University Physics Volume 1 18th Edition
ISBN: 9781938168277
Author: William Moebs, Samuel J. Ling, Jeff Sanny
Publisher: William Moebs, Samuel J. Ling, Jeff Sanny
1 Units And Measurement 2 Vectors 3 Motion Along A Straight Line 4 Motion In Two And Three Dimensions 5 Newton's Law Of Motion 6 Applications Of Newton's Laws 7 Work And Kinetic Energy 8 Potential Energy And Conservation Of Energy 9 Linear Momentum And Collisions 10 Fixed-axis Rotation 11 Angular Momentum 12 Static Equilibrium And Elasticity 13 Gravitation 14 Fluid Mechanics 15 Oscillations 16 Waves 17 Sound Chapter2: Vectors
Chapter Questions Section: Chapter Questions
Problem 2.1CYU: Check Your Understanding Two motorboats named Alice and Bob are moving on a lake. Given the... Problem 2.2CYU: Check Your Understanding A cave diver enters a tong underwater tunnel. When her displacement with... Problem 2.3CYU: Check Your understanding Using the three displacement vectors A , B , and F in Figure 2.13, choose a... Problem 2.4CYU: Check your Understanding A blue fly lands on a sheet of graph paper a point located 10.0 cm to the... Problem 2.5CYU: Check Your Understanding If the displacement vector of a blue fly walking on a sheet of graph paper... Problem 2.6CYU: Check Your Understanding If Trooper runs 20 m west before taking a rest, what is his displacement... Problem 2.7CYU: Check Your Understanding If the average velocity vector of the drone In the displacement in Example... Problem 2.8CYU: Check Your understanding Three displacement vectors A , B , and F in (Figure 2.13) are specified by... Problem 2.9CYU: Check Your Understanding Suppose that Balto in Example 2.10 leaves the game to attend to more... Problem 2.10CYU: Check Your Understanding Verify that vector v V obtained in Example 2.14 is indeed a unit vector by... Problem 2.11CYU: Check Your Understanding For the vectors given in Figure 2.13, find the scalar products AB and FC .... Problem 2.12CYU: Check Your Understanding For vector in a rectangular coordinate system, use Equation 2.29 through... Problem 2.13CYU: Check Your Understanding Find the angle between forces F1and F3in Example 2.16. Problem 2.14CYU: Check Your Understanding How much work is done by the first dog and by the second dog In Example... Problem 2.15CYU: Check Your Understanding For the vectors given in Figure 2.13, find the scalar products AB and CF .... Problem 2.16CYU: Check Your Understanding Given two vectors and , find (a) (b) (c) the angle between and , and (d)... Problem 1CQ: Scalars and Vectors A weather forecast states the temperature is predicted to be 5Cthe following... Problem 2CQ: Which of the following is a vector a person’s height, the altitude on Mt. Everest, the velocity of a... Problem 3CQ: Give a specific example of a vector, stating its magnitude, units, and direction. Problem 4CQ: What do vectors and scalars have in common? How do they differ? Problem 5CQ: Suppose you add two vectors A and B . What relative direction between them produces the resultant... Problem 6CQ: Is it possible to add a scalar quantity to a vector quantity? Problem 7CQ: Is it possible for two vectors of different magnitudes to add to zero? Is it possible for three... Problem 8CQ: Does the odometer in an automobile indicate a scalar or a vector quantity? Problem 9CQ: When a 10,000-rn runner competing on a 400-rn track crosses the finish line, what is the runner’s... Problem 10CQ: A vector has zero magnitude. Is it necessary to specify its direction? Explain. Problem 11CQ: Can a magnitude of a vector be negative? Problem 12CQ: Can the magnitude of a particle’s displacement be greater that the distance traveled? Problem 13CQ: If two vectors are equal, what can you say about their components? What can you say about their... Problem 14CQ: If three vectors sum up to zero, si1at geometric condition do they satisfy? Problem 15CQ: Give an example of a nonzero vector that has a component of zero. Problem 16CQ: Explain why a vector cannot have a component greater than its own magnitude. Problem 17CQ: If two vectors are equal, what can you say about their components? Problem 18CQ: If vectors A and B are orthogonal, what is the component of B along the direction of A ? What Is the... Problem 19CQ: If one of the two components of a vector is not zero, can the magnitude of the other vector... Problem 20CQ: If