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Multi-gear bicycle On a multi-gear bicycle, the rider can change the MA of the machine by choosing the size of one or both gears When accelerating or climbing a hill, the rider increases the ideal mechanical advantage to increase the force that the wheel exerts on the road To increase the IMA, the rider needs to make the rear gear radius large compared to the front gear radius (refer to the IMA equation on page 270) For the same force exerted by the rider, a larger force is exerted by the wheel on the road However, the rider must rotate the pedals through more turns for each revolution of the wheel On the other hand, less force is needed to ride the bicycle at high speed on a level road The rider needs to choose a gear that has a small rear gear and a large front gear that will result in a smaller IMA Thus, for the same force exerted by the rider, a smaller force is exerted by the wheel on the road However, in return, the rider does not have to move the pedals as far for each revolution of the wheel An automobile transmission works in the same way To accelerate a car from rest, large forces are needed and the transmission increases the IMA At high speeds, however, the transmission reduces the IMA because smaller forces are needed Even though the speedometer shows a high speed, the tachometer indicates the engine s low angular speed
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10 Energy, Work, and Simple Machines
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The Human Walking Machine
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Movement of the human body is explained by the same principles of force and work that describe all motion Simple machines, in the form of levers, give humans the ability to walk and run The lever systems of the human body are complex However each system has the following four basic parts
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a rigid bar (bone) a source of force (muscle contraction) a fulcrum or pivot (movable joints between bones) a resistance (the weight of the body or an object being lifted or moved)
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Figure 10-15 shows the parts of the lever system in a human leg Lever systems of the body are not very efficient, and mechanical advantages are low This is why walking and jogging require energy (burn calories) and help people lose weight When a person walks, the hip acts as a fulcrum and moves through the arc of a circle, centered on the foot The center of mass of the body moves as a resistance around the fulcrum in the same arc The length of the radius of the circle is the length of the lever formed by the bones of the leg Athletes in walking races increase their velocity by swinging their hips upward to increase this radius A tall person s body has lever systems with less mechanical advantage than a short person s does Although tall people usually can walk faster than short people can, a tall person must apply a greater force to move the longer lever formed by the leg bones How would a tall person do in a walking race What are the factors that affect a tall person s performance Walking races are usually 20 or 50 km long Because of the inefficiency of their lever systems and the length of a walking race, very tall people rarely have the stamina to win
Figure 10-15 The human walking machine
102 Section Review
29 Simple Machines Classify the tools below as a lever, a wheel and axle, an inclined plane, a wedge, or a pulley a screwdriver c chisel b pliers d nail puller 30 IMA A worker is testing a multiple pulley system to estimate the heaviest object that he could lift The largest downward force he could exert is equal to his weight, 875 N When the worker moves the rope 15 m, the object moves 025 m What is the heaviest object that he could lift 31 Compound Machines A winch has a crank on a 45-cm arm that turns a drum with a 75-cm radius through a set of gears It takes three revolutions of the crank to rotate the drum through one revolution What is the IMA of this compound machine
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