17-119. The solid ball of radius r and mass m rolls without slipping down the 60° trough. Determine its angular acceleration. 30° 30 45°
Q: 17-63. The 10-lb bar is pinned at its center O and connected to a torsional spring. The spring has a…
A: Write the expression of the moment of inertia of the rod. Take moment about point O.
Q: 18-7. The double pulley consists of two parts that are attached to one another. It has a weight of…
A: Given Mass, mA = 30 lb mB = 20 lb Radius of gyration, k…
Q: The pendulum consists of a 10 kg uniform disk and a 3 kg uniform slender rod. If it is released from…
A: It is required to determine the moment of inertia.
Q: *18-4. A force of P = 60N is applied to the cable, which causes the 200-kg reel to turn since it is…
A: Given data: *The force applied to the cable is P=60 N. *The mass of the reel is m=200 kg. *The…
Q: *18-52. The two 12-kg slender rods are pin connected and released from rest at the position 6 = 60°.…
A: Write the given data: Understand the following diagram for the initial and final position of the…
Q: 18-5. A force of P = 20 N is applied to the cable, which causes the 175-kg reel to turn since it is…
A: The data given is, Force applied on cable, P = 20 kN Mass of the reel, MG = 175 kg The radius of…
Q: *18-60. The pendulum consists of a 6-kg slender rod fixed to a 15-kg disk. If the spring has an…
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Q: 19-50. The 20-kg disk strikes the step without rebounding. Determine the largest angular velocity w,…
A: Given data as per question Mass of disk = 20 kg Radius of the roller = 20 mm
Q: This is a dynamics question. Hint: When the man has his arms out, the distance from the CG of his…
A: Write the expression of mass moment of inertia of the system when the arms are in the fully extended…
Q: 18-46. The 12-kg slender rod is attached to a spring, which has an unstretched length of 2 m. If the…
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Q: 17-71. The reel of cable has a mass of 400 kg and a radius of gyration of kA = 0.75 m. Determine its…
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Q: 17-103. The 15-1lb circular plate is suspended from a pin at A. If the pin is connected to a track…
A: The radius of circular plate, r is 5 ft/s2. The weight of circular plate, W is 15 lb.
Q: *17-112. The circular concrete culvert rolls with an angular velocity of w = 0.5 rad/s when the man…
A: Write the expression of the mass moment of inertia of the system about its mass center. Write the…
Q: *17-64. A cord is wrapped around the outer surface of the 8-kg disk. If a force of F = (46) N, where…
A: Given: The mass of the disk is m=8 kg. The radius of the disk is r=300 mm. The force applied on the…
Q: 18-42. The spool has a mass of 20 kg and a radius of gyration of ko = 160 mm. If the 15-kg block A…
A: Given Data: The mass of spool is m = 20 kg. Radius of gyration of spool is kO = 160 mm. Mass of…
Q: 21-54. The 10-kg disk turns around the shaft AB, while the shaft rotates about BC at a constant rate…
A: Given: The mass of the disk, m = 10 kg The speed of shaft BC about x-axis, ωx = 5 rad/s The length…
Q: R19-3. The tire has a mass of 9 kg and a radius of gyration ko = 225 mm. If it is released from rest…
A: Given data: Mass of tire = 9 kg Radius of gyration, ko = 225 mm Time, t= 3s Draw the free body…
Q: 18-17. The center O of the thin ring of mass m is given an angular velocity of wo. If the ring rolls…
A: Given data as per the question Angular velocity of the ring =w0
Q: 16-89. Show that if the rim of the wheel and its hub maintain contact with the three tracks as the…
A: Step-1 Given:…
Q: 21-49. The rod assembly is supported by a ball-and-socket joint at C and a journal bearing at D,…
A: Given data: Angular velocity, ωz = 8 rad/s2 Mass of the rod per unit length = 0.75 kg/m Drawing the…
Q: 18-61. The 500-g rod AB rests along the smooth inner surface of a hemispherical bowl. If the rod is…
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Q: *18-68. The system consists of a 30-kg disk A, 12-kg slender rod BA, and a 5-kg smooth collar A. If…
A: Given data Mass of the disc M = 30kg Mass of the slender rod m = 12kg Mass of the collar mc = 5kg…
Q: This is a Dynamics question. Answers: aG = 11.2 ft/s2, alpha = 7.45 rad/s2
A: Given data as per question Force = 30 lb Roller weight =50 lb Considering free body diagram
Q: 18–30. Motor M exerts a constant force of P = 750 N on %3D the rope. If the 100-kg post is at rest…
A: Given Data The constant force is: P=750 N The length of the post is: 3 m The height of the table is:…
Q: This is a Dynamics question. Answers: alpha = 14.7 rad/s2 Ax = 88.3 N…
A: Given data as per question Weight of plate = 24 kg Dimensions of the plate = 0.5 × 0.5 m
Q: 18-49. The assembly consists of two 10-kg bars which are pin connected. If the bars are released…
A: Given: mass of the rod -10kg mass of the disk = 5kg disk rolls without slipping to find the…
Q: This is a Dynamics question. Answers: w = 65.6 rad/s, alpha = 205.3 rad/s2
A: Calculate the angle turned when the disk turned 5 revolutions,
Q: 17-93. The slender 12-kg bar has a clockwise angular velocity of w = 2 rad/s when it is in the…
A: (a) Drawing the FBD of the system, Consider the position vector of point A, G with respect to point…
Q: 19-1. The rigid body (slab) has a mass m and rotates with an angular velocity o about an axis…
A: Write the expression for the angular momentum about point O.
