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5 Sudhir walks 040 km in a direction 600 west of north, then goes 050 km due west What is his displacement 6 Afua and Chrissy are going to sleep overnight in their tree house and are using some ropes to pull up a box containing their pillows and blankets, which have a total mass of 320 kg The girls stand on different branches, as shown in Figure 5-6, and pull at the angles and with the forces indicated Find the x- and y-components of the net force on the box Hint: Draw a free-body diagram so that you do not leave out a force 7 You first walk 80 km north from home, then walk east until your displacement from home is 100 km How far east did you walk 8 A child s swing is held up by two ropes tied to a tree branch that hangs 130 from the vertical If the tension in each rope is 228 N, what is the combined force (magnitude and direction) of the two ropes on the swing 9 Could a vector ever be shorter than one of its components Equal in length to one of its components Explain 10 In a coordinate system in which the x-axis is east, for what range of angles is the x-component positive For what range is it negative You will use these techniques to resolve vectors into their components throughout your study of physics You will get more practice at it, particularly in the rest of this chapter and the next Resolving vectors into components allows you to analyze complex systems of vectors without using graphical methods

The little grey triangles on all four sides of the white box let you lock the position of the window relative to the sides of the screen Clicking a triangle toggles it between being extended, harpoon-like, to the edge of the mini-screen, or retracted to the edge of the window You can place the window where you want it on your screen, then use those triangles to lock the position relative to the let and top of the screen Let s do that now You need to set a y value that places the window near the menu bar, but not abutting it The easiest way to do this is to simply move your application s main window to where you want it, then press the Use Current button on the size inspector, which will set the initial size and location to the current size and location of the window.

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Figure 5-6 (Not to scale)

11 Distance v Displacement Is the distance that you walk equal to the magnitude of your displacement Give an example that supports your conclusion 12 Vector Difference Subtract vector K from vector L, shown in Figure 5-7

14 Vector Sum Find the sum of the three vectors shown in Figure 5-7 15 Commutative Operations The order in which vectors are added does not matter Mathematicians say that vector addition is commutative Which ordinary arithmetic operations are commutative Which are not 16 Critical Thinking A box is moved through one displacement and then through a second displacement The magnitudes of the two displacements are unequal Could the displacements have directions such that the resultant displacement is zero Suppose the box was moved through three displacements of unequal magnitude Could the resultant displacement be zero Support your conclusion with a diagram

Figure 5-7

13 Components Find the components of vector M, shown in Figure 5-7

ush your hand across your desktop and feel the force called friction opposing the motion Push your book across the desk When you stop pushing, the book will continue moving for a little while, then it will slow down and stop The frictional force acting on the book gave it an acceleration in the direction opposite to the one in which it was moving So far, you have neglected friction in solving problems, but friction is all around you You need it to both start and stop a bicycle and a car If you have ever walked on ice, you understand the importance of friction

You can then tweak the sizes numerically if you need to Once you have the initial position of the window where you want it on your screen, configure the little harpoons so that they are extended on the left and top sides of the white box, and retracted at the right and bottom sides, leaving the inspector looking like Figure 3 9..

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