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Designing Simple Machines Using Mechanical and Ideal Mechanical Advantage

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Why We Use Machines. Machines help us to accomplish tasks more easily. Machines change the amount or direction of the force we must use to accomplish a task.

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There Is a Cost! Whenever we use a machine, the amount of work that we must do will be greater than if we had done the job without the machine. Why? Friction

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Mechanical Advantage Machines are rated by their Mechanical Advantage. Mechanical Advantage is the ratio of how much force is exerted by the machine (F o ) to how much force must be exerted on the machine (F i ). MA = F o F i

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Ideal Mechanical Advantage Ideal Mechanical Advantage is the Mechanical Advantage the machine would have if there were no energy losses due to friction. IMA is the ratio between the input distance to the output distance. IMA = d i d o

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Calculating MA and IMA To calculate the MA and IMA of a machine, you must know the input and output forces and the input and output distances for that machine. As we continue with the presentation, please complete the table passed out by your teacher to help you organize the information about each type of machine.

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The Lever Family Levers Wheel and Axle Pulleys

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First Class Lever Input ForceOutput forceInput Distance Output Distance The force you exert The weight of the object being moved Distance from the input force to the fulcrum Distance from the output force to the fulcrum

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Second Class Lever Input ForceOutput forceInput Distance Output Distance The force you exert The weight of the object being moved Distance from the input force to the fulcrum Distance from the output force to the fulcrum

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Third Class Lever Input ForceOutput forceInput Distance Output Distance The force you exert The weight of the object being moved Distance from the input force to the fulcrum Distance from the output force to the fulcrum

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Wheel and Axle Input Force Output force Input Distance Output Distance The force you exert The force exerted by the axle or the weight being lifted. The radius of the crank, handle, or wheel The radius of the axle

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Pulley The IMA of a pulley can also be calculated by counting the number of ropes pulling up on the load. Input Force Output forceInput Distance Output Distance The force you exert The weight of the object being lifted How far you pull the rope How far the object is lifted

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The Inclined Plane Family Inclined Plane Wedge Screw

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Inclined Plane Input ForceOutput force Input Distance Output Distance The force you exert to push the object up the ramp The weight of the object being moved The length of the incline The height of the incline

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Wedges Input Force Output forceInput Distance Output Distance The force you exert to push the wedge in or under The weight of the object being lifted OR the force to separate the object The length the wedge is pushed in or under How far up or apart the object moves

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Screw Input Force Output forceInput DistanceOutput Distance The force you exert to turn the screw The force needed to separate the material or lift the load The circumference of the screw (2πr) The pitch of the screw threads

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IMA versus MA If the world was perfect and there was no friction then: IMA = MA and W i = W o But, the world is not perfect and IMA is always greater than MA. However, for preliminary designs, we can start by assuming that IMA = MA.

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Designing a Machine To design a machine, you need the following information: The type of machine that best suits the situation. The force that you can exert. The output force that is needed.

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Calculate the MA of the Machine Calculate the MA by dividing the force you need by what you can exert. For example, let us say that we want to lift a rock that weighs 500 N, but can only exert a force of 100 N. The MA of our machine would have to be: MA = F o = 500 N = 5 F i 100 N

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Choose the Machine and Calculate IMA Select the type of machine that is best for the situation. In this example, I would choose a 1 st class lever. Assume that there is no friction and that IMA = MA. In this example, MA =5, therefore, IMA = 5.

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Design the Machine The IMA of a 1 st class lever is: IMA = d i = Distance from the input force to the fulcrum d o Distance from the output force to the fulcrum In this example, the IMA = 5. If I place the fulcrum 50 cm from the rock, then the d o will equal 50 cm.

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Design the Machine Using the formula for IMA, I can calculate how long the lever must be and/or how far away from the fulcrum I must exert my force (d i ). IMA = d i or d i = IMA x d o d o For this example d i = IMA x d o = 5 x 50 cm = 250 cm

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Our Machine 50 cm 100N 500N 250 cm

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Your Turn to Try! You need to lift a 600 N weight using a winch (wheel and axle). You can exert only 75 N and the axle of the winch has a radius of 4 cm. How long must the handle of the winch be? You want to push a 1000 N box up a ramp to a loading dock that is 3 m off the ground. You can only exert a force of 200 N. How long must the ramp be?

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Efficiency The efficiency of a simple machine is a comparison between how much work you put into the machine versus how much you get out. Percent efficiency is easily calculated by using one of the formulas below: % Efficiency = Wo x 100 = F o x d o x 100 Wi F i x d i OR % Efficiency = MA x 100 IMA

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Conclusion Remember, machines change the size and direction of forces, but that change comes at a cost. The use of machines always require more work.

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