PROBLEMS on FORCE SYSTEMS

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Easter Waters
6 years ago
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1 on FORCE SYSTEMS

2 1. The guy cables AB and AC are attached to the top of the transmission tower. The tension in cable AB is 8 kn. Determine the required tension T in cable AC such that the net effect of the two cable tensions is a downward force at point A. Determine the magnitude R of this downward force. (2/13)

3 A T AB =8 kn, T AC =? Net effect of two cable tensions is a downward force at point A. R =? R y R T AC x T AB T AC A (0,0) B( 40, 50) m C(50, 30) m rb / A 40i 50 j TAB TABnAB 8 8 r 2 2 B/ A T 5i 6.25 j kn AB T AC T AC n AC T AC r r C C T AB i j / A TAC, TAC TAC0.857i j 2 2 / A

4 A T AB =8 kn, T AC =? Net effect of two cable tensions is a downward force at point A. R =? R R T AC T AB T AC T AB TAB 5i 6.25 j T AC TAC 0.857i j R TAB TAC Rj Rj 5i 6.25 j T i j AC i TAC 0, TAC 5.83 kn j T R, R9.25 kn AC

2. In the design of the robot to insert the small cylindrical part into a close-fitting circular hole, the robot arm must exert a 90 N force P on the part parallel to the axis of the hole as

5 2. In the design of the robot to insert the small cylindrical part into a close-fitting circular hole, the robot arm must exert a 90 N force P on the part parallel to the axis of the hole as shown. Determine the components of the force which the part exerts on the robot along axes (a) parallel and perpendicular to the arm AB, and (b) parallel and perpendicular to the arm BC. (2/28)

6 Determine the components of P along axes (a) parallel and perpendicular to the arm AB, and (b) parallel and perpendicular to the arm BC.

3. The unstretched length of the spring is r. When pin P is in an arbitrary position q, determine the x- and y- components of the force which the spring exerts on the pin.

7 3. The unstretched length of the spring is r. When pin P is in an arbitrary position q, determine the x- and y- components of the force which the spring exerts on the pin. F spring =kd Evaluate your answer for r = 400 mm, k = 1.4 kn/m and q = 40. Also when pin P is in the position q = 20, determine the n- and t-components of the force which the spring of modulus k = 1.4 kn/m exerts on the pin. Take r = 400 mm. (2/29)

8 2r O A q F spring r F F spring x spring y P F F l 0 =r. For q, determine x- and y-components of the force spring exerts on the pin. Find force for r = 400 mm, k = 1.4 kn/m and q = 40. For q = 20, determine the n- and t- components of the F. spring spring Sine theorem 2r AP sin sin q sin 2rsin q AP cos sin F spring F springx F springy sin 1 2rsin q AP 1 sin sin 90q 1 q 2rsin q 1 90 sin q 90sin 2rsin q AP AP

9 F F spring spring x y F F spring spring Cosine theorem 2 cosq 90sin sin q 90sin l 0 =r. For q, determine x- and y-components of the force spring exerts on the pin. Find force for r = 400 mm, k = 1.4 kn/m and q = 40. For q = 20, determine the n- and t- components of the F rsin q AP 2rsin q AP AP r (2r) 2( r)(2r)cosq 5r 4r cosq APr 54cosq For the givenvalues AP0.4 54cos m 1 2(0.4)sin sin Fspring kd k( l l0) 1400( ) 219 N Fspring 219cos N x F 219sin N spring y F spring 2r F springx 2r q O A F springy F spring r P

10 4. The circular cam has an offset e = 50 mm and a radius r = 100 mm. For the position where q = 30, the smooth undersurface of the plunger exerts a downward force of 1600 N on the cam normal to the contacting surfaces. In designing the cam bearing it is necessary to calculate the rectangular component F' of this force along the line joining the contact point and the center of the shaft which turns the cam. Find F'.

11 e = 50 mm, r = 100 mm. For q = 30, smooth plunger exerts a downward force of 1600 N on the cam normal to the contacting surfaces. Calculate the rectangular component F' of this force along the line joining the contact point and the center of the shaft which turns the cam.

Express T as a vector in terms of its unit vectors i, j and k.

