Overall Indicator: The student: recognizes the effects of forces acting on structures and mechanisms

Transcription

1 Grade 5 Performance Task: Disaster Recovery Content Connections Assessment Criterion Understanding of basic concepts Overall Indicator: The student: recognizes the effects of forces acting on structures and mechanisms Specific concepts: The student is able to identify most of the forces, including tension and compression, acting on their structure and their effect is able to describe most of the advantages and disadvantages of using different mechanisms Key Terms: lever, inclined plane (wedge), wheel and axle, pulley, gear, screw, tension, compression, structure, distance, effort. Part A: Mechanisms A mechanism transfers a force from one place to another in order to do work. A mechanism can be made up of a simple machine (a lever or inclined plane) or by combining and modifying them into more complex machines. A wheel and axle is a lever that can go all the way around, the axle being the fulcrum. A pulley is a modification or combination of wheels. The screw is a circular inclined plane and gears are another modification of the wheel and axle. The function of a machine or mechanism is to either give the user more force out (put in less force but more distance) or more distance (put in more force but over a smaller distance) Part B: Structures A structure is any group or sets of materials organized to support or transfer a load. The structure for this task will have to be 1) strong enough to support a load (the house) and its own weight and 2) help to align and hold the mechanisms to be able to transfer the forces from the operator (the student) to the load. The student will have to identify tension and compression forces within the structure. As a load is applied to the structure the structure will respond with internal forces of tension and compression to balance and hold up the load. Generally, any place where the material of the structure would stretch if it were a soft material (such as plastecine or gum) it is under tension. Conversely, any place where the structure would become squished it would be under compression.

2 Levers are designed to either increase the amount of force or increase the amount of distance that a can be applied to a load. Levers are made up of three parts. They get their class number from the way the fulcrum, load and effort are organized. The distance from the fulcrum to the load is called the load arm, and the distance from the effort to the fulcrum is called the effort arm. Friction is negligible in levers. Class 1 lever A class 1 lever can give more force, or more distance, but it s usually used to create more force and therefore less distance at the load. Wrecking equipment such as crowbars and claw hammers are good examples Effort Fulcrum Class 2 levers are for generating more force at the load, but go through a very small distance. The effort will always be a smaller force, but will go through more distance. Nutcrackers and wheelbarrows are good examples Fulcrum Class 2 lever Effort Class 3 lever Class 3 levers are about getting more distance at the load, but smaller forces. A lot of sports equipment is based on a 3 rd class lever model. Effort Fulcrum

3 Inclined Planes or Wedges are ramps that allow make-work easier by spreading out the distance over which the force has to be applied on an object to get the work done. Friction is a major drawback for ramps as the two surfaces meet and move over one another. 3 times distance applied = 1/3 force needed 5 times distance applied = 1/5 force needed Pulleys are a device designed to help people lift and lower heavy objects. A fixed pulley stays in one place as it is being used. A fixed pulley does not increase your force and therefore gives you no advantage. It helps a person lift things by changing the direction of force. It allows a person to pull down in order to lift a load up Fixed Pulley Ropes A pull down on this end of the rope causes the load to be pulled up. You apply a force in one place, and through the tension forces in the rope, it produces a force to lift the load. If a person lifts a weight by pulling it up, only the person s muscles do the work. But when a person pulls down, the person s own weight due to gravity can help. By using a person s own weight as a force, it enables a person to raise a weight with less effort. Normally a winch

4 device is used to pull down on the rope. This device allows the rope to wind around a drum while the drum is rotated. b) Using a counterweight Fixed Pulley Suppose a person want to lift a load of 100 Kg. If another weight (called a counterweight) were hung on the person s end of the rope, the load would be lifted with less effort force. For example, if the counterweight weighs 90 Kg, that weight alone would not lift the load, but all the person would have to do is supply the difference, or 10 Kg of force. Fixed pulleys and counterweights are often used to lift objects. Counterweight c) Using a movable pulley Using a movable pulley makes lifting a load even easier. It is called a movable pulley because it moves with the load. The pulley is suspended by a rope with one portion of the rope (called a rope segment) on each side. Each rope segment supports half the load. Fixed surface Movable pulley (20 Kg) 10 Kg As an example, with 10 Kg of force, a person can lift a load that weighs 20 Kg. If a person wants to lift a load a distance of 1 m, the effort force must be moved 2 m.

