MECH 220 Final 2009
December 2009 Final Examination
MECHANICS II MECH 220 December 16, 2009, 2:00pm-5:00pm Examiner:
Inna Sharf
Assoc Examiner: John H.S. Lee
Student Name:
McGill ID:
INSTRUCTIONS: This is a CLOSED BOOK examination. Only one hand-written or typed double-sided CRIB SHEET permitted. SPACE IS PROVIDED on the examination to answer questions # 1 - 6. Page 13 includes a Table of inertia properties You are permitted TRANSLATION dictionaries ONLY. STANDARD CALCULATOR permitted ONLY. This examination paper MUST BE RETURNED
MECH 220
Page 1 of 13
PROBLEM 1
[17 marks]
A carnival ride called the octopus consists of eight arms that rotate about the z axis at the constant angular velocity = 6 rpm. The arms have a length L = 22 ft and form an angle with (t ) t where the z axis. Assuming that varies with time as 0 1 sin 0
70.5 ,
25.5 and
= 1 rad/s, determine: (a) The magnitude of the acceleration of the outer end of an arm when achieves its maximum value. [12 marks] (b) At the same instant, the normal force exerted by the seat on the rider if the weight of the rider is 140 lb. [5 marks]
MECH 220
1
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MECH 220
Page 3 of 13
PROBLEM 2
[10 marks]
The mass moment of inertia of the pulley is 0.4 slug-ft2. The pulley starts from rest and the pin is frictionless. a) Determine the pulley’s kinetic energy when it has turned one revolution. [5 marks] b) At the same instant, determine the tension in the string. [5 marks]
MECH 220
Page 4 of 13
MECH 220
Page 5 of 13
PROBLEM 3
[15 marks]
The 5-lb rod AB supports the 3-lb disk at its end A. If the desk is given an angular velocity D 8 rad/s while the rod is held stationary and then released, determine the angular velocity of the rod after the disk has stopped spinning relative to the rod due to frictional resistance at the bearing A. Motion is in the horizontal plane. Neglect friction at the fixed bearing B.
MECH 220
Page 6 of 13
MECH 220
Page 7 of 13
PROBLEM 4
[15 marks]
The plate has a mass of 3 kg and is welded to the fixed vertical shaft, which rotates at the constant speed of 20π rad/s. (a) (b)
MECH 220
determine the angular momentum of the plate (about O); compute the reaction moment M transmitted to the shaft by the plate due to dynamic imbalance.
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MECH 220
Page 9 of 13
PROBLEM 5
[13 marks + 5 BONUS]
A boy starts from the center O of a merry-go-round and walks along the radial line of OM fixed to the rotating platform. When he is 8 ft from the center O of the platform at point P, his velocity relative to the platform in the direction of M is 2 ft/sec and is decreasing at the rate of 1 ft/sec². The merry-go-round rotates in the direction shown at the constant rate of one revolution each 10 sec. If θ = 30° when the boy reaches P, (a) Determine the relative acceleration of the boy (with respect to O) as seen in the rotating x-y-z frame. [3 marks] (b) Determine his absolute acceleration in terms of X-Y components of the inertial (fixed) reference frame. [10 marks\] (c) Is the angular momentum of the boy about O conserved? Justify your answer. [5 BONUS marks]
MECH 220
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MECH 220
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PROBLEM 6
[15 marks]
The robotic device consists of the stationary pedestal OA, member AB pivoted at A and member BC pivoted at joint B. The rotation axes are normal to the plane of the figure. The mass of arm AB is 25 kg and the mass of arm BC is 4 kg and each member can be treated as a uniform slender rod. At the instant of interest, member AB is rotating about joint A with a counterclockwise angular velocity of 2 rad/s and this rate is increasing at 4 rad/s2. Joint B is held in a locked condition during this motion. a) Calculate the kinetic energy of the robotic device at this instant. b) Determine the moment MB exerted by arm AB on arm BC.