12 5. The rigid pole and cross arm assembly is supported by the three cables shown. A turnbuckle at D is tightened until it produces a tension T in CD of 1.2 kn. Express T as a vector in terms of its unit vectors i, j and k. Determine the direction angles q x, q y and q z which T makes with the positive x-, y-, and z-axes. Does it make any difference in the result which coordinate system is used? (2/107)

13 T Tn C( 1.5, 0, 4.5) n n CD CD CD r r D/ C D/ C 0.267i j 0.802k T i j 0.802k m T 0.321i j 0.962k T T =1.2 kn. =? Determine the direction angles q x, q y and q z which T makes with the positive x-, y-, and z-axes. Does it make any difference in the result which coordinate system is used? D(0, 3, 0) 1.5i 3 j 4.5k m kn i k r D / C n CD j

14 T T T x x i T T cosq y T T z cosq z T j T T cosq y y x z It does not matter which coordinate system is used. x-y-z or x'-y'-z' systems can be used. Both systems have the same unit vectors. T T =1.2 kn. =? Determine the direction angles q x, q y and q z which T makes with the positive x-, y-, and z-axes. Does it make any difference in the result which coordinate system is used? k T cosq xi cosq y j cosq zk,,, n Tx cosq x T q x y q z CD q i j 0.802k qx q y q z

15 6. Three forces are acting on the eye bolt. If the resultant force shown, determine the magnitude and direction angles of F 3. F R has a magnitude and direction as

16 Given F R determine the magnitude and direction angles of F 3.

17 z A 7. At a certain instant, the locations 5 km of a plane at A and a train at B are monitored by a radar O antenna at O. Determine the distance d between A and B for this instant. x 25 2 km 40 B y

18 A( 5cos 60 cos35, 5cos 60sin 35,5sin 60) A( 2.05, 1.43, 4.33) km B (2cos 25sin 40, 2cos 25cos40, 2sin 25) B (1.17,1.39, 0.85) km r r A/ B A/ B d i j 4.33( 0.85) 3.22i 2.82 j 5.18k r A/ B Determine the distance d between A and B 6.72 km O k z A 5 km x km B r A / B y

19 8. Two cables exert forces on the pipe. Determine the magnitude of the projected component of along the line of action of F F 1. Also determine the angle q between the two cables. 2 q

20 Determine the magnitude of the projected component of F 1 along the line of action of F 2 and the angle q between the two cables. q

21 9. The access door is held in the 30 open position by the chain AB. If the tension in the chain is 100 N, determine the projection of the tension force onto the diagonal axis CD of the door. (2/116)

A(1.2, 0.9 cos30, 0.9sin 30) A(1.2, 0.78, 0.45) m B (0, 0,0.9) m TAB TABnAB 100nAB 1.2i 0.78 j 0.45k nab 0.8i 0.52 j 0.3k 1.50 TAB 80i 52 j 30k N rd / C 1.2i 0.78 j 0.45k ndc rd C 1.50 x / ndc 0.8i 0.52 j 0.3k TCD TABnDC TCD ( 80)( 0.

22 A(1.2, 0.9 cos30, 0.9sin 30) A(1.2, 0.78, 0.45) m B (0, 0,0.9) m TAB TABnAB 100nAB 1.2i 0.78 j 0.45k nab 0.8i 0.52 j 0.3k 1.50 TAB 80i 52 j 30k N rd / C 1.2i 0.78 j 0.45k ndc rd C 1.50 x / ndc 0.8i 0.52 j 0.3k TCD TABnDC TCD ( 80)( 0.8) ( 52)(0.52) (30)(0.3) 46 N T T n i j k CD CD DC T 36.8i j 13.8k N CD T AB =100 N, determine the projection of T AB onto the diagonal axis CD of the door 80i 52 j 30k 0.8i 0.52 j 0.3k T A / B z r D / C y

23 10. An overhead crane is used to reposition the boxcar within a railroad car-repair shop. If the boxcar begins to move along the rails when the x-component of the cable tension reaches 3 kn, calculate the necessary tension T in the cable. Determine the angle q xy between the cable and the vertical x-y plane. (2/115)

24 boxcar begins to move when the x-component of the cable tension reaches 3 kn, calculate tension T in the cable. Determine the angle q xy between the cable and the vertical x-y plane.

25 11. The spring of constant k = 2.6 kn/m is attached to the disk at point A and to the end fitting at point B as shown. The spring is unstretched when q A and q B are both zero. If the disk is rotated 15 clockwise and the end fitting is rotated 30 counterclockwise, determine a vector expression for the force which the spring exerts at point A.

26 k = 2.6 kn/m, spring is unstretched when q A and q B are both zero. Determine a vector expression for the force the spring exerts at point A.

Problems (Force Systems)

Problems (Force Systems) 1. Problems (orce Sstems) Problems (orce Sstems). Determine the - components of the tension T which is applied to point A of the bar OA. Neglect the effects of the small pulle at B. Assume that r and are