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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 200-kN
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
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 SO-lb
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 ZOO-lb 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 ZOO-lb force FAB at point A that is di- fezsed along the line from A to B. The cable AC exerts a lOO-lb
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 32-lb force T on the collar at A.
Express T in terms of components. ' ' ts a 50-lb 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 4-m 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—m-tall tower is supported by three cables that of componen[s_
£15111 forces FAB, FAG, and FAD on it. The magnitude of each
I fit-cc 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 ﬁll-ﬁg cables in terms of components, is directed along the line from A toward B. Express T in terms of
_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? %
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