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1 Problems (on oment) 1. The rod on the power control mechanism for a business jet is subjected to a force of 80 N. Determine the moment of this force about the bearing at sin 6080sin 00.15cos60 80 cos 0 x y N m (counterclockwise - ccw)
2 . In order to raise the lamp post from the position Problems (on oment) shown, force is applied to the cable. If =00 N, determine the moment produced by about point. Geometry: 00sinq B 6 m q 00cosq 6 m Cosine law: BC 6 6 cos105 m BC 7. 7 m C + m 6 Sine law: 7.7 sin105 sin 00sin q N m q o.15 (counterclockwise - ccw)
3 Problems (on oment). Calculate the moment o of the 50 N force about the base point of the robot.
4 0.50.4sin0+0.sin mm 0 o x = 50sin40 N y = 50cos40 N x 500 mm 60 o 0 o 50 o 40 o 40 o y 00 mm o + 0.4cos0+0.cos40 0.4cos0 0.cos 40 50sin sin 0 0.sin 40 50cos 40 o N m (counterclockwise - ccw)
5 1.5 m 4. The towline exerts a force of P=4 kn at the end of the 0-m-long crane boom. If x=5 m, determine the position of the boom so that this force creates a maximum moment about point. What is this moment? B q 5 m aximum moment, B B kn m o max 5 4cos sin 1.5cos 0 / : cos 1.5 0sec 5tan sec 4sin 5tan 65 tan tan m 75 tan tan 5 tan 75tan m 75m m1, m1, o tan 56. o q
6 5. The 10 N force is applied as shown to one end of the curved wrench. If a=0 o, calculate the moment of about the center of the bolt. Determine the value of a which would maximize the moment about ; state the value of this maximum moment. If a=0 o, =? = 10 N 0 o ( )=90 mm ( ) =190 mm + o sin cos0 y 90 x 190 o N mm N m (clockwise - cw)
7 Determine the value of a which would maximize the moment about. max =? o a = 10 N ( ) =90 mm a ( ) =190 mm N mm or max, must be perpendicular to. 190 a arctan 90 N m o. o d da o cosa 0.9 sin a sin a 0.9 cosa0.19 tan a a o
8 Problems (on oment) 6. The force exerted by the hydraulic cylinder B on the door is kn (constant) directed from to B. Determine the moment of this force about point ( o ) as a fuction of q. lso determine o for q =50 o. 40 cm q 150 cm B 0 cm
9 Problems (on oment) 7. The spring-loaded follower bears against the circular portion of the cam until the lobe of the cam lifts the plunger. The force required to lift the plunger is proportional to its vertical movement h from its lowest position. or design purposes determine the angle q for which the moment of the contact force on the cam about the bearing is a maximum. In the enlarged view of the contact, neglect the small distance between the actual contact point B and the end C of the lobe.
10 Problems (on oment) 8. The pipe assembly is subjected to an 80 N force. Determine the moment of this force about point. lso determine the minimum distance from point to the line of action of force.
11 orce in vector form xy 80cos N x xy sin sin N y xy cos cos N z 80sin 0 40 N 44.5i 5.07 j 40k Position vector from point to point C 0.4 j 0.i 0.k 0.5i 0.55i 0.4 j 0.k r C / r C / oment of force about point rc / 0.55i 0.4 j 0.k 44.5i 5.07 j 40k 9.19k j 17.81k 16i 8.91j 10.61i r C/ x y xy z 5.9i 1.09 j 11.8k
12 minimum distance from point to the line of action of force d: minimum distance r r C / r C / C / d r C / sin q d sin q 5.9i 1.09 j 11.8k q r C/ agnitude of the moment d 80 d = 0. 7 m N m
13 Problems (on oment) 9. Concrete pump is subjected to force acting on point C as shown in the figure. rms, B and BC lie in the same plane which makes 5 o with xz plane. a) Determine the moment of force about point. b) Determine the moment of force about line. 5 o
14 10. The spring which connects point B of the disk and point C on the vertical surface is under a tension of 500 N. Write this tension as it acts on point B as a force vector and determine the moment z of this force about the shaft axis. spring = spring n C/B Coordinates : B 150sin0, 150cos0, 600 C(50, 00, 0) spring B 75, 19. 9, 600 spring 45i j 600k i 11.7 j 97.5k i Position vector from point to point C (It may be written the position vector from point to point B) r C / 0. j oment of force spring about point C spring 0.5i 0. j 81.57i 11.7 j 97.5k 119.5i 19.5 j 45.0 r / k oment about the shaft axis n k N m