two vectors have the same magnitude, do their components have to be the same? Problem 21CQ: What is wrong with the following expressions? How can you correct them? (a) C=AB , (b) C=AB , (c)... Problem 22CQ: If the cross product of two vectors vanishes, what can you say about their directions? Problem 23CQ: If the dot product of two vectors vanishes, what can you say about their directions? Problem 24CQ: What is the dot product of a vector with the cross product that this vector has with another vector? Problem 25P: A scuba diver makes a slow descent into the depths of the ocean. His vertical position with respect... Problem 26P: In a tug-of-war game on one campus, 15 students pull on a rope at both ends in an effort to displace... Problem 27P: Suppose you walk 18.0 m straight west and then 25.0 m straight north. How far are you from your... Problem 28P: For the vectors given in the following figure, use a graphical method to find the following... Problem 29P: A delivery man starts at the post office, chives 40 km north, then 20 km west, then 60 km northeast,... Problem 30P: An adventurous dog strays from home, runs three blocks east, two blocks north, one block east, two... Problem 31P: In an attempt to escape a desert island, a castaway builds a raft and sets out to sea. The wind... Problem 32P: A small plane flies 40.0 km in a direction 60 north of east and then files 30.0 km in a direction 15... Problem 33P: A trapper walks a 5.0-km straigt4ine distance from his cabin to the lake, as shown in the following... Problem 34P: A surveyor measures the distance across a river that flows straight north by the following method.... Problem 35P: A pedestrian walks 6.0 km east and then 13.0 km north. Use a graphical method to find the... Problem 36P: The magnitudes of two displacement vectors are A=20mand B=6m . What are the largest and the smallest... Problem 37P: Assuming the +x -axis is horizontal and points to the tight, resolve the vectors given In the... Problem 38P: Suppose you walk 18.0 m straight west and then 25.0 m straight north. How far are you from your... Problem 39P: You drive 7.50 km in a straight line in a direction 15 east of north. (a) Find the distance you... Problem 40P: A sledge is being pulled by two horses on a flat terrain. The net force on the sledge can be... Problem 41P: A trapper walks a 5.0-lan straight-line distance from her cabin to the lake, as shown in the... Problem 42P: The polar coordinates of a point are 4/3and 5.50 m. What are its Cartesian coordinates? Problem 43P: Two points in a plane have polar coordinates P1(2.500m,/6) and P2(3.800m,2/3). Determine their... Problem 44P: A chameleon is resting quietly on a lanai screen, waiting for an insect to come by. Assume the... Problem 45P: Two points in the Cartesian plane are A(2.00m,4.00m) and B(-3.00m,3.00m) . Find the distance between... Problem 46P: A fly enters through an open window and zooms around the room. In a Cartesian coordinate system with... Problem 47P: For vectors and , calculate (a) and its magnitude and direction angle, and (b) and its magnitude and... Problem 48P: A particle undergoes three consecutive displacements given by vectors , and . (a) Find the resultant... Problem 49P: Given two displacement vectors A=(3.00i-4.00j-4.00K)m and B=(2.00i+3.00j-7.00K)m , find the... Problem 50P: A small plane flies 40.0 km ma direction 60 north of east and then flies 30.0 km in a direction 15... Problem 51P: In an attempt to escape a desert island, a castaway builds a raft and sets out to sea. The wind... Problem 52P: Assuming the +x -axis is horizontal to the right for the vectors given in the following figure, use... Problem 53P: Given the vectors in the preceding figure, find vector Rthat solves equations (a) D+R=Fand (b)... Problem 54P: A delivery man starts at the post office, drives 40 km north, then 20 km west, then 60 km northeast,... Problem 55P: An adventurous dog strays from home, runs three blocks east, two blocks north, and one block east,... Problem 56P: If , and , find the unknown constants a and b such that . Problem 57P: Given the displacement vector , find the displacement vector so that . Problem 58P: Find the unit vector of direction for the following vector quantities: (a) Force , displacement ,... Problem 59P: At one point in space, the direction of the electric field