MECH 220
Page 12 of 13
MECH 220
Page 13 of 13
MECHANICS II MECH 220 December 16, 2009, 2:00pm-5:00pm Examiner:
Inna Sharf
Assoc Examiner: John H.S. Lee
Student Name:
McGill ID:
INSTRUCTIONS: This is a CLOSED BOOK examination. Only one hand-written or typed double-sided CRIB SHEET permitted. SPACE IS PROVIDED on the examination to answer questions # 1 - 6. Page 13 includes a Table of inertia properties You are permitted TRANSLATION dictionaries ONLY. STANDARD CALCULATOR permitted ONLY. This examination paper MUST BE RETURNED
MECH 220
Page 1 of 13
PROBLEM 1
[17 marks]
A carnival ride called the octopus consists of eight arms that rotate about the z axis at the constant angular velocity = 6 rpm. The arms have a length L = 22 ft and form an angle with (t ) t where the z axis. Assuming that varies with time as 0 1 sin 0
70.5 ,
25.5 and
= 1 rad/s, determine: (a) The magnitude of the acceleration of the outer end of an arm when achieves its maximum value. [12 marks] (b) At the same instant, the normal force exerted by the seat on the rider if the weight of the rider is 140 lb. [5 marks]
MECH 220
1
Page 2 of 13
MECH 220
Page 3 of 13
PROBLEM 2
[10 marks]
The mass moment of inertia of the pulley is 0.4 slug-ft2. The pulley starts from rest and the pin is frictionless. a) Determine the pulley’s kinetic energy when it has turned one revolution. [5 marks] b) At the same instant, determine the tension in the string. [5 marks]
MECH 220
Page 4 of 13
MECH 220
Page 5 of 13
PROBLEM 3
[15 marks]
The 5-lb rod AB supports the 3-lb disk at its end A. If the desk is given an angular velocity D 8 rad/s while the rod is held stationary and then released, determine the angular velocity of the rod after the disk has stopped spinning relative to the rod due to frictional resistance at the bearing A. Motion is in the horizontal plane. Neglect friction at the fixed bearing B.
MECH 220
Page 6 of 13
MECH 220
Page 7 of 13
PROBLEM 4
[15 marks]
The plate has a mass of 3 kg and is welded to the fixed vertical shaft, which rotates at the constant speed of 20π rad/s. (a) (b)
MECH 220
determine the angular momentum of the plate (about O); compute the reaction moment M transmitted to the shaft by the plate due to dynamic imbalance.
Page 8 of 13
MECH 220
Page 9 of 13
PROBLEM 5
[13 marks + 5 BONUS]
A boy starts from the center O of a merry-go-round and walks along the radial line of OM fixed to the rotating platform. When he is 8 ft from the center O of the platform at point P, his velocity relative to the platform in the direction of M is 2 ft/sec and is decreasing at the rate of 1 ft/sec². The merry-go-round rotates in the direction shown at the constant rate of one revolution each 10 sec. If θ = 30° when the boy reaches P, (a) Determine the relative acceleration of the boy (with respect to O) as seen in the rotating x-y-z frame. [3 marks] (b) Determine his absolute acceleration in terms of X-Y components of the inertial (fixed) reference frame. [10 marks\] (c) Is the angular momentum of the boy about O conserved? Justify your answer. [5 BONUS marks]
MECH 220
Page 10 of 13
MECH 220
Page 11 of 13
PROBLEM 6
[15 marks]
The robotic device consists of the stationary pedestal OA, member AB pivoted at A and member BC pivoted at joint B. The rotation axes are normal to the plane of the figure. The mass of arm AB is 25 kg and the mass of arm BC is 4 kg and each member can be treated as a uniform slender rod. At the instant of interest, member AB is rotating about joint A with a counterclockwise angular velocity of 2 rad/s and this rate is increasing at 4 rad/s2. Joint B is held in a locked condition during this motion. a) Calculate the kinetic energy of the robotic device at this instant. b) Determine the moment MB exerted by arm AB on arm BC.
MECH 220
Page 12 of 13
MECH 220
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