5 d) Using a combined pulley system The big problem with movable pulleys is that a person has to pull up to lift a load. In order to make the job of lifting a load easier, a fixed pulley can be added to allow lifting a load by pulling down. Fixed surface Movable pulley Fixed pulley By combining a fixed pulley to a movable pulley, a person gets the advantages of both. The movable pulley doubles the person s force, and at the same time the fixed pulley lets the person pull down to lift the load up. e) Mechanical advantage One way to compare different pulley arrangements is to use the idea of mechanical advantage. Since the combined pulley arrangement shown above doubles a person s force, it has a mechanical advantage of two. You can find the mechanical advantage of any pulley arrangement by simply counting the rope segments that support the movable pulley. If a person needs to raise very heavy loads, more lifting force is needed, and combinations of pulleys that give you more rope segments can achieve this. Suppose another fixed pulley is added as follows: Fixed pulleys Now three rope segments support the movable pulley so the mechanical advantage is three. Movable pulley and load Or, suppose you start again with this combination, and then add another combination just like it so that you have 2 movable pulleys and 2 fixed pulleys. Now, hang the load from both movable pulleys as follows:

6 Fixed surface Fixed pulleys Because there are four rope segments connecting to the movable pulleys, the mechanical advantage if four. If the load weighs 80 Kg, each rope segment supports the weight of 20 Kg. This means that if a person pulls down with a force equal to 20 Kg, he/she could lift a load of 80 Kg with no extra effort. The pulley system multiplies the person s force by 4, so 4 is the mechanical advantage. And in the exchange, the person has to exert the force over four times the distance that the load moves. f) Using a block and tackle Movable pulleys and load Fixed surface Fixed pulley The two fixed pulleys can be placed next to each other on the same axle. The same thing can be done with the two movable pulleys as follows: Movable pulley The whole system with pulleys, blocks, and ropes is called a block and tackle. The more pulleys and rope segments in a block and tackle, the greater the mechanical advantage and the heavier the loads that can be lifted. The general rule for finding the mechanical advantage is to count the number of rope segments that are holding up the load. In this example there are 4 segments holding up the load and therefore, 1/4 of the force is needed to lift the load, however, 4 times the distance of rope will have to be pulled through

7 Gears Gears are designed to transfer forces directly from a crank arm (lever) to a driver gear and subsequent follower gears Key Terms: gear (e.g., spur, bevel, rack & pinion, worm), gear train driver, idler, follower a) Using gears A gear is a wheel with teeth around the outside. If it is designed to work on a flat surface it is called a spur gear. A combination of 2 or more gears is called a gear train. The gear train starts with a driver and may be followed by a follower or an idler. If the train is 3 or more gears long, the gears in between the driver and the follower (the last or output gear) are called idlers. Idlers are used to reverse the rotation. Photo of a spur gear system (arrows show direction of rotation as well as the force transferred) Photo of a gear train (2 or more gears connected together)

8 A bevel gear system is designed to change the direction of movement through 90 degrees. In this case, the gear s teeth mesh at 45 degrees to another gear. A crown gear also changes the direction of movement through 90 degrees. In this case the teeth mesh at 90 degrees to one another. Picture of a bevel gear and bevel gear system (actual size: about 4cm for 40 tooth gear) If an axle or shaft has a screw thread that connects with another gear, the system is called a worm gear. This system is often used to change the direction of the motion through 90 degrees. In a worm gear system, the worm gear is always the driver, and the circular gear is the follower. This system also prevents slippage. That is, once the worm gear stops, the whole system stops. A worm gear system

9 In another gear system, a single gear, called a pinion, meets with a toothed strip called a rack. The rack (or the pinion) can slide or stay in one place. This rack and pinion gear system changes circular motion into motion in a straight line, or linear motion. picture of a rack and pinion gear system b) Using two similar-sized gears When two interlocking gears have the same number of teeth (i.e., gears of the same size), they turn at the same speed, but in opposite directions, and there is no advantage.

10 c) Using two different-sized gears When two gears have different numbers of teeth, they turn at different speeds and exert different forces. If a large gear turns a small gear, the large gear turns once to make the small gear turn several times. So the large gear turns more slowly than the small gear. In this way, gears can be used to change the speed of motion or change the force output. A two gear system The large gear has 40 teeth; the small one has only 12. For every one rotation of the large gear, the small one will turn 40/12 times or 3 1/3 times. The large gear has 40 teeth; the small one has only 12. For every one rotation of the large gear, the small one will turn 40/12 times or 3 1/3 times, and the small gear exerts 1/3 times the force applied to the large gear. The mechanical advantage of this arrangement is 1/3. However, if the system is reversed, and the driver is the smaller gear, the mechanical advantage would be 3.3. In the special case of the worm gear, which is always the driver and has only one tooth, the mechanical advantage of the system is greatly increased according to the number of teeth of the driver gear. In the case where there are more than 2 gears: A driver, 1 or more idlers and a follower, the idler does not affect the mechanical advantage. You can directly get the advantage from the comparison of the driver as related to the follower (there is no advantage in the 5 gear train pictured here)