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A screw is an inclined plane wrapped around a tube. We see the screw shape in bolts, screws of course, and worm gears. The screw puts the inclined plane into a very compact form. The angle of the plane can be low and we can get a lot of force out of it. This force is applied by turning the screw, which is essentially the same thing as moving a block up the ramp or driving a wedge into a gap. Einstein said that all motion is relative, and whether the resistance (the block or tower) moves, or the inclined plane (ramp, wedge, screw) moves, the e ect is the same.
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A lever is another way to apply mechanical advantage. Though the lever is a more complicated machine, it can be described with simpler math than the inclined plane.
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Try This: For levers, let s build a LEGO lever machine. In the ne tradition of these types of projects, the construction steps are depicted in pictures, shown in Fig. 3-9. The last step, and an informative example showing range of motion, is in Fig. 3-10. Pushing down on the long arm of the lever creates an upward force on the short arm. While the long arm moves four times as far, the short arm creates four times the force. You can hang weights at di erent points on this machine to get a feel for how it works. How does it feel when you hang the weight on the long end
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Fig. 3-9.
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Building the lever.
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Fig. 3-10.
LEGO lever.
Fig. 3-11.
First-class lever.
instead of the short end Try the weight at di erent positions and see how it a ects the force and range of motion. A formal description of the lever is given in Fig. 3-11. This lever is known as a rst-class lever. All levers have the same three pieces. The pivot in the middle is the fulcrum. The distance from the fulcrum to where the input force, or e ort (E), is applied is the e ort arm (dE). The distance from the fulcrum to where the force is used is the resistance arm (dR). The lever is applied against resistance
CHAPTER 3 Simple Machines
Fig. 3-12.
Second-class lever.
Fig. 3-13. Third-class lever.
(R). If dE is larger than dR, then your force is increased. The mechanical advantage is calculated as: MA dE dR 3-7
Equation (3-7) is essentially the same as equation (3-4) for the wedge. Though we look at several di erent simple machines, each with their own approach to increasing force, the principles behind each one are the same. Force is force, and the rules governing force are not going to change. If we seem to be getting more force at the output of a mechanism, somewhere inside it we are spending velocity or distance to get it. A second-class lever is shown in Fig. 3-12, and a third-class lever in Fig. 3-13. These have the same pieces as a rst-class lever, just in di erent positions. Note that the third-class lever has you pushing harder to get greater distance, backward from the rst and second-class levers. Your arm is a third-class lever with your elbow at one end, your wrist at the other, and the muscle attached in between.
Pulleys
A pulley is essentially a wheel. Where a wheel wears a skirt of rubber so it has a lot of friction, the pulley has a groove for a rope around its edge. Pulleys are designed so they don t add much friction to the machine they are a part of. Methods for removing friction are explored in a later chapter.
CHAPTER 3 Simple Machines
Fig. 3-14.
Pulley.
A pulley provides an easy way to change the direction of motion, as shown in Fig. 3-14. When you pull down on the rope, the force is used to lift an object. The pulley itself is xed into position so that it can rotate but not travel.
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