DepartamentodeEngenhariaMecânicaÁreaCientíficadeMecânicadosMeiosSólidos

RMM–2015/16

MecânicaAplicada

Cap.161-Cinéticadomovimentoplano(2)

Problema16.78

O obturador mostrado na figura foi formado removendo-se umquarto de um disco de15 𝑚𝑚de raio e é usado para interromperumfeixedeluzemitidoapartirdeumalenteem𝐶.Sabendoqueoobturador tem massa de 50 𝑔 e gira à taxa constante de24 𝑐𝑖𝑐𝑙𝑜𝑠 𝑝𝑜𝑟 𝑠𝑒𝑔𝑢𝑛𝑑𝑜, determine a intensidade da força exercidapeloobturadorsobreoeixoem𝐴.

Problema16.117

Ahasteuniforme𝐴𝐵𝐷de45 𝑁estápresaàmanivela𝐵𝐶eéajustadacomuma pequena roda que pode rolar sem atrito ao longo de uma fendavertical. Sabendo que no instantemostrado amanivela𝐵𝐶gira comumavelocidade angular de 6 𝑟𝑎𝑑/𝑠 no sentido horário e uma aceleraçãoangularde15 𝑟𝑎𝑑/𝑠!nosentidoanti-horário,determineareaçãoem𝐴.

Problema16.119

A haste uniforme𝐵𝐷de300 𝑚𝑚de comprimento e massade3 𝑘𝑔é ligada comomostra a figura à manivela𝐴𝐵e aocursor 𝐷 , de massa desprezível, que pode deslizarlivrementeaolongodeumahastehorizontal.Sabendoqueamanivela𝐴𝐵gira no sentido anti-horário à taxa constantede300 𝑟𝑝𝑚,determineareaçãoem𝐷quando𝜃 = 0.

Problema16.149

As extremidades da haste uniforme𝐴𝐵 de 10 𝑘𝑔 são presas acursoresdepesodesprezávelquedeslizamsematrito ao longodehastes fixas. Se a haste é libertada a partir do repouso quando𝜃 = 25°,determineimediatamenteapósasualibertação:

(a) aaceleraçãoangulardahaste;(b) areaçãoemA;(c) AreaçãoemB.

1Osproblemasapresentadosreferem-seaolivro“MecânicaVetorialparaEngenheiros–Dinâmica,FerdinandP.Beer,E.RussellJohnstonJr.,WilliamE.Clausen,7ªEdMcGraw-Hill”

1064 Plane Motion of Rigid Bodies:Forces and Accelerations

16.81 A large flywheel is mounted on a horizontal shaft and rotates at a constant rate of 1200 rpm. Experimental data indicate that the total force exerted by the flywheel on the shaft varies from 55 kN upward to 85 kN downward. Determine (a) the mass of the flywheel, (b) the distance from the center of the shaft to the mass center of the flywheel.

16.82 A turbine disk of mass 26 kg rotates at a constant rate of 9600 rpm. Knowing that the mass center of the disk coincides with the center of rotation O, determine the reaction at O immediately after a single blade at A, of mass 45 g, becomes loose and is thrown off.

16.83 The shutter shown was formed by removing one quarter of a disk of 0.75-in. radius and is used to interrupt a beam of light emanating from a lens at C. Knowing that the shutter weighs 0.125 lb and rotates at the constant rate of 24 cycles per second, determine the magnitude of the force exerted by the shutter on the shaft at A.

16.84 and 16.85 A uniform rod of length L and mass m is supported as shown. If the cable attached at end B suddenly breaks, determine (a) the acceleration of end B, (b) the reaction at the pin support.

ABC

L

b = L4

Fig. P16.85

0.6 m

0.3 m

B

A

C

q

Fig. P16.87

B

C

A

rw

Fig. P16.83

D

B

h

C

A

Fig. P16.86

A B

L

Fig. P16.84

AO 300 mm

Fig. P16.82

16.86 A slender uniform cone of mass m can swing freely about the horizontal rod AB. If the cone is released from rest in the position shown, determine (a) the acceleration of the tip D, (b) the reaction at C.

16.87 The object ABC consists of two slender rods welded together at point B. Rod AB has a mass of 1 kg and bar BC has a mass of 2 kg. Knowing the magnitude of the angular velocity of ABC is 10 rad/s when u 5 0, determine the components of the reaction at point C when u 5 0.

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1069Problems 16.120 The 4-lb uniform rod AB is attached to collars of negligible mass which may slide without friction along the fixed rods shown. Rod AB is at rest in the position u 5 25° when a horizontal force P is applied to collar A, causing it to start moving to the left with an acceleration of 12 ft/s2. Determine (a) the force P, (b) the reaction at B.

25 in.

q 70°

A

B

Fig. P16.120 and P16.121

60° q

LA

B

Fig. P16.122

200 mm

200 mm

100 mm

A

B

D

C

Fig. P16.124

16.121 The 4-lb uniform rod AB is attached to collars of negligible mass which may slide without friction along the fixed rods shown. If rod AB is released from rest in the position u 5 25°, determine imme-diately after release (a) the angular acceleration of the rod, (b) the reaction at B.

16.122 The motion of the uniform rod AB of mass 5 kg and length L 5 750 mm is guided by small wheels of negligible mass that roll on the surface shown. If the rod is released from rest when u 5 20°, determine immediately after release (a) the angular acceleration of the rod, (b) the reaction at A.

