95sin15 1. mechanic pulls on the 1-mm combination wrench with the 140 N force shown. Determine the moment of this force about the bolt center. //y = 140 N y = 140cos5 N 15 o 5 o + o 15 o 95cos15 //x x = 140sin5 N 0.095cos15140sin 50.095sin15 140 cos 5 y x o 1. 098 N m (counterclockwise - ccw)
. Calculate the moment o of the 50 N force about the base point of the robot.
0.5-0.4sin0+0.sin40 400 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 400.5-0.4sin 0 0.sin 40 50cos 40 o 189. 55 N m (counterclockwise - ccw)
. 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 (70+150+70)=90 mm (5+70+70+5) =190 mm + o 70 150 7010sin 05 70 70 5 10cos0 y 90 x 190 o 41500 N mm 41. 5 N m (clockwise - cw)
Determine the value of a which would maximize the moment about. max =? o a = 10 N (70+150+70) =90 mm a (5+70+70+5) =190 mm 10 190 90 4160.85 N mm 41. 6 or max, must be perpendicular to. 190 a arctan 90 N m o. o d da o cosa 0.9 sin a0.19 0 - sin a 0.9 cosa0.19 tan a a. 0.19 0.9 o
4. The small crane is mounted along the side of a pickup bed and facilitates the handling of heavy loads. When the boom elevation angle is q=40 o, the force in the hydraulic cylinder BC is 4.5 kn, and this force applied at point C is in the direction from B to C (the cylinder is in compression). Determine the moment of this 4.5 kn force about the boom pivot point.
5. 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.
6. ssume that the hydraulic cylinder B exerts a force of constant magnitude.5 kn as the bin is elevated. Determine the moment of about the point for the range 0 q 90 o. t what angle q is this moment a maximum and what is the maximum moment? B. 4 m 0.8 m 0.8 m
7. 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.
orce in vector form xy 80cos0 69. 8 N x xy sin 40 69.8sin 40 44. 5 N y xy cos 40 69.8cos 40 5. 07 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
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 5.9 1.09 11.8 18. 16 18.16 d 80 d = 0. 7 m N m
8. The pipe assembly is secured on the wall by the two brackets. Determine, a) the moment of force about point, b) the moment of force about line, c) the minimum distance from point B to the line.
9. 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 45i 170.1 j - 600k 500 754.69 B 75, 19. 9, 600 Position vector from point to point C (It may be written the position vector from point to point B) oment of force spring about point 0.5i 0. j 81.57i 11.7 j - 97.5k spring 81.57i 11.7 j - 97.5k rc / 0.5i r C / spring 0. j -119.5i 19.5 j - 45.0k oment about the shaft axis n k -45. 0 N m
10. 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. z z 0.5sin0, 0.5 + 0.5cos0, 0 B 0, 1cos0, 1sin0 0. 5, 0. 9, 0 B(0, 0. 866, 0. 5) B 0 o 0.5 m 0 o y 450 0-0.5i 0.866-0.9 j 0.5-0 0.5 0.067 0.5 x k -00.89i - 5.84 j 401.79k
-00.89i - 5.84 j 401.79k z Position vector from point to point B (It may be written the position vector from point to point ) r B / 0.866 j 0.5k rb / 0.866 j 0.5k - 00.89i - 5.84 j 401.79k 74.86i -100.45 j 179.97k 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, = = 74.86 + 100.45 + 179.97 = 47.84 N. m d = = 0.951 m
11. force of magnitude 70 N is acting at the end D of the pipeline in the direction indicated. a) Determine the moment of force about point,. b) Determine the moment of force about line B, B. c) Determine the minimum distance from point to the line of action of force.
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 f C 00 mm z 150 mm q x
q=70, y =-0 N m and z =-7.5 N m x =? B, C 00 mm f y P z 70 o, P -Psin fj P cosfk y B z r 50i 00sin 70 j 00cos70k r 50i 187.94 j 68.4k o r P i j k 50 187.94 68.4 - Psin fj P cosfk -50Psin fk - 50P cosfj 187.94P cosfi 68.4Psin fi r C / o o q C f P 00 mm x
q=70, y =-0 N m and z =-7.5 N m x =? o -50Psin fk - 50P cosfj 187.94P cosfi 68.4Psin fi y z -50P cosf -010 N mm 1-50Psin f -7.510 N mm 1-50Psin f - 50P cosf - 7.510-010 tan f 1.875 f 61.9 P 170 N x N mm 5. N m 187.94P cosf 68.4Psin f 594 94
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
z D (0,, ) (0, 5, ) m y C (4, 6, 0) m T T n 6i - j - k TnT 14 7 1i - 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 1 8-9. 10. 67 8-1 kn m i j - 1 k
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 1-4 - 6-14(1) cosq, cosq 0.5 4 q 58.67 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 10.67 14sin 58.67 0.89 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
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
x i y j z k a) x y z -8Cos 45Sin0-1. 9-8Sin45-5. 66 N 8Cos 45Cos 0 5. N N -1. 9i - 5. 66 j 5. k r r C / C /? 0. 45Sin45 0. 5Sin50Cos 0i 0. 45Cos 45-0. 5Cos50 j 0. 45Sin45 0. 5Sin50 0. 491i 0. 11 j 0. 85k rc /. 19i -. 16 j -. 57k 0. 491i 0. 11 j 0. 85k -1. 9i - 5. 66 j 5. k Sin0k B 450 mm, BC 5 mm
b) r r n B B B B B? nb 0. 45Sin45Cos0i 0. 45Cos 45 j 0. 45Sin45Sin0k 0. 75i 0. 18 j 0. 159k r B 0. 61i 0. 71 j 0. 5k r B B 450 mm, BC 5 mm c) B B n B. 19i -. 16 j -. 57k 0. 61i 0. 71 j 0. 5k -1. 1.81 0. 61i 0. 71 j 0. 5k -1. 1i -1. 8 j - 0. 64k - n Cosq -1. 9i - 5. 66 j 5. k 0. 61i 0. 71 j 0. 5k 8 1 -. 8Cosq B q 114. 6 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 1. 81 8Sin114. 6 0. 49 m