PROBLEMS ON RESULTANTS

Transcription

1 PRBLES N RESULTNTS

2 PRBLES 1) The tie-rod B eerts the 50 N force on the steering nucle as shown. Replace this force b an equivalent force couple sstem at. (/73)

3 PRBLES Replace b an equivalent force couple sstem at. 50cos10 50 N + 50cos10(0.35) 50sin10(0.05) 60 N m ( cw) 50cos10i 50sin i N 50sin10 50sin10 50 mm 50cos10

4 PRBLES ) Where does the resultant of the two forces act? (/83)

5 PRBLES Where does the resultant act? 1 660(0.3) 198 Nm 0 N 660 N 0 N 0( ) 198 Nm m 0 Resultant (0 N) acts = 10.7 m left of point 1

6 PRBLES 3) utilit pole of mass m is being slowl erected b the winch and cable arrangement shown. When q=60, the cable tension is 35 percent of the weight of the pole. Determine the force couple sstem at, which is equivalent to the tension force applied to the top of the pole. Neglect the diameter of the hoisting drum compared with l.

7 PRBLES for q=60 cable tension is 35 % of the weight of the pole. Determine the force couple sstem at, which is equivalent to the tension force applied to the top of the pole. T T + T 0.35mg T 0.35mg 1.5l 0.34mg 1.544l 0.366l 0.083mg 1.544l T (0.866l) T (0.5l) 0.34mg(0.866l) 0.083mg(0.5l) 0.54mgl ( ccw) l0.5l l T T 0. 35mg l0.5l 1. 5l mg T 0.866l q=60 0.5l

8 PRBLES 380 mm 150 mm 800 N 160 mm 800 N 30 mm B 4) The forces acting on the belts on a pulle sstem are equal with a magnitude of 800 N. The pulle is secured to the steel column b means of two bolts at and B. Replace the two forces with a force-couple sstem, in which the equivalent force will be at the midpoint of the bolts. Then, determine the force each bolt will sustain b distributing this force and couple to forces acting at points and B.

9 PRBLES Replace with a force-couple sstem, in which the equivalent force will be at the midpoint of the bolts. Determine the force each bolt will sustain b distributing this force and couple to forces acting at points and B. 380 mm 150 mm 800 N 160 mm 800 N 30 mm B

10 PRBLES 5) Under nonuniform and slipper road conditions, the four forces shown are eerted on the four drive wheels of the all-wheel-drive vehicle. Determine the resultant of this sstem and the - and - intercepts of its line of action. Note that the front and rear tracs are equal (i. e., ). (/97) B D

11 PRBLES Determine the resultant of the sstem and the - and -intercepts of its line of action. B D

12 PRBLES 6) The pedal-chain wheel unit of a biccle is shown in the figure. The left foot of the rider eerts the 160 N force, while the use of toe-clips allows the right foot to eert the nearl upward 80 N force. Determine the equivalent force couple sstem at point. lso, determine the equation of the line of action of the sstem resultant treated as a single force R. Treat the problem as two dimensional. (/100)

13 PRBLES Determine the equivalent force couple sstem at point and the equation of the line of action of the sstem resultant treated as a single force R.

14 PRBLES 7) Determine the force-couple sstem at which is equivalent to the two forces applied to the shaft B. Is R perpendicular to? (/157)

15 PRBLES Determine the force-couple sstem at which is equivalent to the two forces applied to the shaft B. Is R perpendicular to? R(600sin cos30 ) ( 800sin cos45 ) R ( N) r1 1 r 0.08i i ( N m) if R, then R 0 R the are not perpendicular toeach other

16 PRBLES 8) Represent the resultant of the force sstem acting on the pipe assembl b a single force at and a couple.

17 Represent the resultant of the force sstem acting on the pipe assembl b a single force at and a couple. PRBLES ) ( N i R ) ( m N i i r r 1 = m N d (0.5)? 50 1

18 PRBLES 9) The tension in cable B is 450 N and the tension in cable D is 70 N. Suppose that ou want to replace these two cables b a single cable E so that the force eerted on the wall at E is equivalent to the two forces eerted b cables B and D on the walls at and. What is the tension in cable E and what are the coordinates of points E and? 1.,1.8,0 m

19 PRBLES T B = 450 N, T D = 70 N, replace two cables b a single cable E so that the force eerted on the wall at E is equivalent to the two forces eerted b cables B and D on the walls at and. What is the tension in cable E and what are the T T B D or cables B and D coordinates of points E and? 0.9i ( ).1 i N 0.9i i ( N) i r / TB 1.i i r / TD i ( Nm) T B 1.,1.8,0 m T D

20 PRBLES T B = 450 N, T D = 70 N, replace two cables b a single cable E so that the force eerted on the wall at E is equivalent to the two forces eerted b cables B and D on the walls at and. What is the tension in cable E and what are the or cable E coordinates of points E and? TB TD TE i ( N) TE 70 i re / TE E E E E i i i E 54.58, E , E.7 m E (0,.7, 0.83) m r / TE i i i i , (1.35, 0,1.7) m, E E 0.83 m 1.7 m 1.35 m E N E T B T E 0, E,,0, 1.,1.8,0 m T D E m m