16.123 End A of the 8-kg uniform rod AB is attached to a collar that can slide without friction on a vertical rod. End B of the rod is attached to a vertical cable BC. If the rod is released from rest in the posi-tion shown, determine immediately after release (a) the angular acceleration of the rod, (b) the reaction at A.

L = 750 mm

30° = qA

B

C

Fig. P16.123

16.124 The 4-kg uniform rod ABD is attached to the crank BC and is fit-ted with a small wheel that can roll without friction along a vertical slot. Knowing that at the instant shown crank BC rotates with an angular velocity of 6 rad/s clockwise and an angular acceleration of 15 rad/s2 counterclockwise, determine the reaction at A.

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1070 Plane Motion of Rigid Bodies:Forces and Accelerations

16.125 The 250-mm uniform rod BD, of mass 5 kg, is connected as shown to disk A and to a collar of negligible mass, which may slide freely along a vertical rod. Knowing that disk A rotates counterclockwise at a constant rate of 500 rpm, determine the reactions at D when u 5 0.

16.126 Solve Prob. 16.125 when u 5 90°.

16.127 The 15-in. uniform rod BD weighs 8 lb and is connected as shown to crank AB and to a collar D of negligible weight, which can slide freely along a horizontal rod. Knowing that crank AB rotates coun-terclockwise at the constant rate of 300 rpm, determine the reac-tion at D when u 5 0.

16.128 Solve Prob. 16.127 when u 5 90°.

16.129 The 3-kg uniform rod AB is connected to crank BD and to a collar of negligible weight, which can slide freely along rod EF. Knowing that in the position shown crank BD rotates with an angular veloc-ity of 15 rad/s and an angular acceleration of 60 rad/s2, both clock-wise, determine the reaction at A.

50 mm

150 mm

A

B

D

q

Fig. P16.125

D

A

B

q

3 in.9 in.

Fig. P16.127

30°

80 mm

500 mm

B

D

AE

F

Fig. P16.129

16.130 In Prob. 16.129, determine the reaction at A, knowing that in the position shown crank BD rotates with an angular velocity of 15 rad/s clockwise and an angular acceleration of 60 rad/s2 counterclockwise.

16.131 A driver starts his car with the door on the passenger’s side wide open (u 5 0). The 80-lb door has a centroidal radius of gyration k 5 12.5 in., and its mass center is located at a distance r 5 22 in. from its vertical axis of rotation. Knowing that the driver maintains a constant acceleration of 6 ft/s2, determine the angular velocity of the door as it slams shut (u 5 90°).

16.132 For the car of Prob. 16.131, determine the smallest constant accel-eration that the driver can maintain if the door is to close and latch, knowing that as the door hits the frame its angular velocity must be at least 2 rad/s for the latching mechanism to operate.

16.133 Two 8-lb uniform bars are connected to form the linkage shown. Neglecting the effect of friction, determine the reaction at D immediately after the linkage is released from rest in the position shown.

A

Bq

a

w

Fig. P16.131

15 in. 15 in.

30 in.

AC

B

D

Fig. P16.133

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1068 Plane Motion of Rigid Bodies:Forces and Accelerations

16.113 A small clamp of mass mB is attached at B to a hoop of mass mh. The system is released from rest when u 5 90° and rolls without sliding. Knowing that mh 5 3mB, determine (a) the angular accel-eration of the hoop, (b) the horizontal and vertical components of the acceleration of B.

16.114 A small clamp of mass mB is attached at B to a hoop of mass mh. Knowing that the system is released from rest and rolls without sliding, derive an expression for the angular acceleration of the hoop in terms of mB, mh, r, and u.

16.115 The center of gravity G of a 1.5-kg unbalanced tracking wheel is located at a distance r 5 18 mm from its geometric center B. The radius of the wheel is R 5 60 mm and its centroidal radius of gyration is 44 mm. At the instant shown the center B of the wheel has a velocity of 0.35 m/s and an acceleration of 1.2 m/s2, both directed to the left. Knowing that the wheel rolls without sliding and neglecting the mass of the driving yoke AB, determine the horizontal force P applied to the yoke.

16.116 A 2-kg bar is attached to a 5-kg uniform cylinder by a square pin, P, as shown. Knowing that r 5 0.4 m, h 5 0.2 m, u 5 20°, L 5 0.5 m and v 5 2 rad/s at the instant shown, determine the reac-tions at P at this instant assuming that the cylinder rolls without sliding down the incline.

16.117 The ends of the 10-kg uniform rod AB are attached to collars of negligible mass that slide without friction along fixed rods. If the rod is released from rest when u 5 25°, determine immediately after release (a) the angular acceleration of the rod, (b) the reaction at A, (b) the reaction at B.

B

A

r

q

Fig. P16.113 and P16.114

P

A

B G

r = 18 mm

R = 60 mm

Fig. P16.115

w

L

hr

P

q

Fig. P16.116

A

B

q

l = 1.2 m

Fig. P16.117 and P16.118

30 in.

30°A

B

Fig. P16.119

16.118 The ends of the 10-kg uniform rod AB are attached to collars of negligible mass that slide without friction along fixed rods. A verti-cal force P is applied to collar B when u 5 25°, causing the collar to start from rest with an upward acceleration of 12 m/s2. Deter-mine (a) the force P, (b) the reaction at A.

16.119 The motion of the 8-lb uniform rod AB is guided by small wheels of negligible weight that roll along without friction in the slots shown. If the rod is released from rest in the position shown, deter-mine immediately after release (a) the angular acceleration of the rod, (b) the reaction at B.

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60 𝑚𝑚

180 𝑚𝑚