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.)

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter7: Hamilton's Principle-lagrangian And Hamiltonian Dynamics

Section: Chapter Questions

Problem 7.1P

See similar textbooks

Similar questions

Find the cross product for (a) and (b) and (c) and and (d) and
I am confused on how to start this problem. I know I need to use the y(x,t)=Asin(kx+wt+phi) formula, but do I need to take the derivative of that once I enter in all the variables? I am referenceing the problem 14 in the pic I attached. Thanks!
ELEMENTARY APPLICATION OF DE/LINEAR DE OF ORDER, n, Case 1 and 2
A ladder of length L and mass M is leaning against a wall. Assuming thewall and the floor are friction-less, the ladder will slide down the wall andalong the floor until the left end loses contact with the wall. Before the ladder loses contact with the wall there is one degree of freedom (θ). Using the formula for Euler-Lagrange EOM to find the Lagrangian and then the EOM for the ladder. Assume that gravity is present.
Show that (BC)A is the volume of the parallelepiped, with edges formed by the three vectors in the following figure.
Let's consider a ring with a diameter of 0.1 m and a total load of -2 mC. The ring lies in the x-y plane, with its center at the origin. What is the force on a 1 mC load located at z = 3 m? In what direction would the force be on this load if it were in the x-y plane, but outside the ring?
The x any components of a force vector are -3.0 N and +4.0 N respectively, solve for the direction the given vector make with the +x axis and determine at what quadrant in the cartesian coordinate system the calculated direction of the equilibrant vector is located.
The PE curve of a particle moving along the xaxis due to some conservative force is depicted in this diagram. At what intervals of x is the force on the particle to the right? At what intervals of x is the force on the particle to the left? What points show that the force is zero? At what positions of x is does there exist stable and unstable equilibria? Should the particle be pushed lightly to the right at rest when x is 0 meters, what is the distance that it will travel along the xaxis?
Let r be a vector with an initial point located on the axis of rotation and with a terminal point located at the point where a force F is applied. Find the torque and explain what the torque is measuring.
Show that a set of vectors V (not containing the 0 vector)is linearly dependent if and only if there exists some vectorin V that can be written as a nontrivial linear combinationof other vectors in V.
Calculate the moments Mx and My and the center of mass (x¯,y¯)(x¯,y¯) of a lamina with the given density and shape.
Get the resultant in x and y. Also the θ. Show the complete and step by step solution. It is a Static of Rigid Bodies subject.