Q: This is a Dynamics question. Answers: ax = 21.47 ft/s2, ay = 26.45 ft/s2,…
A: Given data as per question Mass of the beam = 150 lb considering free body diagram
Q: R19-5. The spool has a weight of 30 lb and a radius of gyration ko = 0.65 ft. If a force of 40 lb is…
A: Write the expression of the spool about the origin. Write the expression of the velocity at point…
Q: 17-71. The reel of cable has a mass of 400 kg and a radius of gyration of ka = 0.75 m. Determine its…
A: The mass moment of inertia of the reel about A is given by the equation:
Q: *17-60. The bent rod has a mass of 2 kg/m. If it is released from rest in the position shown,…
A: Due the symmetry the y coordinate of the centroid of the given frame will lie at the center. Write…
Q: 19-35 The 10 kg bullet having of 800 m/s is fired into the edge of the 5 kg disk as shown.…
A: Given: the mass of the bullet, m= 10 g = 0.001 kg The mass of the disk is, M = 5 kg The speed of the…
Q: Specifically a dynamics problem. Question in pic below. Answer: omega = 3.75 rad/s
A: When theta is equal to 30º then the spring is in a stretched condition. At this stage, the spring…
Q: *18-16. A motor supplies a constant torque M = 6 kN •m to the winding drum that operates the…
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Q: 21-25. The large gear has a mass of 5 kg and a radius of gyration of k, = 75 mm. Gears B and C each…
A: Given: The mass of gear A is m=5 kg. The radius of gyration for gear A is kz=75 mm=0.075 m. The…
Q: 200 mm
A: Draw a diagram for the problem. Write the formula for mass moment of inertia of the spool.…
Q: 18-39. The spool has a mass of 50 kg and a radius of gyration of ko = 0.280 m. If the 20-kg block A…
A:
Q: *17-116. The disk of mass m and radius r rolls without slipping on the circular path. Determine the…
A:
Q: 18-17. The center O of the thin ring of mass m is given an angular velocity of wn. If the ring rolls…
A: Given: The mass of the thin ring is m. The angular velocity of the ring is ω0. The distance…
Q: 18-30. Motor M exerts a constant force of P = 750 N on the rope. If the 100-kg post is at rest when…
A: To find out the ACf and ACi ACf=42+32-2(4)(3)cos60°2=2.05mACi=32+42=5m
Q: 19-23. The hoop (thin ring) has a mass of 5 kg and is released down the inclined plane such that it…
A: Apply conservation of momentum in the y-direction mvy1+∑.∫Fydt=mvy20+Nh(1)-5(9.81)tcos30°=0Nh=42.479…
Q: 19-21. The spool has a weight of 30 lb and a radius of gyration ko = 0.45 ft. A cord is wrapped…
A: mass of spool (m)=13.6078 kg ;weight of spool (W)=133.447 N ;load or force( P)=5 lb= 22.241 N…
Q: Specifically a dynamics problem. Question in pic below. Answer: omega = 6.11 rad/s
A: Write the expression of mass moment of inertia of the rod. Write the expression of the kinetic…
Q: *19-8. The assembly weighs 10 lb and has a radius of gyration kg = 0.6 ft about its center of mass…
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Q: *18-28. The 10-kg rod AB is pin connected at A and subjected to a couple moment of M = 15 N · m. If…
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Q: 17-71. The reel of cable has a mass of 400 kg and a radius of gyration of ka = 0.75 m. Determine its…
A: Draw the free body diagram of the reel.
