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Understanding Simple Machines Task 1: Understanding Mechanical Advantage (10 minutes) Imagine that you are on a car trip with friends, far from the nearest city, and suddenly the car gets a flat tire. The driver opens the trunk to take out the spare tire—but there is no car jack! The car is too heavy to life. What can you do? The answer is to use a machine, of course, and one that you can assemble quickly from available materials. A lever would work. One person can lift a corner of a car using a long lever, such as a sturdy log placed securely on a large rock. Thinking back to last week, you learnt that simple machines can magnify the force applied to make a job easier. We can calculate this by working out the Mechanical Advantage of a machine. The Mechanical Advantage of a machine is the amount by which a machine can multiply a force. The force applied to a machine is called the input force. The force the machine applies to an object is called the output force. 1. Looking at the diagram above, describe the input and output forces. Page 280 of your textbook can also help with this. Task 2: Calculating Mechanical Advantage (30 minutes) The Mechanical Advantage is a ratio of forces in the mechanical device, with the output force divided by the input force. For this reason, Mechanical Advantage is also called the force ratio of the machine. 푂푢푡푝푢푡 푓표푟푐푒 푀푒푐ℎ푎푛푐푎푙 퐴푑푣푎푛푡푎푔푒 (푀퐴) = 퐼푛푝푢푡 푓표푟푐푒 We already know from the last unit that force is measured in Newtons (N) and that 1N is approximately 100g. Example: It takes 45N to lift a 180N box with a pulley. Calculate the Mechanical Advantage of the pulley system. Step 1: Write the formula for Mechanical Advantage. 푂푢푡푝푢푡 푓표푟푐푒 푀푒푐ℎ푎푛푐푎푙 퐴푑푣푎푛푡푎푔푒 (푀퐴) = 퐼푛푝푢푡 푓표푟푐푒 퐹 푀퐴 = 표푢푡푝푢푡 퐹푖푛푝푢푡 Step 2: Substitute your values for output and input force into the formula. 180푁 푀퐴 = 45푁 Step 3: Calculate Mechanical Advantage by dividing output force by input force 푀퐴 = 4 Try these ones yourself! 1. Suppose that you are riding a bicycle. You exert an effort force of 697 N downward as you push on the pedals. The resulting load force that causes the bicycle to move forward is 93 N. What is the Mechanical Advantage of the bicycle? 2. You are a passenger in a truck that gets stuck in mud. You and the driver use a tree branch as a lever to lift up the truck. The back of the truck weighs 2400 N. What input force do you need to exert to have a Mechanical Advantage of 3? 3. What is meant by a Mechanical Advantage of less than 1? Can you think of any scenarios where this might occur? 4. Thinking about levers, how does Mechanical Advantage relate to the length of the lever and the position of the fulcrum? 5. Thinking about pulleys, how does Mechanical Advantage relate to the number of pulleys? Task 3: Calculating Speed Ratio (40 minutes) The textbook refers to something called Speed Ratio (page 281). Speed measures the distance an object travels in a given amount of time. However, distance is the variable being explored when calculating Speed Ratio. To calculate Speed Ratio, the input distance is divided by the output distance. Be sure the distances are in the same units! 푛푝푢푡 푑푠푡푎푛푐푒 푆푝푒푒푑 푅푎푡표 (푆푅) = 표푢푡푝푢푡 푑푠푡푎푛푐푒 Example: Using the same pulley scenario as above, calculate the Speed Ratio of a pulley system that requires 4m of rope to be pulled to lift a box 1m off the ground. Step 1: Write the formula for Speed Ratio 푖푛푝푢푡 푑푖푠푡푎푛푐푒 푆푝푒푒푑 푅푎푡표 (푆푅) = 표푢푡푝푢푡 푑푖푠푡푎푛푐푒 Step 2: Substitute the values for input and output distances into the formula. 4푚 푆푅 = 1푚 Step 3: Calculate the Speed Ratio by dividing the input by the output distances. 푆푅 = 4 A Speed Ratio of 4 means that for every metre you want to lift the load off the ground, you will need to pull 4m of rope. How much rope would you need to pull to lift the box 3m off the ground? How high would the box be lifted if you pulled down on 22m of rope? Try these ones yourself! 