15 11. Strut B of the 1 meter diameter hatch door exerts a force of 450 N on point B. Determine the moment of this force about point. Line B of the hatch door lies in the yz plane. 0.5sin0, cos0, 0 B 0, 1cos0, 1sin0 0. 5, 0. 9, 0 B(0, , 0. 5) z z B 0 o 0.5 m 0 o y i j x k 00.89i 5.84 j k
16 00.89i 5.84 j k z Position vector from point to point B (It may be written the position vector from point to point ) r B / j 0.5k rb / j 0.5k 00.89i 5.84 j k 74.86i j k x 0 o 0.5 m B 0 o y! btain the same result using position vector r / 0.5 j 0.5cos 0 j 0.5i 0.5i 0.9 j r / r / inimum distance from point to line B, d: = 450 N, = = = N. m d = = m
17 Problems (on oment) 1. Concentrated force is acting perpendicular to the crank arm BC at point C. or the position q=70, what is x, the moment of about the x axis? t this instant, y =0 N m and z =7.5 N m. P y B 100 mm C 00 mm z 150 mm q x
18 q=70, y =0 N m and z =7.5 N m x =? B, C 00 mm y P z 70 o, P Psin j P cosk y B z r 50i 00sin 70 j 00cos70k r 50i j 68.4k o r P i j k Psin j P cosk 50Psin k 50P cosj P cosi 68.4Psin i r C / o o q C P 00 mm x
19 q=70, y =0 N m and z =7.5 N m x =? o 50Psin k 50P cosj P cosi 68.4Psin i y z 50P cos 010 N mm 1 50Psin N mm 1 50Psin 50P cos tan P 170 N x N mm 5. N m P cos 68.4Psin
20 Problems (on oment) z D (0,, ) (0, 5, ) m C (4, 6, 0) m B (6,, 0) m y 1. Rectangular plate DC is held in equilibrium by string B which has a tension of T=14 kn. Determine, a) The magnitude of the moment of about the axis DC, b) The perpendicular distance between lines B and DC. x
21 z D (0,, ) (0, 5, ) m y C (4, 6, 0) m T T n 6i j k TnT i 4 j 6k 4i 4 j k i 6 DC j 1 k B (6,, 0) m x a) The magnitude of the moment of about the axis DC DC C DC DC? rb / C T 18i 1 j 8k n 18i 1 j 8k 18 C DC 1 i j 1i 4 j 6k kn m i j 1 k
22 z D (0,, ) b) The perpendicular distance between lines B and DC T 1i 4 j 6k T n DC T n DC, cosq n DC i j k (1) cosq, cosq q The parallel component of a force to a line does not generate moment with respect to that line. If is resolved into two components parallel and normal to line DC, then T DC T (0, 5, ) m x sin θ d, y C (4, 6, 0) m B (6,, 0) m d DC T sin θ sin m The magnitude of moment DC is equal to the normal component of perpendicular distance between and line DC. T T to line DC and the
23 14. The arms B and BC of a desk lamp lie in a vertical plane that forms an angle of 0 o with xy plane. To reposition the light, a force of magnitude 8 N is applied as shown. Determine, a) the moment of the force about point, b) the moment of the force about the axis of arm B, c) the angle between the line of action of force and line B, d) the perpendicular distance between the line B and line of action of force. Direction CD is parallel to the z-axis and lies in a parallel plane to the horizontal plane. B 450 mm, BC 5 mm y 45 o 50 o C 45o D 0 o 150 mm x 0 o z
24 x i y j z k a) x y z 8Cos 45Sin Sin N 8Cos 45Cos 0 5. N N 1. 9i j 5. k r r C / C /? 0. 45Sin Sin50Cos 0i 0. 45Cos Cos50 j 0. 45Sin Sin i j 0. 85k rc /. 19i. 16 j. 57k i j 0. 85k 1. 9i j 5. k Sin0k B 450 mm, BC 5 mm
25 b) r r n B B B B B? nb 0. 45Sin45Cos0i 0. 45Cos 45 j 0. 45Sin45Sin0k 0. 75i j k r B 0. 61i j 0. 5k r B B 450 mm, BC 5 mm c) B B n B. 19i. 16 j. 57k 0. 61i j 0. 5k i j 0. 5k 1. 1i 1. 8 j 0. 64k n Cosq 1. 9i j 5. k 0. 61i j 0. 5k Cosq B q Cosq 81 Nm d) If the force is resolved into two components parallel and normal to line B, only normal component generate a moment. The parallel component of a force to a line does not generate moment with respect to that line. d B Sinqd B Sinq Sin m
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