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Unformatted text preview: CUSTOM GENERATED PROBLEMS 428. Determine the smallest force F that must be applied
to the rope, when held in the direction shown, in order to
cause the pole to break at its base 0.'Ihis requires a moment of M = 900 N m to be developed at 0.
Z 4—29. The force F = [6i + 8j + 10k] N creates a moment about point 0 of M0 = {414i + 8} + 2k}Nm. If the force
passes through a point having an x coordinate of 1 m, determine the y and z coordinates of the point. Also,
realizing that M0: Fd, determine the perpendicular
distance d from point 0 to the line of action of F. Prob. 4—29 4—30. The 50lb force acts on the gear in the direction
shown. Determine the moment of this force about the y axis. F=501b Prob. 430 4—31. The cutting tool on the lathe exerts a force F on the
shaft in the direction shown. Determine the moment of this force about the y axis of the shaft.
2 F={6i—4je7k}kN _....A,‘.._".L__...g.1._,..,,. .. .. .. 124—32. The lug nut on the wheel of the automobile is to be
removed usmg the wrench with the cheater pipe AB slipped erits handle and applying a force F = 30 N at any point
d In any directlon on the assembly. Determine if this force sadequate, provided 14 Nm of tor ue ab . _
‘ ' O t
 . tially fequ1red to turn the nut. q u the x am '5 The wooden shaft is held in a lathe. The cutting tool
a force F on the shaft in the direction shown. F= t—5i e 3j +8k}N y
Prob. 433 CUSTOM GENERATED PROBLEMS 33 434. The Aframe is being hoisted into an upright position by the vertical force of F = 30 lb. Determine the moment of HMS f()rce about the XIS when t [la 3 IS 1 he
y a
he m n t Prob. 4—34 a .
4735. Determine the moment of the force F about the an
axrs. Express the result as a Cartesian vector. 2 F: {30i +40j+20k1N Prob. 435 CUSTOM GENERATED PROBLEMS 4—36. Determine the magnitude of the moment of each of
the three forces about the axis AB. Solve the problem (a)
using a Cartesian vector approach and (b) using a scalar
approach. . Prob. 436 4—37. A horizontal force of F: [—50i}N is applied perpendicular to the handle of the pipe wrench. Determine
the moment that this force exerts along the axis 0A (1 axis)
of the pipe assembly. Both the wrench and pipe assembly.
OABC, lie in the yz plane. Suggestion: Use a scalar analysis. Prob. 4—37 438. Determine the moment of the force F about the an
axis. Express the result as a Cartesian vector. Z Prob. 438 4—39. The chain AB exerts a force of F = 20 lb on the
door at B. Determine the moment of this force along the
hinged axis x of the door. , : _0. Determine the magnitude and sense of the couple
{13011191115 Prob. 4—42 CUSTOM GENERATED PROBLEMS 35 4—43. 'l‘hree couple moments act on the pipe assembly.
Determme the magnitude of M3 and the bend angle 9 so that the resultant couple moment is zero.
M3 M2 = 500 N  m
Prob. 4—43 4:4. The ends of the triangular plate are subjected to
t ree couples. Determlne the magnitude of the force F so that the resultant couple moment is 400 N m clockwise.
600 N F Prob. 4—44 CUSTOM GENERATED PROBLEMS
CUSTOM GENERATED PROBLEMS 37 e frame. If d = 4ft, determine I . ~
6 the result by at“? Elisha resultant couple of the two couples acting on 4—51 A couple acts on e h f
' II‘ ' = — '  . ' ac 
ts and (a) finding . ‘ . e y 'ragt ls MR [ 15' + 30]}N'm. determine the valve. Determine the magnitud: £1: (iloamgjlfas Of “'18 dual
. e magnltu e R angles of the resultant couple moment 0r Inate dlrectron
Z *4—45. If the couple moment acting on the pipe has a 4.41 Two couples act on th
the resultant couple moment. Comput magnitude of 400 Nm, determine the magnitude F of the
vertical force applied to each wrench. resolving each force into x and y componen
' the moment of each couple (Eq. 4—13) and (b) summing the '
moments of all the force components about point B. '  . z Prob. 4—51 4—52.. If the couple moment acting on the pipe has a
magnitude of 300 Nm, determine the magnitude F of the Prob. 4—49
forces applied to the wrenches. Prob. 445
4—48. Determine the couple moment. Express the result as 446. Tvvo couples act on the frame. If the resultant couple a Cartesian vector. 4_
moment IS to be zero, determine the distance d between the '"F50' blExpress the moment 0f the couple 301ng on the pipe
80lb couple forces. , ssem y in Cartesian vector form Solve th
,  e problem (a)
1131113 Eq. 413, and (b) summin th
. boat point 0 g e moment of each force —F= [—8i+4j—10k}N F={—6i+2j+3k}N CUSTOM GENERATED PROBLEMS 453. If the couple moment has a magnitude of 250 N m,
determine the magnitude F of the couple forces. Prob. 4—53 4—54. Determine the magnitude and sense of the. couple
moment. Each force has a magnitude of F = 8 kN.
