy load, pulleys can make the job easier. In real world, the pulley system is used to lift loads to heights.’)
Takal diubahsuai daripada takal yang ringkas kepada sistem takal bergabung, untuk membantu manusia mengangkat beban – beban yang berat.(‘Pulleys have been modified from simple system to compound system, to help human being lift heavier loads.’)
Terdapat tiga jenis sistem takal iaitu :(‘There are three different types of pulley systems. They are’)
#1. Takal tetap atau sistem takal kelas 1 (‘Fixed or class 1 Pulley System’) :
Dalam sistem ini gandar takal tetap pada satu tempat. Roda tidak bergerak. Beban diikat pada satu hujung tali sementara daya dikenakan pada hujung tali yang satu lagi. (‘In this system the axle of the pulley is fixed at one place. The wheel does not move. While the load is tied to the one end of the rope, force is applied on the other end to lift the load.’)
Takal tetap hanya mengubah arah daya yang dikenakan untuk melakukan kerja ke atas beban. Ia tidak meningkatkan saiz daya.(‘A fixed pulley only changes the direction of the force applied to do 'work' on the load. It does not increase the size of the effort force.’)
Daya yang dikenakan adalah sama dengan berat beban yang ditarik ke atas.(‘The force applied on one end of the rope is the same as that being applied on the load to lift it.’)
Apabila tali ditarik ke bawah, beban akan ditarik ke atas. Jarak pergerakan beban adalah sama dengan jarak daya yang dikenakan.(’When the rope is pulled, the load is pulled up. The distance the load moves is equal to the effort moved.’)
Contoh – contoh takal tetap ialah (‘Examples of fixed pulley are’) :
Takal tetap digunakan pada tiang bendera - Menaik dan menurunkan bendera
(‘A simple pulley is used in a flagpole - raising or lowering a flag’)
Mengangkat objek yang berat (‘Lifting up a heavy object’)
#2. Takal bergerak atau sistem takal kelas 2 (‘Movable or class 2 Pulley System’) :
Dalam sistem ini gandar takal bebas bergerak. Hujung tali disambungkan pada satu titik tetap, manakala daya dikenakan pada hujung yang satu lagi.(‘In this system the axle of the pulley is free to move in space. While one end of the rope is attached to some fixed object, force is applied at the other end.’)
Apabila daya dikenakan pada hujung tali yang satu lagi, beban dan akan diangkat dan menggelunsur di sepanjang tali, atau dengan kata lain, takal bergerak adalah takal yang bergerak bersama- sama dengan beban pada arah yang sama. (‘Hence when force is applied at one end, the load gets lifted or drifted as the pulley rolls over the length of the rope, or in simple words, a movable pulley is a pulley that moves with the load in the same direction.’)
Takal bergerak tidak mengubah arah daya yang dikenakan untuk melakukan kerja ke atas beban.(‘A movable pulley does not change the direction of the force applied to do 'work' on the load.’)
Daya akan dikenakan pada hujung tali menggandakan daya yang dikenakan ke atas beban. Takal bergerak menyebabkan daya yang dikenakan berkurangan berbanding berat beban.(‘The force applied on the free end of the pulley doubles the force being applied on the load. The movable pulley allows the effort to be less than the weight of the load.’)
Jarak pergerakan daya yang dikenakan adalah lebih jauh berbanding beban.(’The distance of the effort is greater than the load.’)
Kekurangan utama takal bergerak ialah kita perlu menarik dan menolak takal ke atas atau ke bawah. Kelebihan utama takal bergerak ialah kita menggunakan daya yang sedikit untuk menarik beban.(‘The main disadvantage of a movable pulley is that you have to pull or push the pulley up or down. The main advantage of a movable pulley is that you use less effort to pull the load.’)
Takal bergerak juga boleh dikatakan sebagai tuas kelas ketiga. Beban berada di antara fulkrum dan daya.(‘The movable pulley also acts as a second class lever. The load is between the fulcrum and the effort.’)
Contoh takal bergerak ialah (‘Examples of movable pulley is’) :
#3. Takal bergabung (‘Compound Pulley’) :
Takal bergabung ialah kombinasi takal tetap dan takal bergerak dalam satu sistem takal.(‘A compound pulley is a combination of fixed and movable pulley systems.’)
Ia mengubah arah gerakan daya.(‘It changes the direction of the effort.’)
Takal bergabung memudahkan kerja yang dilakukan kerana daya yang diperlukan untuk mengangkat beban adalah kurang daripada separuh berat beban.(‘A combined pulley makes life easier as the effort needed to lift the load is less than half the weight of the load.’)
Kelebihan utama menggunakan takal bergabung ialah jumlah daya yang diperlukan ialah kurang daripada separuh berat beban. Kekurangan yang utama ialah daya perlu bergerak jauh. (‘The main advantage of this pulley is that the amount of effort is less than half of the load. The main disadvantage is it travels a very long distance.’)
Contoh peralatan yang menggunakan takal bergabung ialah kren.(‘Example machine that uses compound pulley is crane.’)
