Question
In: Physics
Consider a particle which is constrained to move along the surface of the sphere of radius...
Consider a particle which is constrained to move along the surface of the sphere of radius 5, centered at the origin.
(a) If we write r(t) for the motion, write down the condition ‘constrained to move along the surface of the sphere of radius 5 centered at the origin’ in terms of r(t). (Hint. For later use, try to get rid of square roots.)
(b) Explain why, for such a motion, we must have r 0 (t) ⊥ r(t). (Hint. Differentiate your answer from the previous part.)
(c) What can you say about the acceleration? (Hint. Differentiate your answer from the previous part. Draw a picture.)
Solutions
genius_generous answered 2 years agoRelated Solutions
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 mass of 1.1kg is attached to a spring and constrained to move without friction along...
A mass of 1.1kg is attached to a spring and constrained to move
without friction along the x-axis. The mass is attached to a spring
of spring constant 80?? N m ; one end of the spring is attached to
a fixed point along the x-axis while the other is attached to the
mass. The equilibrium position of the mass is the origin. The mass
has a position as a function of time which can be expressed:
?(?)=?cos(??+?) x (...
A particle of mass m is constrained to lie along a frictionless, horizontal plane subject to...
A particle of mass m is constrained to lie along a frictionless,
horizontal plane subject to a force given by F (x) = −kx + kx^3/A^2
where k and A are positive constants. The particle is projected
from x = 0 to the right with initial kinetic energy T0. Find the
turning points of the motion and the condition the total energy of
the particle must satisfy if its motion is to exhibit turning
points.
A particle of mass m is constrained to lie along a frictionless, horizontal plane subject to...
A particle of mass m is constrained to lie along a frictionless,
horizontal plane subject to a force given by F (x) = −kx + kx^3/A^2
where k and A are positive constants. The particle is projected
from x = 0 to the right with initial kinetic energy T0. Find the
turning points of the motion and the condition the total energy of
the particle must satisfy if its motion is to exhibit turning
points.
The Simple harmonic oscillator: A particle of mass m constrained to move in the x-direction only...
The Simple harmonic oscillator: A particle of mass m constrained
to move in the x-direction only is subject to a force F(x) = −kx,
where k is a constant. Show that the equation of motion can be
written in the form d^2x/dt2 + ω^2ox = 0, where ω^2o = k/m . (a)
Show by direct substitution that the expression x = A cos ω0t + B
sin ω0t where A and B are constants, is a solution and explain the...
Find the distribution of temperature inside a sphere of radius a when the surface of the...
Find the distribution of temperature inside a sphere of radius a
when the surface of the upper half is held at 100°C and the surface
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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.
The particle has a mass of 0.6 kg and is confined to move along the smooth...
The particle has a mass of 0.6 kg and is confined to move along
the smooth horizontal slot due to the rotation of the arm OA.
Assume the particle contacts only one side of the slot at any
instant. The arm has an angular acceleration of θ¨ = 3 rad/s2 when
θ˙ = 2 rad/s at θ = 30∘. (Figure 1) Part A Determine the magnitude
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The surface area of a sphere of radius r is S = 4πr2. Its volume is
The surface area of a sphere of radius r is S = 4πr2. Its volume is
V = 4πr3/3.
a. Use MuPAD to find the expression for dS/dV.
b. A spherical balloon expands as air is pumped into it. What is the rate of increase in the balloon’s surface area with volume when its volume is 30 in.3?
7.1.2. A pulsating sphere of radius a vibrates with a surface velocity amplitude U0 and at...
7.1.2. A pulsating sphere of radius a vibrates with a
surface velocity amplitude U0 and at such a
high frequency that ka >> 1. Derive
expressions for the pressure amplitude, the particle velocity
amplitude, the intensity, and the total acoustic power radiated in
the resulting acoustic wave.
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