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Recall from 4 that when the net force on an object is zero, the object is in equilibrium According to Newton s laws, the object will not accelerate because there is no net force acting on it; an object in equilibrium is motionless or moves with constant velocity You have already analyzed several equilibrium situations in which two forces acted on an object It is important to realize that equilibrium can occur no matter how many forces act on an object As long as the resultant is zero, the net force is zero and the object is in equilibrium Figure 5-11a shows three forces exerted on a point object What is the net force acting on the object Remember that vectors may be moved if you do not change their direction (angle) or length Figure 5-11b shows the addition of the three forces, A, B, and C Note that the three vectors form a closed triangle There is no net force; thus, the sum is zero and the object is in equilibrium Suppose that two forces are exerted on an object and the sum is not zero How could you find a third force that, when added to the other two, would add up to zero, and therefore cause the object to be in equilibrium To find this force, first find the sum of the two forces already being exerted on the object This single force that produces the same effect as the two individual forces added together is called the resultant force The force that you need to find is one with the same magnitude as the resultant force, but in the opposite direction A force that puts an object in equilibrium is called the equilibrant Figure 5-12 illustrates the procedure for finding this force for two vectors Note that this general procedure works for any number of vectors.

Description Match any one character at that position Match zero or more characters Match repetitions of the previous character zero or more times Match repetitions of the previous character one or more times Match one or more characters listed between the brackets Group items into a single logical item

Find the equilibrant for the following forces F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 610 N at 170 north of east 380 N at 640 north of east 540 N at 80 west of north 930 N at 530 west of north 650 N at 210 south of west 1020 N at 150 west of south 260 N south 770 N at 220 east of south 510 N at 330 east of south 820 N at 50 south of east

6 5 4 3 2 1

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In addition to downloading and installing Xcode, you ll also need to download the sample projects that go with this book. You can find the code archive on the Apress Learn Cocoa on the Mac web page: http://www.apress.com/book/view/1430218592 You ll find the source code archive in the Book Resources area on the left side of the page. Click the link, download the .zip archive, and move the Learn Cocoa Projects folder to a location in your Documents folder. You ll also find a link on the Apress Learn Cocoa on the Mac web page, in the Book Resources area, that lets you submit and view errata. If you find an error in the book (much as we d like to think otherwise, all books have errors) please do take a moment to report the error. This will help us make the book better in subsequent printings. We thank you in advance.

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Figure 6-15 At the top of the loop, when the plane is completely upside-down for an instant, the pilot hangs freely in the seat and does not push against the seat belt The airspeed indicator reads 120 m/s What is the radius of the plane s loop

18 m from the axis of rotation in a horizontal circle, as shown in Figure 6-14 If the hammer makes one revolution in 10 s, what is the centripetal acceleration of the hammer What is the tension in the chain

Figure 6-15

Figure 6-14

As you make your way through the book, you ll no doubt have some questions you d like to get answered. Fortunately, there is a great community you can join, designed specifically for this series of books. Check out: http://learncocoa.org Register with the site, find the appropriate book forum and post your questions. You are sure to find other folks who can answer your questions and, who knows, after a while you might find yourself answering questions for other folks as well.

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