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Unformatted text preview: 56 Chapterz Vectors 2.69 The cable exerts a force F on the hook at 0 whose magni
tude is 200 N. The angle between the vector F and the x axis is
40°, and the angle between the vector F and the y axis is 70°. Refer to the following diagram when solving Problems
2.72 through 2.75. (a) What is the angle between the vector F and the z axis?
(b) Express F in terms of components. Strategy: (3) Because you know the angles between the
vector F and the x and y axes, you can use Eq. (2.16) to determine
the angle between F and the z axis. (Observe from the figure that
the angle between F and the z axis is clearly within the range
0 < Hz < 180°.) (b) The components of F can be obtained
with Eqs. (2.15). Problems 2.72—2.75 2.72 Determine the components of the position vector ['33 from point B to point D. Use your result to determine the distance
from B to D. 2.73 What are the direction cosines of the position vector rBD
from point B to point D? 2.74 Determine the components of the unit vector eCD that
points from point C toward point D. 2.75 What are the direction cosines of the unit vector 9CD that
points from point C toward point D? )* 2.76 In Example 2.7, suppose that the caisson shifts on the
ground to a new position. The magnitude of the force F remains
600 1b. In the new position, the angle between the force F and the
x axis is 60" and the angle between F and the z axis is 70°. Express
F in terms of components. Problem 2.69 2, 70 A unit vector has direction cosines cos 0.. : 0.5 and
cos 6), x 0.2. Its z component is positive. Express it in terms of componﬁms 2.77 Astronauts on the space shuttle use radar to determine the magnitudes and direction cosines of the position vectors of two
satellites A and B. The veCtor rA from the shuttle to satellite A has
magnitude 2 km and direction cosines cos 6x = 0.768, cos 6}. =
0.384, cos dz = 0.512. The vector ['3 from the shuttle to satellite
B has magnitude 4 km and direction cosines cos 6I = 0.743,
cos 6), = 0.557, cos 6Z : ~0.371. What is the distance between
the satellites? 2.71 The airplane’s engines exert a total thrust force T of 200kN
magnitude. The angle between T and the x axis is 120°, and the
angle between T and the y axis is 130°. The z component of T
is positive. (a) What is the angle between T and the z axis? (b) Express T in terms of components. Problem 2.71 Problem 2.77 58 Chapter 2 Vectors 2.84 The magnitudes of the two force vectors are IF AI : 140 lb 2.88 The cable BC exerts an S—kN force F on the bar AB at B.
and iFBl = 10011). Determine the magnitude of the sum of the
forces FA + F3. 5
g (a) Determine the components of a unit vector that points from
E point B toward point C.
(b) Express F in terms of components.
2.85 Determine the direction cosines of the vectors F A and F3. E
l
l
i
r C (3,0,4)m Problems 2.84/2.85 Problem 2.88 F286 In Example 2.8, suppose that a change in the wind
causes a change in the position of the balloon and increases the
magnitude of the force F exerted on the hook at 0 to 900 N. In
the new position, the angle between the vector component F},
and F is 35”, and the angle between the vector components F},
and FE is 40°. Draw a sketch showing the relationship of these
angles to the components of F. Express F in terms of its
components. 2.89 Acable extends from point C to point E. It exerts a SOlb
force T on the plate at C that is directed along the line from C to
E. Express T in terms of components. 2.8? An engineer calculates that the magnitude of the axial force
in one of the beams of a geodesic dome is IPI : 7.65 kN. The
cartesian coordinates of the endpoints A and B of the straight beam are (412.4, 22.0, —18.4) m and (—9.2, 24.4, 715.6) m,
respectively. Express the force P in terms of components. Problem 2.89 F 2,90 In Example 2.9, suppose that the metal loop at A is moved upward so that the vertical distance to A increases from
i 7 ft to 8 ft. As a result, the magnitudes of the forces FAB and ,3 FAG increase to IFABI = IFACl = 2401b. What is the magni
§ tude of the total force F = FAB + F AC exerted on the loop by
t the rope? Problem 2.87 Problems 59 AB at B, ' .191 The cable AB exerts a ZOOlb force FAB at point A that is h 2.95 In Example 2.10, suppose that the distance from point
ims from ercted along the line from A to 8. Express FAB in terms of C to the collar A is increased from 0.2 m to 0.3 m, and the
zemponents. magnitude of the force T increases to 60 N. Express T in terms of its components.
1.92 Cable AB exerts a ZOOlb force FAB at point A that is di fezsed along the line from A to B. The cable AC exerts a lOOlb
free FAC at point A that is directed along the line from A to C.
:e:ermine the magnitude of the total force exerted at point A
r: the two cables. 2.96 The cable AB exerts a 32lb force T on the collar at A.
Express T in terms of components. ' ' ts a 50lb Problems 237/ 2.98 from C to z A (6, 0, 10) ft Problem 2.96
PrOblemS 291/232 2.97 The circular bar has a 4m radius and lies in the x—y plane.
Express the position vector from point B to the collar atA in terms
_ I. 93 The 70—mtall tower is supported by three cables that of componen[s_
£15111 forces FAB, FAG, and FAD on it. The magnitude of each
I fitcc is 2 kN. Express the total force exerted on the tower by 2‘98 The cable AB exerts a 60'N force T 011 the WHEY atA that
 :33 ﬁllﬁg cables in terms of components, is directed along the line from A toward B. Express T in terms of
components.
_x ' L94 The magnitude of the force FAB is 2 RN. The x and z
ozmponents of the vector sum of the forces exerted on the
I’Z'CI‘ by the three cables are zero. What are the magnitudes of E
F; _‘ and FAD? %
i
at A is l
:ases from ‘
FAB and l
e magni :3 loop by E
l Problems 233/234 ...
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This note was uploaded on 04/18/2011 for the course ENGR 200 taught by Professor Mullen during the Spring '08 term at Case Western.
 Spring '08
 mullen

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