y ' ' f an airplane is
1155. The mam beam along the wrng o _ ‘ _
swept back at an angle of 25". From load calculations it IS
determined that the beam is subjected to couple moments M =17 kipft and My=25 kipft. Determine the
I f I
resultant couple moments created about the x and y
axes.The axes all lie in the same horizontal plane. Prob. 4—55 4—56. Replace the force and couple moment system by an
equivalent force and couple moment acting at pornt P. 4;_5“7. Replace the force and couple system by an
equivalent force and couple moment acting at point P. Prob. 4—57 €58. The main beam along the wing of an airplane is
' ept back at an angle of 25". From load calculations it is
rmined that the beam is subjected to couple moments ' )4: .= 25 000 lb'ft and My = 17000 lb‘ft. Determine the CUSTOM GENERATED PROBLEMS 39 4—59. The crossbar wrench is used to remove a lug nut
from the automobile wheel. The mechanic applies a couple
to the wrench such that his hands are a constant distance apart. Is it necessary that a = b in order to produce the
most effective turning of the nut? Explain. Also, what is the
effect of changing the shaft dimension c in this regard? The
forces act in the vertical plane. Prob. 459 *4—60. The cord passing over the two small pegs A and B
of the board is subjected to a tension of 100 N. Determine the minimum tension P and the orientation 3 of the cord
passing over pegs C and D, so that the resultant couple moment produced by the two cords is 20 Nm, clockwise. Prob. 4—60 CUSTOM GENERATED PROBLEMS
. CUSTOM GENERATED PROBLEMS 43 4—70. Replace the force system acting on the frame by an *4—72. The three forces acting on the block each have a {42.74. Replace the force system by an equivalent resultant equivalent resultant force and specify where the resultant’s magnitude 0f 10 lb. Replace this system by a wrench and ' _ mg and specify its point of application,m easure d along the
line of action intersects member BC, measured from specrfy the pornt where the wrench intersects the 2, arms, . is from point B.
' measured from point 0.  i‘ Z 4—77. The column is used to support the floor which exerts
a force of 3000 lb on the top of the column.The effect of soil
pressure along its side is distributed as shown. Replace this
loading by an equivalent resultant force and specify where it
acts along the column, measured from its base A. l = ' = ' 3000 lb point B. Prob. 4—72 473. Replace the force at A by an equivalent resultant
th 4‘70 force and couple moment at point 0. *4—71. The belt passing over the pulley is subjected to 3’
*4'73 Replace the loading by an equivalent force and forces F1 and F2, each havingamagnitude of 40 N. FI acts " , . ‘ _ ‘ . ' T . 6R of the bridge. Replace this system of forces by an couple moment actin at 0i t0
1n the —k direction. Replace these forces by an equivalent HIValent resultant force and specify its location measured 3 P n .
force and couple moment at point A. Express the result in m point A. 15 kN/m Cartesian vector form.Set 8 = 0° so that F2 acts in the —j ~ direction. Prob. 4—78 4—79. Replace the distributed loadin '
g by an e urvalent
Prob. 4.75 resultant force, and specify its location on ma beam The loading on the bookshelf is distributed as shown. measured from the pin at C' mine the magnitude of the equivalent resultant  Prob. 4—79 CUSTOM GENERATED PROBLEMS 4—80. The beam supports the distributed load caused by
the sandbags. Determine the resultant force on the beam and specify its location measured from point A. 4—81. Replace the loading by an equivalent resultant force
and specify its location on the beam, measured from point B. 300 lbfft 4—82. Replace the loading by an equivalent resultant force
and couple moment acting at point 0. 483. Determine the equivalent resultant force and its
location, measured from point 0.
w = w.) sin% 1: Prob. 4—83 484. Replace the distributed loading by an equivalent
resultant force and specify its location on the beam, measured from the pin at A. Prob. 4—84 485. Determine the coordinate direction angles a, ,6, y
of F, which is applied to the end A of the pipe assembly, so that the moment of F about 0 is zero.
F = 20 lb Prob. 4—85 4—86. Replace the force F having a magnitude of F = 50 lb and acting at point A by an equivalent force and
couple moment at point C. Prob. 4—86 4—87. The horizontal 30N force acts on the handle of the
wrench. Determine the moment of this force about point 0. _ Specify the coordinate direction angles a, ,8, y of the moment axis. CUSTOM GENERATED PROBLEMS 45 488. If the resultant couple moment of the three couples acting on the triangular biock is to be zero, determine the
magnitudes of forces F and P. SI—l. Draw the freebody diagram of the beam, which is
pinsupported at A and rests on the smooth incline at B. 300 lb 800 lb
600 lb 600 lb ...
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 Spring '10
 Michael

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