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Mechanical Advantage and Efficiency Machines

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What is a Machine? Shovels and bulldozers are examples of machines. A machine is a device with which you can do work in a way that is easier or more effective. You may think of a machine as a complex gadget that runs on electricity, but a machine can be as simple as a shovel or even a ramp.

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Making Work Easier A machine makes work easier by changing the amount of force you exert, the distance over which you exert your force, or the direction in which you exert your force. You might say that a machine makes work easier by multiplying either force or distance, or by changing dirction.

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Input and Output Force When you do work with a machine, you exert a force over some distance. For example, you exert a force on the handle when you use a shovel to lift mulch. The force you exert on the machine is called the input force, or sometimes the effort force. The machine then does work, by exerting a force over some distance. The shovel, in this case, exerts a force to lift mulch. This force exerted by the machine is the output force. Sometimes the term resistance force is used, because the machine must overcome some resistance.

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Multiplying Force In some machines, the output force is greater than the input force. How can you exert a smaller force than is necessary for a job if the amount of work is the same? Remember Work = Force x Distance If the amount of work stays the same, a decrease in force must mean an increase in distance. If a machine allows you to use less force to do work, you must apply the input force over a greater distance. In the end, you do as much work with the machine as you would without the machine, but the work is easier to do.

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Think about this… What kind of device might allow you to exert a smaller force over a longer distance? Think about e. Suppose you have to lift a piano onto he stage in your school auditorium. You could try to lift it vertically, or you could push it up a ramp. If you use the ramp, the distance over which you must exert your force is greater than if you lift the piano directly. This is because the length of the ramp is greater than the height of the stage. The advantage of the ramp is that it allows you to exert a smaller force to push the piano than to lift it.

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Multiplying Distance In some machines, the output force is less than the input force. Why would you want to use a machine like this? The advantage of this kind of machine is that it allows you to exert your input force over a shorter distance than you would without the machine. For you to apply a force over a shorter distance, you need to apply a greater force.

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Think about this… When would you use this kind of machine? Think about taking a shot with a hockey stick. You move your hands a short distance, but the other end of the stick moves a greater distance to hit the puck. The hockey puck moves much faster than your hands. What happens when you fold up a sheet of paper and wave it back and forth to fan yourself? You move your hand a short distance, but the other end of the paper moves a longer distance, to cool you off on a warm day.

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Changing Direction Some machines don’t multiply either force or distance. What could be the advantage of these machines? Think about raising a sail on a boat. You could raise the sail by climbing the mast of the boat and pulling up on the sail with a rope. But it is much easier to stand on the deck and pull down than to lift up. By running a rope through the top of the mast as shown on page 112, you can raise the sail by pulling down on the rope. This rope system is a machine that makes your job easier by changing the direction in which you exert your force.

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Mechanical Advantage If you compare the input force to the output force, you can determine the advantage of using a machine. A machine’s mechanical advantage is the number of times a force exerted on a machine is multiplied by the machine. Finding the ratio of output force to input force gives you the mechanical advantage of a machine. Mechanical advantage = output force input force

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Mechanical Advantage of Multiplying Forces For a machine that multiplies force, the mechanical advantage is greater than 1. That is because the output force is greater than the input force. For example, suppose you would have to exert 3200 N to lift a piano. If you use a ramp, you might need to exert only 1600 N. The mechanical advantage of this ramp is 3200 N divided by 1600N or 2. The ramp doubles the force that you exert.

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Mechanical Advantage of Multiplying Distance For a machine that multiplies distance, the output force is less than the input force. So in this case, the mechanical advantage is less than 1. If, for example you exert an input force of 20 N and the machine produces an output force of 10 N, the mechanical advantage is 10 N divided by 20 N or.5. The output force of the machine is half your input force, but the machine exerts that force over a longer distance.

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Mechanical Advantage of Changing Direction What can you predict about the mechanical advantage of a machine that changes the direction of the force? If only the direction changes, the input force will be the same as the output force. The mechanical advantage will be 1.

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Efficiency of Machines So far you have leaned that the work you put into a machine (input work) is exactly equal to the work done by the machine (output work). In an ideal situation this is true. In a real situation, however, the output work is always less than the input work. This is due to the force of friction. In any machine, some work is wasted overcoming friction. The less friction there is, the closer the output work is to the input work.

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Efficiency The efficiency of a machine compares the output work to the input work. Efficiency is expressed as a percent. The higher the percent, the more efficient the machine is. If you are cutting a piece of paper with tight scissors, you are losing a great deal of efficiency. Suppose the efficiency of the scissors was 60%, a little more than half the work you do goes into cutting the paper. The rest is wasted overcoming the friction in the scissors. A machine that has an efficiency of 95% loses very little work. An ideal machine would have an efficiency of 100%.

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The Formula for Efficiency You cut the lawn with a hand lawn mower. You do 200,000 j of work to move the mower. If the work done by the mower in cutting the lawn is 250,000 j, what is the efficiency of the lawnmower? Efficiency = output x 100% input Efficiency = 200,000 x 100% 250,000 Efficiency =.8 x 100% = 80%

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Actual and Ideal Mechanical Advantage The mechanical advantage that a machine provides in a real situation is called the actual mechanical advantage. You can only determine the actual mechanical advantage by measuring the true input and output forces. It cannot be determined in advance because the actual values depend on the efficiency of the machine.

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The Ideal Mechanical Advantage Although you cannot predict the actual mechanical advantage of a machine, you can predict the quantity related to the actual mechanical advantage if you ignore losses due to friction. The mechanical advantage of a machine without friction is called the ideal mechanical advantage of the machine. The more efficient a machine is, the closer the actual mechanical advantage is to the ideal mechanical advantage. By keeping a machine clean and well lubricated, you can make its operation closer to ideal, increase the machine’s efficiency, and make your own work easier.

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