Question
In: Physics
A particle with mass m moves on the surface of a cylinder with radius R. At...
A particle with mass m moves on the surface of a cylinder with radius R. At the same time, the force F = -kr on the particle affects it through the z axis. Using the z-and θ generalized coordinates, find the system's hamitonians. Solve the Hamilton equation after defining the conservative quantities.
Solutions
genius_generous answered 2 years agoRelated Solutions
A particle of mass m moves under the influence of gravity g on the inner surface...
A particle of mass m moves under the influence of gravity g on
the inner surface of a smooth cone of half-angle α. The axis of the
cone is vertical, with its vertex downward. (a) Find the
equation(s) of constraint of the system. (b) Find Lagrange’s
equations of motion using the method of undetermined multipliers.
(c) Determine the condition on the angular velocity ω such that the
particle can describe a horizontal circle at a height h above the
vertex.
A uniform cylinder of mass m and radius r is rolling down a slope of inclination...
A uniform cylinder of mass m and radius r is rolling down a
slope of inclination 30°. The cylinder rolls without slipping. At
what rate does the cylinder accelerate down the slope?
A uniform cylinder of radius R and mass M is mounted so as to rotate freely...
A uniform cylinder of radius R and mass M is
mounted so as to rotate freely about a horizontal axis that is
parallel to, and a distance h from the central
longitudinal axis of the cylinder. (a) What is the
rotational inertia of the cylinder about the axis of rotation?
(b) If the cylinder is released from rest with its
central longitudinal axis at the same height as the axis about
which the cylinder rotates, what is the angular speed...
1) A cylinder of Mass M and radius R, and initial speed V, starts rolling up...
1) A cylinder of Mass M and radius R, and initial
speed V, starts
rolling up an incline of angle theta relative to horizontal.
Assuming
no slipping, how high up does the cylinder get?
2) teeter/totter
a) Peewee has mass m and his big buddy Delilah has mass 2m. If
Peewee
sits at one end of a uniform teeter totter of length L and mass M,
how
far from the central pivot should Delilah sit (ie on the other end)...
Two smooth spheres of radius are placed inside a cylinder of radius R. The mass of...
Two
smooth spheres of radius are placed inside a cylinder of radius R.
The mass of each sphere is M Assume that R < 2r < 2R All
answers should be in terms of . R.M and What is the force of the
bottom sphere on the top sphere? What is the force of the cylinder
wall on the top sphere ?
A particle of mass m is constrained to a circle of radius r0: that is, the...
A particle of mass m is constrained to a circle of radius
r0: that is, the potential for the particle is 0 when
the
particle is anywhere on that circle and infinite everywhere
else,
?(?) = 0 (r=r0)
V(r) = ∞ (? ≠ ?0)
Find the eigenvalues and normalized eigenfunctions of the
Hamiltonian for a particle on a ring.
What is the degeneracy of eigenvalues for this system. how many
eigenfunctions are
there for each eigenvalue)?
A solid sphere of radius R, a solid cylinder of radius R, and a hollow cylinder...
A solid sphere of radius R, a solid cylinder of radius R, and a
hollow cylinder of radius R all have the same mass, and all three
are rotating with the same angular velocity. The sphere is rotating
around an axis through its center, and each cylinder is rotating
around its symmetry axis. Which one has the greatest rotational
kinetic energy?
both cylinders have the same rotational kinetic energy
the solid cylinder
the solid sphere
they all have the same...
3) A solid cylinder with mass 4kg and radius r=0.5 m rolls without slipping from a...
3) A solid cylinder with mass 4kg and radius r=0.5 m rolls
without slipping from a height of 10 meters on an inclined plane
with length 20 meters. a) Find the friction force so that it rolls
without slippingb) Calculate the minimum coefficient of rolling
friction muc) Calculate its speed as it arrives at the bottom of
the inclined plane.
A material particle with mass M moves under the gravitational effect of the earth. Solve the...
A material particle with mass M moves under the gravitational
effect of the earth. Solve the Hamilton-jacobi equation of the
particle.
A material particle with mass M moves under the gravitational effect of the earth. Solve the...
A material particle with mass M moves under the gravitational
effect of the earth. Solve the Hamilton-jacobi equation of the
particle.
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