1. An 4m long ramp is used to walk up a height of 1.5m. What is the Speed Ratio of the ramp? 2. A lever is used to lift a car that has a flat tyre. If the lever has a Speed Ratio of 6 and is pushed down a distance of 3.2m, how high will the car be lifted? Leave your answer in centimetres. 3. Explain how the picture to the right illustrates a large Speed Ratio to reach the top of the hill. 4. How could Speed Ratio be used to explain the disadvantage of simple machines? 5. Thinking about pulleys, how could Speed Ratio relate to the number of pulleys? Task 4: Friction and Efficiency (45 minutes) You might be thinking that Mechanical Advantage and Speed Ratio will always be the same, but this is not the case. Friction can cause the Mechanical Advantage of a simple machine to decrease, but it doesn’t affect Speed Ratio. Friction is a force that opposes motion. Friction is caused by the surface roughness of materials. A rough surface creates more friction than a smooth one. Even surfaces that we think are very smooth are uneven if seen under a magnifying glass or microscope. Extra force is needed to overcome friction, which reduces the Mechanical Advantage of a simple machine compared to ideal situations where there is no friction. Therefore, you can think of Speed Ratio as ideal Mechanical Advantage! Friction affects the Mechanical Advantage of a mechanical device, so it also affects its efficiency. Efficiency is a measurement of how well a machine or device uses energy. In any system, energy can be lost as heat, friction from different parts rubbing against each other or sound, just to name a few! The more energy that is lost, the less efficient a machine is. Efficiency is calculated as a percentage. So, a machine that is 40% efficient loses more energy than one that is 70% efficient. You can calculate the efficiency of a machine by dividing its Mechanical Advantage by its Speed Ratio and multiplying the result by 100. 푀푒푐ℎ푎푛푐푎푙 퐴푑푣푎푛푡푎푔푒 (푀퐴) 퐸푓푓푐푒푛푐푦 (%) = × 100 푆푝푒푒푑 푅푎푡표 (푆푅) Example: A pulley has a Speed Ratio of 3 and a Mechanical Advantage of 2. What is the efficiency of the pulley system? Step 1: Write the formula for Efficiency 푀퐴 퐸푓푓푐푒푛푐푦 (%) = × 100 푆푅 Step 2: Substitute the values for Mechanical Advantage and Speed Ratio into the formula. 2 퐸푓푓푐푒푛푐푦 (%) = × 100 3 Step 3: Calculate the efficiency by dividing the Mechanical Advantage by the Speed Ratio, and multiplying the answer by 100. 퐸푓푓푐푒푛푐푦 (%) = 66.67% Note: In complex machines, each individual simple machine subsystem is affected by friction, so the overall efficiency of the complex machine is usually low. For example, a typical car engine is only 15% efficient (so, about 85% of energy from the fuel is not used to move the car!). Try these ones yourself! 1. The Mechanical Advantage of a rusty pulley is 2.5 and the Speed Ratio is 5. What is the efficiency of the pulley? 2. Calculate the efficiency of the lever in the picture to the right. 3. A block and tackle is a rope and pulley system that uses multiple pulleys. It multiplies a small force into a large one. If a motor has a weight of about 2500 N and people pull 4.0 m of rope with a force of 700 N to raise the motor 1.0 m, how efficient is the block and tackle? 4. A pulley system has been found to be about 96% efficient. If you need to raise a 30N object 1.5m off the ground, how much rope do you need to pull if you use 15.6N of force? 5. Calculate the efficiency of the lever in the diagram below. Task 5: Consolidate your Understanding (25 minutes) Complete the Assess Your Learning task to check your understanding of Simple Machines, Mechanical Advantage, Speed Ratio and Efficiency. CLICK HERE TO ACCESS THE GOOGLE FORM TASK. .
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