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Simple Machines In a simple machine, input work is done by a person applying a single force, and the machine does output work also by means of a single force. Conservation of energy demands that the work input be equal to the sum of the work output and the heat lost to friction.

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Energy: Ability to do work Work= Force x Distance Force: A Push or a Pull Definitions:

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The 6 Simple Machines Lever Pulley Wheel and Axle WedgeScrew Inclined Plane

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The Egyptians used simple machines to build the pyramids. One method was to build a very long incline out of dirt that rose upward to the top of the pyramid very gently. The blocks of stone were placed on large logs and pushed slowly up the long, gentle inclined plane to the top of the pyramid.

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Inclined Planes An inclined plane is a flat surface that is higher on one end. Inclined planes make the work of moving things easier – less force is required.

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Inclined Planes An inclined plane can be used to alter the force and distance involved in doing work, such as lifting loads. The trade-off is that an object must be moved a longer distance than if it were lifted straight up, but less force is needed.

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Work input and output Work input is the amount of work done on a machine. (What work you did using it.) Input force x input distance Work output is the amount of work done by a machine. (What did the machine accomplish?) Output force x output distance W out = W in F out x D out = F in x D in D in D out

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Work input and output Example: If you lift an object that weighs 10 N straight up 3 meters, the work required will be W = F x d = 10 N x 3 m = 30 J If you push it up this ramp, the work has to be the same amount. (Why?) But the force you have to exert will be less: 15 m 3 m W out = W in F out x D out = F in x D in 10N x 3m = 2N x 15m 10 N F in D in D out

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Mechanical Advantage of any simple machine: The mechanical advantage, M A, is the ratio of F out to F in.

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Mechanical Advantage of any simple machine: The mechanical advantage, M A, is the ratio of F out to F in. The mechanical advantage is also: M A = input distance output distance Can you see why?

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Mechanical Advantage In our previous example, the output force is 10 N, the input force is 2 N. What is the mechanical advantage of this inclined plane? 15 m 3 m 10 N 2 N

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Mechanical Advantage So… The advantage of using this inclined plane is that your force is multiplied by five. 15 m 3 m W out = W in F out x D out = F in x D in 10N x 3m = 2N x 15m 10 N 2 N D in D out

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So far, weve been talking about imaginary machines. In real life, W in will never equal W out. (Why not?)

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Remember Mechanical Advantage? What is the mechanical advantage of this inclined plane? The mechanical advantage you calculate using the distances is the ideal mechanical advantage. Thats what the mechanical advantage would be if there were no friction. 15 m 3 m

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Remember Mechanical Advantage? The ideal mechanical advantage of this inclined plane is 5. In real life, it will be less than 5. To find the actual mechanical advantage, you need to try out the machine. AMA = Force out Force in 15 m 3 m

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The Lever Once again, the input work F i d i is equal to the output work F o d o. A lever shown here consists of input and output forces at different distances from a fulcrum. F in F out d out d in Fulcrum

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3 Classes of Levers

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Ideal Mechanical Advantage What is the ideal mechanical advantage if the rock is 2 meters from the fulcrum, and you push down 3 meters from the fulcrum?

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Ideal Mechanical Advantage What is the ideal mechanical advantage if the rock is 2 meters from the fulcrum, and you push down 3 meters from the fulcrum? 1.5 How much force should be required if the rock weighs 30 N?

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Actual Mechanical Advantage What is the actual mechanical advantage if the rock weighs 30 N, and you have to push down with 25 N of force?

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In real-life Simple Machines… Input work = output work + work against friction Efficiency is defined as the ratio of work output to work input. Efficiency = Work output Work input

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Example The efficiency of a simple machine is 80%, and a 400-N weight is lifted a vertical height of 2 m. If an input force of 20 N is required, what distance must be covered by the input force? The efficiency is 80% or e = 0.80, therefore: 0.80 = F out x d out F in x d in F in x d in 0.80 = 400 N x 2 m 20 N x d in 20 N x d in

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Practice Problem: Clyde, a stubborn 3500-N mule, refuses to walk into the barn, so Farmer McDonald must drag him up a 5.0 m ramp to his stall, which stand 0.50 m above ground level. a. What is the ideal MA of the ramp? b. If Farmer McDonald needs to exert a 450-N force on the mule to drag him up the ramp, what is the actual mechanical advantage? c. What is the efficiency of the ramp?

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Example A 1-m metal lever is used to lift a 800-N rock. What force is required at the left end if the fulcrum is placed 20 cm from the rock? d1d1d1d1 d2d2d2d2 800 N F = ? 1. Draw and label sketch: 2. List given info: F o = 8 00 N; d 2 = 20 cm d 1 = 100 cm - 20 cm = 80 cm 3. To find F i we recall that W in = W out F x d = F x d F x d = F x d F x 80 = 800 x 20 F = 200 N F = 200 N

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Example A 1-m metal lever is used to lift a 800-N rock. What force is required at the left end if the fulcrum is placed 20 cm from the rock? d1d1d1d1 d2d2d2d2 800 N F = ? What is the mechanical advantage of the lever? What is the mechanical advantage of the lever?

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Screw A screw is an inclined plane wrapped around a pin. A screw lifts objects by pulling them together. The longer the incline plane, the tighter the screws threads. The Mechanical Advantage of a screw is the length of thread (length of the inclined plane) over height of screw (hight of the inclined plane). MA = Distance In Distance Out MA = Thread Length Pin Length

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Wheel & Axel A simple machine consisting of an axle that is attached to a wheel. The torque (force) that is applied to the wheel is increased in the axel – which does the work on larger loads. Mechanical Advantage of a wheel and axle radius of wheel over radius of axle. MA = Wheel Radius Axle Radius

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Everyday Wheel & Axles

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Pulley Mechanical Advantage of a pulley is equal to the number of supporting strands The pulley is a wheel & axle designed to support a load with a cord about its circumference.

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Wedge A wedge is a simple machine used to separate two objects, or portions of objects, through the application of force. A wedge is made up of two inclined planes. These planes meet and form a sharp edge. This edge can split things apart. Wedges are used as either separating or holding devices. There are two major differences between inclined planes and wedges. First, in use, an inclined plane remains stationary while the wedge moves. Second, the effort force is applied parallel to the slope of an inclined plane, while the effort force is applied to the vertical edge (height) of the wedge. Ideal Mechanical Advantage of a wedge; sloping side over thickness

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