vector Is given In the Cartesian system... Problem 60P: A barge is pulled by the two tugboats shown in the following figure. One tugboat pulls on the barge... Problem 61P: In the control tower at a regional airport, an air traffic controller monitors two aircraft as their... Problem 62P: Assuming the axis is horizontal to the right for the vectors in the following figure, find the... Problem 63P: Assuming the +x-axis is horizontal to the right for the vectors in the preceding figure, find (a)... Problem 64P: Find the angle between vectors for (a) D=(-3.0i-4.0j)m and A=(-3.0i+4.0j)m and (b) D=(2.0i+4.0j+K)m... Problem 65P: Find the angles that vector makes with the and axes. Problem 66P: Show that the force vector is orthogonal to the force vector Problem 67P: Assuming the +x-axis is horizontal to the right for the vectors in the previous figure, find the... Problem 68P: Find the cross product for (a) and (b) and (c) and and (d) and Problem 69P: For the vectors in the earlier figure, find (a) (AF)D , (b) (AF)(DB) , and (c) (AF)(DB) . Problem 70P: (a) If AF=BF , can we conclude A=B ? (b) If AF=BF , can we conclude A=B ? (c) If FA=BF , can we... Problem 71AP: You fly 32.0 km in a straight line in still air in the direction 35.0 south of west. (a) Find the... Problem 72AP: Rectangular coordinates of a point are given by (2,y) and its polar coordinates are given by (r,/6)... Problem 73AP: If the polar coordinates of a point are (r,)and its rectangular coordinates are (x,y) , determine... Problem 74AP Problem 75AP: Starting at the island of Moi in an unknown archipelago, a fishing boat makes a round trip with two... Problem 76AP: An air traffic controller notices two signals from two planes on the radar monitor. One plane is at... Problem 77AP: Show that when A+B=C then A2+B2+2ABcos , where is the angle between vectors A and B . Problem 78AP: Four force vectors each have the same magnitude f.What is the largest magnitude the resultant force... Problem 79AP: A skater glides along a circular path of radius 5.00 m in clockwise direction. ‘When he coasts... Problem 80AP: A stubborn dog is being walked on a leash by its owner. At one point, the dog encounters an... Problem 81AP: If the velocity vector of a polar bear is u=(-18.0 i -13.0 j)km/h , how fast and in what geographic... Problem 82AP: Find the scalar components of three-dimensional vectors G and H in the following figure and write... Problem 83AP: A diver explores a shallow reef off the coast of Belize. She initially swims 90.0 m north, makes a... Problem 84AP: A force vector A has x and y components, respectively, of -8.80 units of force and 15.00 units of... Problem 85AP: Vectors A and B are two orthogonal vectors in the xy -plane and they have identical magnitudes. If... Problem 86AP: For the three-dimensional vectors in the following figure, find (a) GH , (b) GH , and (c) GH . Problem 87AP: Show that (BC)A is the volume of the parallelepiped, with edges formed by the three vectors in the... Problem 88CP: Vector B is 5.0 cm long and vector A is 4.0 cm long. Find the angle between these two vectors when... Problem 89CP: What is the component of the force vector G=(3.0 i+4.0 j+10.0 k)N along the force vector H=(1.0... Problem 90CP: The following figure shows a triangle formed by the three vectors A , B , and C . If vector C is... Problem 91CP: between points in a plane do not change when a coordinate system is rotated In other words, the... Problem 86AP: For the three-dimensional vectors in the following figure, find (a) GH , (b) GH , and (c) GH .
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Two forces of magnitude 50 N, as shown in the figure below, act on a cylinder of radius 4 m and mass 6.25 kg. The cylinder, which is initially at rest, sits on a frictionless surface. After 1 second, the velocity and angular velocity of the cylinder in m/s and rad/s are respectively
Transcribed Image Text: F
F
Definition Definition Rate of change of angular displacement. Angular velocity indicates how fast an object is rotating. It is a vector quantity and has both magnitude and direction. The magnitude of angular velocity is represented by the length of the vector and the direction of angular velocity is represented by the right-hand thumb rule. It is generally represented by ω.
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