Three identical cylinders of radius r are placed inside a hollow cylinder of radius R. All cylinder axes (perpendicular to the paper) are horizontal. There is no friction. The cylinders B and C are on the verge of separating (= infinitesimally separated, as shown). B (a) From the statics equations for A and B, show that the angle between the normal under B and the vertical is given by tan 0 1 (The same result is obtained for A and C, of course, since B 3/3 and C have mirror image forces on them.) (b) By trigonometry of geometry, show that R must be r(1+2/7 Jin order for B and C to be on the verge of separating. (Find sin 0 and cos 0 from a triangle; don't find 0.) (Problem from a senior-year high school physics book used in England.)

Three identical cylinders of radius r are placed inside a hollow cylinder of radius R. All cylinder axes (perpendicular to the paper) are horizontal. There is no friction. The cylinders B and C are on the verge of separating (= infinitesimally separated, as shown). B (a) From the statics equations for A and B, show that the angle between the normal under B and the vertical is given by tan 0 1 (The same result is obtained for A and C, of course, since B 3/3 and C have mirror image forces on them.) (b) By trigonometry of geometry, show that R must be r(1+2/7 Jin order for B and C to be on the verge of separating. (Find sin 0 and cos 0 from a triangle; don't find 0.) (Problem from a senior-year high school physics book used in England.)

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Rigid Body

A rigid body is an object which does not change its shape or undergo any significant deformation due to an external force or movement. Mathematically speaking, the distance between any two points inside the body doesn't change in any situation.

Rigid Body Dynamics

Rigid bodies are defined as inelastic shapes with negligible deformation, giving them an unchanging center of mass. It is also generally assumed that the mass of a rigid body is uniformly distributed. This property of rigid bodies comes in handy when we deal with concepts like momentum, angular momentum, force and torque. The study of these properties – viz., force, torque, momentum, and angular momentum – of a rigid body, is collectively known as rigid body dynamics (RBD).

Question

Three identical cylinders of radius r are placed inside a hollow cylinder
of radius R. All cylinder axes (perpendicular to the paper) are horizontal.
There is no friction. The cylinders B and C are on the verge of separating
(= infinitesimally separated, as shown).
A
B
(a) From the statics equations for A and B, show that the angle between the normal under B and the
vertical is given by tan 0
1
(The same result is obtained for A and C, of course, since B
3/3
and C have mirror image forces on them.)
(b) By trigonometry of geometry, show that R must be r(1+2/7 Jin order for B and C to be on the
verge of separating. (Find sin 0 and cos 0 from a triangle; don't find 0.)
(Problem from a senior-year high school physics book used in England.)
ogbo

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