CHAPTER 5 Forces in Two Dimensions - Mr. Nguyen's Website

1 CHAPTER . 5 Forces in Two Dimensions Practice Problems Vectors pages 119 125. page 121. 1. A car is driven km due west, then km due south. What is the magnitude of its displacement? Solve this problem both graphically and mathematically, and check your answers against each other. R 2 ! A2 " B2 km R ! !". A2 " B2". km "". ! !( km)2 ". " (12". km". )2 141 km ! 141 km 2. Two shoppers walk from the door of the mall to their car, which is m down a lane of cars, and then turn 90 to the right and walk an additional m. What is the magnitude of the displacement of the shoppers' car from the mall door?

2 Solve this problem both graphically and mathematically, and check your answers against each other. R 2 ! A2 " B2 Mall m door R ! !". A2 " B2" m 257 m Car ! !". ( ". m)2 "". ( ". m)2. Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. ! 257 m 3. A hiker walks km in one direction, then makes a 45 turn to the right and walks another km. What is the magnitude of her displacement? R 2 ! A2 " B 2 # 2AB cos ! R! ". !A2 " B". 2 # 2A". B cos". ! ! !". ( k". m)2 "". ( k". m)2 #". 2( ". km)(6" "135 )..4 km)(cos ".

3 ! $101 km 4. An ant is crawling on the sidewalk. At one moment, it is moving south a distance of mm. It then turns southwest and crawls mm. What is the magnitude of the ant's displacement? R 2 ! A2 " B 2 # 2AB cos ! R! !". A2 " ". B2 # ". 2AB c". os ! ! ". !( ". mm) 2 "". ( m". m)2 #". 2( ". mm)(" "". mm)(co ". s 135 ). ! mm Physics: Principles and Problems Solutions Manual 87. CHAPTER 5 continued page 125. Solve problems 5 10 algebraically. You may also choose to solve some of them graphically to check your answers. 5.

4 Sudhir walks km in a direction west of north, then goes km due west. What is his displacement? Identify north and west as the positive directions. d1W ! d1 sin ! ! ( km)(sin ) ! km d1N ! d1 cos ! ! ( km)(cos ) ! km d2W ! km d2N ! km RW ! d1W " d2W ! km " km ! km RN ! d1N " d2N ! km " km ! km R! ". !RW "". 2 RN2. ! !". ( ". km)2 "". ( ". km)2. ! km !R ". RW. ! ! tan#1 ! N. ! tan#1!!!". km km ! 77 . R ! km at 77 west of north 6. Afua and Chrissy are going to sleep overnight in their tree house and are Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

5 Using some ropes to pull up a box containing their pillows and blankets, which have a total mass of 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. Identify up and right as positive. FA on box,x ! FA on box cos !A. ! ( N)(cos 120 ) Figure 5-6. ! # N. FA on box,y ! FA on box sin !A. ! ( N)(sin 120 ). ! N. FC on box,x ! FC on box cos !

6 A. ! ( N)(cos 55 ). 88 Solutions Manual Physics: Principles and Problems CHAPTER 5 continued ! N Fcombined ! Frope1 on swing cos ! ". FC on box,y ! FC on box sin !A Frope2 on swing cos ! ! ( N)(sin 55 ) ! 2 Frope2 on swing cos ! ! N. ! (2)( N)(cos ). Fg,x ! N. ! N upward Fg,y ! #mg 9. Could a vector ever be shorter than one of ! #( kg)( m/s2) its components? Equal in length to one of ! # N its components? Explain. Fnet on box,x ! FA on box,x " It could never be shorter than one of its components, but if it lies along either FC on box,x " Fg,x the x- or y-axis, then one of its compo- !

7 # N " N " N nents equals its length. ! N 10. In a coordinate system in which the x-axis is Fnet on box,y ! FA on box,y " east, for what range of angles is the x-compo- nent positive? For what range is it negative? FC on box,y " Fg,y The x-component is positive for angles ! N " N # N less than 90 and for angles greater ! N than 270 . It's negative for angles The net force is N in the upward greater than 90 but less than 270 . direction. 7. You first walk km north from home, then Section Review walk east until your displacement from home Vectors is km.

8 How far east did you walk? pages 119 125. Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. The resultant is km. Using the page 125. Pythagorean Theorem, the distance east 11. Distance v. Displacement Is the distance is that you walk equal to the magnitude of R 2 ! A2 " B2, so your displacement? Give an example that B! !" "2. R2 # A supports your conclusion. Not necessarily. For example, you could ! !". ( ". km)2 ". # ( ". km)2. walk around the block (one km per ! km side). Your displacement would be zero, but the distance that you walk would be 8.

9 A child's swing is held up by two ropes tied 4 kilometers. to a tree branch that hangs from the vertical. If the tension in each rope is N, 12. Vector Difference Subtract vector K from what is the combined force (magnitude and vector L, shown in Figure 5-7. direction) of the two ropes on the swing? The force will be straight up. Because the angles are equal, the horizontal Forces will be equal and opposite and cancel out. The magnitude of this vertical force is Physics: Principles and Problems Solutions Manual 89. CHAPTER 5 continued 16.

10 Critical Thinking A box is moved through one displacement and then through a sec- M. ond displacement. The magnitudes of the # . K two displacements are unequal. Could the displacements have directions such that the resultant displacement is zero? Suppose the box was moved through three displace- L ments of unequal magnitude. Could the Figure 5-7 resultant displacement be zero? Support # (# ) ! to the right your conclusion with a diagram. No, but if there are three 13. Components Find the components of displacements, the sum can vector M, shown in Figure 5-7.