21 PRBLES 10) The weight of the robot arm B is 00 N and its direction * Line N lies in a plane parallel to the horiontal plane * Line D lies in the plane =7 N. m cosines are cos q =0.6, cos q (q <90 ) and cos q =0. or arm B the weight is 160 N with cos q =7/9, cos q =4/9 and cos q =-4/9. The mass 540 mm // =50 N N centers of both arms are at their midpoints. force of magnitude =50 N and a couple of magnitude B 160 N 53 o 37 o =7 Nm along the ais B are applied to the end of arm B. Replace the three forces and one 500 mm // 00 N // couple acting on the robot assembl with an equivalent force-couple at point. D 37 o

22 PRBLES W B = 00 N, cos q =0.6, cos q (q <90 ) and cos q =0 dır. W B = 160 N, cos q =7/9, cos q =4/9 and cos q =-4/9. =50 N and =7 Nm act to the end of arm B. Replace the three forces and one couple acting on the robot assembl with an equivalent =7 N. m force-couple at point. 540 mm // =50 N N B 160 N 53 o 37 o 500 mm 00 N // // * Line N lies in a plane parallel to the horiontal plane * Line D lies in the plane D 37 o

23 PRBLES 11) student using a pencil opener applies on the machine the two forces and the couple shown in the figure. If it is nown that the force and couple components of the equivalent force-couple sstem at are R17i R 5 ( N) and i 1.5 ( Nm) R respectivel, determine the vector epressions of the forces applied to points B and and also values of R and. Bi B.75 N. m 100 mm i 60 mm 50 mm

24 determine the vector epressions of the forces applied to points B and and also values of R and. PRBLES ) ( 5 17 N R i R ) ( 1.5 m N i R 100 mm 50 mm 60 mm B.75 N. m i i B N R B B i B R i Bi B i B R 5, 5 17, ,, i i i r couple B R 0.1 ) 0.05 ( ) 5 ( ) 0.05 (0.1 / m B m,0,0.11) ( (0.1, 0, 0.05) (0,0,0)

25 PRBLES B rb / B( i 0.11 ) Bi 0.11B couple.75i R B i 1.5 ( ) i (0.11B ) , 15 N, R 15 N N B10.83 N 6.17i 15 5 B 10.83i ( N) determine the vector epressions of the forces applied to points B and and also values of R and. Nm B ( N) Bi B.75 N. m 100 mm i 60 mm couple 50 mm

26 PRBLES 1) The force-couple stem acting at is equivalent to the wrench acting at. If R600i ( N) and 100 ( N ), determine. R // m R R// R m 3 m

27 PRBLES The force-couple stem acting at is equivalent to the wrench acting at. If R 600i ( N) and R // 100 ( N m) determine. R R// R m 3 m

28 PRBLES 13) portion of the flue for a furnace is attached to the ceiling at. While supporting the free end of the flue at, a worer applies the forces indicated at E and and the couple (applied to portion B) to align end E with the furnace. Knowing that the 95 N force at lies in a plane parallel to the plane, determine (a) the angle a the force at should form with the horiontal if duct B is not to tend to rotate about the vertical ais, (b) the equivalent force-couple sstem at of the given sstem, (c) further reduce the sstem to a wrench and determine the coordinates of the point the line of action of the wrench passes in the plane. Line EG lies in the plane and forms a 45 angle with the // ais. The line of action of the 75 N force forms an angle of 53 with line EG.

29 PRBLES Determine (a) the angle a the force at should form with the horiontal if duct B is not to tend to rotate about the vertical ais, (b) the equivalent force-couple sstem at of the given sstem, (c) further reduce the sstem to a wrench and determine the coordinates of the point the line of action of the wrench passes in the plane. 95 N force at lies in a plane parallel to the plane, line EG lies in the plane and forms a 45 angle with the // ais. The line of action of the 75 N force forms an angle of 53 with line EG.

30 Z 1 = 30 N = 75 N 3 = 40 N 1 = 60 Nm = 100 Nm (in plane) q 3 = 80 Nm (in plane BD) q < 90 o 45 X 6 m 37 3 G 53 E 30 3 Y (0, 0, 0) m (1, 0, 0) m B (in plane) (1, 8, 0) m E (6, 10, -3) m G (10, 4, 4) m B 4 m D 14) Replace the sstem comprising two forces, two couples and a positive wrench with an equivalent force-couple acting at point. Then, reduce the sstem further into a wrench and determine the coordinates of point P, of which the line of action of the wrench cuts through the plane.

31 i i R R n i R i 40cos30 40cos60sin 53 40cos60cos53i i ) (0 0) (8 i i cos60 cos60 30 cos45i 60 1 cos 60 cos 45 cos R 3 1 o q q orce:

32 i 3 64i 100i i i i i i i 4 8 6i BD B 100i i cos60 cos60 60 cos45i i i i i i 8 1i i i r r r r o oment:

33 Equivalent force-couple sstem at point R1.95i i Reduction to a wrench in plane // // nr n i i i i // R Positive wrench R1.95i i // Positive wrench // i Nm R1.95i

34 The coordinates of point P, of which the line of action of the wrench cuts through the plane: o // i i i r R i i i m m i i R1.95i r // P(0;391.7;474.66) Positive wrench i