Q: This is a dynamics question. Answer: w = 0.0906 rad/s
A: Calculating the initial moment of inertia of the system,
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- The 21-kg wheel has a radius of gyration about its center O of ko =260 mm, and radius r = 0.5 m. When the wheel is subjected to the constant force F = 247 N, applied to the wheel's center axle at an angle = 6°, it starts rolling from rest. Determine the wheel's angular velocity W (in rad/s) after 4.0 seconds if the wheel has been rolling without slipping. Please pay attention: the numbers may change since they are randomized. Your answer must include 1 place after the decimal point. Take g = 9.81 m/s². Your Answer: G Answer r 0 FThe circular disk of 270-mm radius has a mass of 36 kg with centroidal radius of gyration k = 235 mm and has a concentric circular groove of 105-mm radius cut into it. A steady force T is applied at an angle to a cord wrapped around the groove as shown. If T = 59N, 0 = 29°, μs = 0.08, and μk = 0.07, determine the angular acceleration a of the disk, the acceleration a of its mass center G, and the friction force F which the surface exerts on the disk. The angular acceleration a is positive if counterclockwise, negative if clockwise; the acceleration a is positive if to the right, negative if to the left; and the friction force F is positive if to the right, negative if to the left. m= 36 kg k 235 mm 270 mm T G Ug = 0.08 Uh = 0.07 105 mm.The 213-kg wheel has a radius of gyration about its center O of ko = 240 mm, and radius r = 0.4 m. When the wheel is subjected to the constant couple moment M = 85 N·m, it starts rolling from rest. Determine the wheel's angular velocity W (in rad/s) after 4.4 seconds if the wheel has been rolling without slipping. Please pay attention: the numbers may change since they are randomized. Your answer must include 2 places after the decimal point. Take g = 9.81 m/s². M Your Answer: Answer
- 3. The wheel has a mass of 100 kg and a radius of gyration about the z-axis of k: = 300 mm rests on a smooth horizontal plane. If the belt is subjected to a force of P= 170 N, determine the angular velocity of the wheel and the speed of its center of mass two seconds after the 400 mm force is applied.The 250-kg wheel has a radius of gyration about its center O of ko = 260 mm, and radius r = 0.4 m. When the wheel is subjected to the constant couple moment M = 64 N.m, it starts rolling from rest. Determine the total angular impulse L (in N.m.s) about the wheel's IC after 7.3 seconds if the wheel has been rolling without slipping. Please pay attention: the numbers may change since they are randomized. Your answer must include 1 place after the decimal point. Take g = 9.81 m/s². M Your Answer: AnswerThe double pulley consists of two parts that are attached to one another. It has a mass of 20 kg and a radius of gyration about its center of ko= 200 mm and is turning with an angular velocity of 15 rad/s clockwise. Determine the kinetic energy of the system. Assume that neither cable slips on the pulley.
- Gear B is rigidly attached to drum A and is supported by two small rollers at E and D. Gear B is in mesh with gear C which is subjected to a torque of M= 60 N.m. Determine the angular velocity of the drum A after C has rotated 5 revolutions, starting from rest. Gear B and the drum have a mass of 100 kg and a radius of gyration about their rotating axis of 250 mm. Gear C has a mass of 30 kg and the radius of gyration about its rotating axis of 125 mm. 300 mm 200 mm E ΕΟ 150 mm M BThe double pulley consists of two parts that are attached to one another. It has a weight of 52 lb and a radius W= 20 rad/s of gyration about its center of k = 0,9 ft. If it rotates with O an angular velocity of 20 rad>s clockwise, determine the kinetic energy of the system. Assume that neither cable slips on the pulley. @= 20 rad/s 0.5ft 1 ft B 30 lb A 20 lbEach of the two links has a mass of 2 kg and a centroidal radius of gyration of 60mm. The slider at B has a mass of 3 kg and moves freely in the vertical guide. The springhas a stiffness of 6 kN/m. If a constant torque M = 20 N∙m is applied to link OA throughits shaft at O starting from the rest position at θ = 45°, determine the angular velocity ofOA when θ = 0.
- The 20-kg wheel has a radius of gyration about its center O of ko = 280 mm, and radius r = 0.5 m. When the wheel is subjected to the constant force F= 388 N, applied to the wheel's center axle at an angle = 11°, it starts rolling from rest. Determine the total angular impulse L (in N.m.s) about the wheel's /C after 5.5 seconds if the wheel has been rolling without slipping. Please pay attention: the numbers may change since they are randomized. Your answer must include 1 place after the decimal point. Take g = 9.81 m/s². F Ө Your Answer: AnswerThe 23-kg wheel has a radius of gyration about its center O of kO = 300 mm. When it is subjected to a couple moment of M = 50 N⋅m, it rolls without slipping. Determine the angular velocity of the wheel after its center O has traveled through a distance of sO = 20 m, starting from rest.The cable drum has a mass of 610 kg with radius of gyration of 385 mm about its center O and is mounted in bearings on the 1325-kg carriage. The carriage is initially moving to the left with a speed of 1.8 m/s, and the drum is rotating counterclockwise with an angular velocity of 2.0 rad/s when a constant horizontal tension T = 345 N is applied to the cable at time t = 0. Determine the velocity v of the carriage and the angular velocity w of the drum when t = 20 s. Neglect the mass of the carriage wheels. The velocity v is positive if to the right, negative if to the left. The angular velocity is positive if counterclockwise, negative if clockwise. %3D %3D T = 345 N 610 kg 415 mm 1325 kg