Kren menggunakan takal tetap dan takal bergerak untuk mengangkat beban yang berat.(‘A crane uses fixed and movable pulleys to lift heavy loads.’)
Contoh yang bagus bagi takal bergabung ini ialah Sistem Blok dan Takal. ‘Blok’ merujuk kepada bekas yang mengandungi takal sebelah menyebelah, dan juga memegang gandar pada tempatnya. ‘Takal’ ialah tali yang digunakan bersama dengan takal – takal ini untuk mengangkat beban. (‘A good example of a compound pulley is the Block and Tackle system. The 'block' refers to the case that contains the pulleys side by side, and also holds the axle in place. The 'tackle' is the rope that are used with these pulleys to lift loads.’)
Sistem blok dan takal digunakan pada kapal, untuk mengangkat layar.(‘Block and tackle systems are used on ships, to lift heavy sails.’)
Hubungan di antara beban, bilangan tali takal dan daya dalam takal bergabung(‘The relationship between the load, number of tackle and effort in compound pulley’)
Daya yang dikenakan, ditarik ke arah bawah untuk mengangkat beban, akan menyebabkan ketegangan tali. Ketegangan tali akan menampung berat beban. Berat beban akan diimbangi oleh ketegangan tali yang disambungkan kepada takal bergerak.(‘Effort is applied, the direction of the effort is downward to lift a load, will cause tension in a rope. The tension of the rope will support the weight of the load. The weight of the load will be balanced by the tension of the rope which is attached to the movable pulley.’)
Dalam takal bergabung, takal bergerak mempunyai gandar yang bebas, dan ia berfungsi untuk mentranformasi daya – daya pada gandar mengimbangi jumlah daya yang diberikan oleh ketegangan tali (yang mana bermagnitud tetap pada setiap segmen.)(‘In compound pulleys, a movable pulley has a free axle, and is used to transform forces - when stationary the total force on the axle balances the total force provided by the tension in
the rope (which is constant in magnitude in each segment).’)
Sepertimana yang digambarkan di bawah, jika satu hujung tali disambungkan kepada objek tetap, dengan menarik hujung yang satu lagi daya akan dikenakan dua kali ganda ke atas mana – mana objek yang disambungkan pada gandar. (‘As illustrated below, if one end of a rope is attached to a fixed object, pulling on the other end will apply a doubled force to any object attached to the axle.’)
Lihat diagram di bawah (‘See the diagram below’) :
L = Load
T = TensionE = Effort
Berat beban ‘L’ diimbangi oleh daya pada setiap ketegangan tali ‘T’. Daya yang dikenakan untuk mengangkat beban semakin berkurangan. Semakin banyak bilangan ketegangan tali, semakin kurang daya yang dikenakan.(‘The weight of the load ‘L’ is balanced by the force in each tension of the rope ‘T’. The effort used to lift the load is decreasing. The more the tension of the rope, the less the effort is needed.’)
Archimedes was a great mathematician and engineer who was born in 287 BC in Syracuse, Sicily. He is credited with the development of many of our modern day mathematical and mechanical principles (such as Archimedes' principle, the concept of pi, and geometric proofs) and machines like the lever, a pump, and pulleys. According to Plutarch, Archimedes had stated in a letter to King Hieron that he could move any weight with pulleys; he boasted that given enough pulleys he could move the world! The king challenged him to move a large ship in his arsenal, a ship that would take many men and great labor to move to the sea. On the appointed day, the ship was loaded with many passengers and a full cargo, and all watched to see if Archimedes could do what he said. He sat a distance away from the ship, pulled on the cord in his hand by degrees, and drew the ship along "as smoothly and evenly as if she had been in the sea."
Archimedes understood the concept of mechanical advantage and how to use it to move or lift heavy objects with less force. The mechanical advantage of a machine is the ratio of the output and input forces that are used within the machine. A good mechanical advantage is a number that is greater than 1. The output force generated should be larger than the input force used to start the machine. For a simple machine like a pulley or a lever, these forces are easy to determine. For a pulley, the output force is the weight of the object and the input force is the force applied on the end of the rope.
A force is a push or a pull on an object or machine that may cause an action. Forces are measured in units of pounds-force (lbf) or newtons (N). A newton is a kilogram times a meter divided by seconds squared (N = kg m/s2). A force is a vector; it has both a magnitude (numerical value) and a direction. If an object is held up by a rope, for example, it has a force called the weight (the mass times the gravitational acceleration) acting downward, and it causes a tension in the rope, which acts upward. If the object is in equilibrium, the downwards weight of the object will be equal to the upwards tension. When something is in equilibrium, it means that it is not moving; all the forces are balanced. A book sitting on a table is in equilibrium. The weight of the book is balanced by the reaction force of the table on the book. The study of objects with forces in equilibrium is called Statics.
Archimedes knew that he could improve his mechanical advantage for lifting or moving an object by using pulleys. A pulley is an object that is usually round with a smooth groove around its outside edge. A pulley transfers a force along a rope without changing its magnitude. When engineers work with pulleys, they often assume that the rope through the groove of a pulley moves smoothly and evenly, without catching. They say it moves without friction. When two rough surfaces are rubbed together (like two wooden blocks), they become warm; the heat is caused
by friction. If the two surfaces were slicked with oil and then rubbed together, they would move much more smoothly and very little heat would be generated. There is much less friction. Engineers also assume that the pulley and rope weigh very little compared to the weight on the end of the rope, so they can ignore these two weights and make their calculations with only the heavy weight on the end of the rope.
