Angular Momentum and Mass Center
ES 12: Dynamics of Rigid Bodies First Semester, 2012-2013
Due: October 5, 2012/ Class Hours PROBLEM SET FOR LQ4
Instructions: 1. Answer this problem set at the back page of used short/A4 size bond paper. 2. At the TOPMOST portion of the first page of your answer sheets, write the following: “I hereby certify that I have worked on this problem set by my own honest effort, without giving or receiving any inappropriate help. I understand that any evidence which contradicts the foregoing statement may be used against me, and I am prepared for the ensuing consequences thereof.” 3. Maximum of 2 problems per sheet. Show all relevant solutions neatly and state any assumptions used in solving. Box all final answers.
PROBLEM NO.1 In the crank piston system shown, a piston P is connected to a crank AB (b 16 cm.) by a 2 kg slender rod B ( l 40 cm.). The mass of the crank AB can be considered to be very small. During a test of the system, crank AB is made to rotate with a constant angular velocity of 60 rad/s clockwise. There is no force applied to the face of the piston. When 60the distance between points D and A , d, is 43.081 cm and the angle of connecting rod BD from the horizontal is 30o. Consider this instant when 60, answer the following questions:
d
1.A) Show by kinematic analysis that the angular acceleration of connecting rod BD is 1328.5 rad/s2 1.B) Show by kinematic analysis that the acceleration of the mass center G of connecting rod BD has the horizontal and vertical components of acceleration aGx = 188.60 m/s2 and aGy = 249.42 m/s2; respectively. 1.C) Draw clearly the FBD = EFD diagram for the connecting rod BD. Label all points and vectors properly. 1.D) Determine the force acting at point B. 1.E) Determine both the horizontal and vertical components of the force acting on the bar BD at hinge D. PROBLEM NO.2 A uniform slender bar AB of mass m is suspended as shown from a uniform disk of the same mass m. Neglecting the
Due: October 5, 2012/ Class Hours PROBLEM SET FOR LQ4
Instructions: 1. Answer this problem set at the back page of used short/A4 size bond paper. 2. At the TOPMOST portion of the first page of your answer sheets, write the following: “I hereby certify that I have worked on this problem set by my own honest effort, without giving or receiving any inappropriate help. I understand that any evidence which contradicts the foregoing statement may be used against me, and I am prepared for the ensuing consequences thereof.” 3. Maximum of 2 problems per sheet. Show all relevant solutions neatly and state any assumptions used in solving. Box all final answers.
PROBLEM NO.1 In the crank piston system shown, a piston P is connected to a crank AB (b 16 cm.) by a 2 kg slender rod B ( l 40 cm.). The mass of the crank AB can be considered to be very small. During a test of the system, crank AB is made to rotate with a constant angular velocity of 60 rad/s clockwise. There is no force applied to the face of the piston. When 60the distance between points D and A , d, is 43.081 cm and the angle of connecting rod BD from the horizontal is 30o. Consider this instant when 60, answer the following questions:
d
1.A) Show by kinematic analysis that the angular acceleration of connecting rod BD is 1328.5 rad/s2 1.B) Show by kinematic analysis that the acceleration of the mass center G of connecting rod BD has the horizontal and vertical components of acceleration aGx = 188.60 m/s2 and aGy = 249.42 m/s2; respectively. 1.C) Draw clearly the FBD = EFD diagram for the connecting rod BD. Label all points and vectors properly. 1.D) Determine the force acting at point B. 1.E) Determine both the horizontal and vertical components of the force acting on the bar BD at hinge D. PROBLEM NO.2 A uniform slender bar AB of mass m is suspended as shown from a uniform disk of the same mass m. Neglecting the