Radius of Wheel Radius of Axle. Ideal Mechanical Advantage =
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1 Simple Machines
2 Wheels and Pulleys Wheels and Axles have been used for thousands of years. Two ways that s wheels and axels help work: 1. Buy reducing the amount of surface in contact and lowers friction (ie: a wheel on a car) 2. By multiplying the amount of output force (ie: Screwdriver) The amount of force you apply to the wheel is multiplied in the axle. Think of it like a larger force being concentrated into a smaller area. Calculated by comparing the radius of the wheel to the radius of the axle. Ideal Mechanical Advantage = Radius of Wheel Radius of Axle
3 Wheels and Pulleys In some wheels and axles the force is applied to the wheel and increased in the axle. (ie: Screwdriver, Doorknob) In other wheels and axles the force is applied to the axle and applied to the wheel. (ie: Paddleboats/Ferries, Cars) *In which is the input energy greater? *In which is the distance the wheel moves greater? (And thus the distance the machine moves is greater)
4 Wheels and Pulleys Pulleys are a grooved wheel with a rope, chain, or cable wrapped around it. They reduce friction and can help redistribute force. Fixed Pulleys: Simply change the direction of pull. Does not change the amount of force applied. (ie: clothes lines, flagpoles, blinds) Movable Pulleys can change direction of pull and the amount of force required. The output force is twice the input force, but you must also pull on the rope a greater distance. (You are trading distance of pull for output force)
5 Wheels and Pulleys Pulley Systems use a combination of fixed and moveable pulleys and have an even greater output force. These are called block and tackle systems.
6 Levers A lever is a rigid bar that pivots or rotates around a fixed point called a fulcrum.
7 Levers We will now do a mini lab to figure out how levers work and how to calculate their output force.
8 So how does it work? Levers In a lever you decrease output distance and that increases force.
9 Levers: Calculating Output Force 1. Calculate what percentage the output arm is of the input arm. 2. Divide the amount of input force by this amount to find the output produced.
10 More things are levers than you probably realize:
11 Classes of Levers First Class Levers: What you normally think of when thinking of a lever. Fulcrum is between Input and Output Force. Direction of force is also changed. If Fulcrum is close to Output Force it multiplies it. If closer to Input Force, Distance is multiplied (like in a catapult) Examples: Seesaw, Scissors, Pliers, etc.
12 Classes of Levers Second Class Levers: The fulcrum is on the end. Output force is in the center. Input force on other end. Multiply force, but do not change its direction. Examples: Wheelbarrow, Nutcracker, Bottle Opener
13 Classes of Levers Third Class Levers: The fulcrum is on the end. Input force is in the center. Output force is on the end. These levers multiply distance, but do not change direction. Examples: Broom, Baseball bat/hockey stick, Shovel, etc. Where is the fulcrum in the girl sweeping?
14
15 Key Concept of Machines: Force and Distance Review Questions: Can the amount of force applied to something effect the distance it goes? (This is obvious) But can distance effect force? (Think of the simple machines we just looked at) Is there a relationship between distance and force? If so, How do they relate?
16 Key Concept of Machines: Force and Distance Lets look at a few formulas: d F = ma F = m v F = m t t t Therefore there is a relationship between force and distance. Here is an even better formula to understand: (we haven t learned this yet) Work = Force x Distance *Therefore: (given the amount of work stays the same) If you decrease distance, you increase the amount of force (like in a lever). If you decrease force, you have increased distance somewhere (like in wheels and pulleys). It is an Inverse Relationship In other words if you decrease force: you have done the same amount of work, it just took less effort (less force) at the expense of more distance.
17 Important Formula F In d In = F Out d Out Work input should equal the work output (ignoring friction). Thus we can derive this formula from the work formula. It can be used for figuring out the forces and distances within simple machines (especially useful for levers)
18 The Elephant and the Stage What would be the shortest distance to getting it on the stage? Would this require a great or lower amount of energy? What is a better way to get the elephant on the stage?
19 Inclined Planes Inclined Planes also trade distance for force. The greater distance at a slant means less force is required. (To just lift the object strait up would require more force) Inclined Planes also increase friction. This causes a loss of work but also helps step the object up against gravity. (Without friction we could not use this machine) Examples: Ramps, Slides, etc.
20 Wedges A wedge is two inclined planes back to back. Instead of the object moving up the inclined plane, the wedge moves into or against an object to do work. Force is applied to the wedge. Examples: Wedges, Ax, Doorstops, Zippers
21 Screws Screws are an Inclined Plane wrapped around a cylinder. This once again increases distance to decrease the input force required to drive the screw into a material. (Output force against the wood is increased) The groves also grip into the material and hold it in place. Examples: Screws, bolts, jar lids.
22 Compound (Complex) Machines Consist of several simple machines working together.
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