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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 10-12

n this chapter, we explore moving up and down and across dimensions and hierarchies The general term for doing this is navigation MDX allows you to navigate both horizontally and vertically MDX (unlike SQL) is positionally aware it knows where you are in the cube and can help you in your navigation Key concepts Finding dimension members that have some relationship to a particular member, using ranges Keywords children, Descendants, Exists, parent, Ancestor, Ascendants, Hierarchize, siblings, rstchild, rstsibling, lastchild, lastsibling, Cousin, lead, lag, Head, Tail, prevmember, nextmember

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

32 Efficiency Suppose you increase the efficiency of a simple machine Do the MA and IMA increase, decrease, or remain the same 33 Critical Thinking The mechanical advantage of a multi-gear bicycle is changed by moving the chain to a suitable rear gear a To start out, you must accelerate the bicycle, so you want to have the bicycle exert the greatest possible force Should you choose a small or large gear b As you reach your traveling speed, you want to rotate the pedals as few times as possible Should you choose a small or large gear c Many bicycles also let you choose the size of the front gear If you want even more force to accelerate while climbing a hill, would you move to a larger or smaller front gear

Can you estimate the power you develop as you climb a flight of stairs Climbing stairs requires energy As the weight of the body moves through a distance, work is done Power is a measure of the rate at which work is done In this activity you will try to maximize the power you develop by applying a vertical force up a flight of stairs over a period of time

Predict the factors that affect power Calculate the power developed Define power operationally Interpret force, distance, work, time and power data Make and use graphs of work versus time, power versus force, and power versus time

books returned and the second is an array containing details about those books On failure it returns a single element array with the value FALSE It requires these arguments: $search A standard search query $start The first result to return $count The maximum number of results to return $type The type of result to return If this is 'none', then all books are returned; if 'partial', then books with partial previews are returned; or if 'full', then only books with full previews are returned