The first figure shows a single pulley with a weight on one end of the rope. The other end is held by a person who must apply a force to keep the weight hanging in the air (in equilibrium). There is a force (tension) on the rope that is equal to the weight of the object. This force or tension is the same all along the rope. In order for the weight and pulley (the system) to remain in equilibrium, the person holding the end of the rope must pull down with a force that is equal in magnitude to the tension in the rope. For this simple pulley system, the force is equal to the weight, as shown in the picture. The mechanical advantage of this system is 1! The output force is the weight to be held in equilibrium and the input force is the applied force.
Figure 1 and Figure 2
The pulley in the first figure is a fixed pulley; it doesn't move when the rope is pulled. It is fixed to the upper bar. In the second figure, the pulley is moveable. As the rope is pulled up, it can also move up. The weight is attached to this moveable pulley. Now the weight is supported by both the rope end attached to the upper bar and the end held by the person! Each side of the rope is supporting the weight, so each side carries only half the weight (2 upward tensions are equal and opposite to the downward weight, so each tension is equal to 1/2 the weight). So the force needed to hold up the pulley in this example is 1/2 the weight! Now the mechanical advantage of this system is 2; it is the weight (output force) divided by 1/2 the weight (input force).
Each additional figure shows different possible pulley combinations with both fixed and moveable pulleys. The mechanical advantage of each system is easy to
determine. Count the number of rope segments on each side of the pulleys, including the free end. If the free end is to be pulled down, subtract 1 from this number. This number is the mechanical advantage of the system! To compute the amount of force necessary to hold the weight in equilibrium, divide the weight by the mechanical advantage! In the third figure, for example, there are 3 sections of rope. Since the applied force is downward, we subtract 1 for a mechanical advantage of 2. It will take a force equal to 1/2 the weight to hold the weight steady. The fourth figure has the same two pulleys, but the rope is applied differently and it is pulled upwards. The mechanical advantage is 3, and the force to hold the weight in equilibrium is 1/3 the weight. Each additional figure shows another possible pulley configuration and lists the force necessary to lift and hold the weight still. The mechanical advantage for the system will be the number in the denominator of the force. Check out the pulley problems in the interactive section to test your knowledge of the mechanical advantage of pulleys!
Figure 3 and Figure 4
Figure 5 and Figure 6
Figure 7 and Figure 8
These systems are known as simple pulley systems because they use the same rope throughout the system. If the pulleys were attached with several different ropes (not one continuous rope), the system would be a complex pulley system. The force necessary to hold a complex pulley system in equilibrium would have to be computed using other Statics methods. Once it was known, however, the mechanical advantage of the system would still be computed by dividing the weight to be held by the force applied to hold it!
You will learn about simple pulley systems and how to tell the difference between a simple system and a complex pulley system. You will build a simple pulley system using pulleys and weights to demonstrate the mechanical advantages of pulleys.
STEPS TO FOLLOW:
Discuss the information in the background section with the students. Be sure to emphasize the difference between moveable and
2 or more small pulleys (can be purchased at a hardware store)
Weights (2 1/2 lb, 5 lb, for example)
Slat of wood Cup hook Medium weight twine Scissors S-hook 2 chairs 2 or more heavy books
Attach the slip knot to the hook, and use the S-hook to attach the weight to the pulley. Thread the twine
fixed pulleys, simple and complex pulley systems, and the concept of equilibrium.
Collect the materials for the demonstrations. Have the cup hook screwed into the wooden slat. Have small loops of twine tied around the weight(s). Cut a length of twine and put a slip knot in one end. This will make it easier to trade off from one pulley system to another.
Place the slat across 2 chairs, hook down, with the books on either side to hold the slat secure. Attach one pulley at the hook. Attach the length of twine to the weight with the slip knot and thread the twine through the pulley so that the students can pull down on the twine. Discuss the mechanical advantage (1) and how much force it takes
around the pulley and let the students pull up to hold the weight steady. Ask them if it feels lighter (less effort to pull up than before). Have them compute the mechanical advantage (2). How much force are they using to hold it up? (W/2)
Using the slip knot, tie the twine to the center of one pulley and hang it from the hook. Thread the twine around the bottom pulley with the weight attached and back through the top pulley. The students should pull down on the twine and feel the same weight as in step 4. Have them show that the mechanical advantage is still 2.
Now tie the twine to the bottom pulley and thread it around the top pulley and down through the bottom pulley. Hang the weight off the bottom pulley. Have the students pull up on the twine. It should take even less effort to hold the weight up. See if they can compute the mechanical advantage of this system (3).
to hold the weight up and steady.
Variation: If an accurate fishing scale is available (test it on the purchased weight to check for its accuracy), the input force (the pull) could be measured. It should be fairly close to the calculated effort when the system is in equilibrium.