The two uniform thin discs shown in the figure rest on a horizontal plane and are connected through frictionless pin-joints at A and B by a rigid light rod which remains horizontal. The mass of disc A is 15 kg. and that of disc B is 25 kg. The static coefficients of friction between the plane and discs A and B are, respectively, (,),= 0.2 and (,), = 0.55. At th 405

International Edition---engineering Mechanics: Statics, 4th Edition
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Chapter7: Dry Friction
Section: Chapter Questions
Problem 7.24P: A uniform plank is supported by a fixed support at A and a drum at B that rotates clockwise. The...
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The two uniform thin discs shown in the figure rest on a horizontal plane and are
connected through frictionless pin-joints at A and B by a rigid light rod which
remains horizontal. The mass of disc A is 15 kg. and that of disc B is 25 kg. The
static coefficients of friction between the plane and discs A and B are, respectively,
(,),= 0.2 and (,), = 0.55.
At the instant shown, a counter-clockwise moment T = 125 Nm. is applied to disc
B. You are required to,
(a) identify the type of ensuing motion of the discs,
(b) draw the free-body, kinematic and kinetic diagrams of the discs,
(c) assuming motion initiates with pure rolling, write down the
appropriate kinematic and kinetic relationships with respect to a
suitable global axes system, and
(d) determine, in magnitude and direction, the angular accelerations
of the discs and force developed in the rod AB at the instant the
moment T is applied.
(e) Validate the pure rolling assumption in part(c) and if slipping is
anticipated, explain with supporting arguments, whether one of
the discs will first slip, or both discs will slip at the same time.
You must clearly show details of the analysis that you have carried out using
relationships in part (c) to arrive at subsequent results in a neat, logical way.
0.45 m
60⁰
0.6 m
3
0.45 m
60°
0.6 m
Transcribed Image Text:Question The two uniform thin discs shown in the figure rest on a horizontal plane and are connected through frictionless pin-joints at A and B by a rigid light rod which remains horizontal. The mass of disc A is 15 kg. and that of disc B is 25 kg. The static coefficients of friction between the plane and discs A and B are, respectively, (,),= 0.2 and (,), = 0.55. At the instant shown, a counter-clockwise moment T = 125 Nm. is applied to disc B. You are required to, (a) identify the type of ensuing motion of the discs, (b) draw the free-body, kinematic and kinetic diagrams of the discs, (c) assuming motion initiates with pure rolling, write down the appropriate kinematic and kinetic relationships with respect to a suitable global axes system, and (d) determine, in magnitude and direction, the angular accelerations of the discs and force developed in the rod AB at the instant the moment T is applied. (e) Validate the pure rolling assumption in part(c) and if slipping is anticipated, explain with supporting arguments, whether one of the discs will first slip, or both discs will slip at the same time. You must clearly show details of the analysis that you have carried out using relationships in part (c) to arrive at subsequent results in a neat, logical way. 0.45 m 60⁰ 0.6 m 3 0.45 m 60° 0.6 m
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