Answered: Consider the Atwood machine, (a) write… | bartleby

Related questions

Question

Consider the Atwood machine,
(a) write the Lagrangian,
(b) write the equation of constraint,
(c) write the possible equations of motion,
(d) find the acceleration of motion,
(e) ind the force of constraint and give its meaning,
(f) discuss the case of equal masses.

Expert Solution

Step by step

Solved in 4 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Blurred answer

Similar questions

My system is a pendulum attached to moving horizontal mass m_1 and the pendulum m_2 that is shifted by X_o from origin. I have the lagrangian of my system what would be my equations of motions in terms of small angle approximation and what’s is their frequency?
Prove the following: if the Hamiltonian is independent of time, then ∆E doesn't change in time. Show work and be explicit to prove the statement.
For a one dimensional system, x is the position operator and p the momentum operator in the x direction.Show that the commutator [x, p] = ih
Problem 3: A mass m is thrown from the origin att = 0 with initial three-momentum po in the y direction. If it is subject to a constant force F, in the x direction, find its velocity v as a function of t, and by integrating v find its trajectory. Check that in the non-relativistic limit the trajectory is the expected parabola. Hint: The relationship F = P is still true in relativistic mechanics, but now p = ymv instead of p = mv. To find the non-relativistic limit, treat c as a very large quantity and use the Taylor approximation (1+ x)" = 1 + nx when a is small.
Consider a 3-body system again. This time, let the particles be the Sun, the Earth, and the Moon. (a) Write the relative vector equations of motion for the Moon relative to the Earth. (b) At the very instance where the following right angle triangle geometry is achieved, compute the dominant and perturbing accelerations. Compare the magnitudes of both accelerations, is it reasonable to model the Moon's motion by considering a two-body problem with the Earth? Explain your answer.
This problem deals quantitatively with the experiment of problem 1.1. Let 5denote the ground frame of reference and 5' the train's rest frame. Let the speedof the train, as measured by ground observers, be 30 m/sec in the x direction, andsuppose the stone is released at t' = a at the point x' = y' = 0, z' = 7.2 m.(a) Write the equations that describe the stone's motion in frame 5'. That is,give x', y', and z' as functions of t'. (Note: A body starting from rest and movingwith constant acceleration g travels a distance 1/2 gt2 in time t. Gravity produces aconstant acceleration whose lnagnitude is approximately 10 m/sec/sec.)(b) Use the Galilean transform,ation to write the equations that describe theposition of the stone in frame S. Plot the stone's position at intervals of 0.2 sec,and sketch the curve that describes its trajectory in frame 5. What curve is this?(c) The velocity acquired by a body starting from rest with acceleration g is gt.Write the equations that describe the three…
Let's say we have a particle in motion. If f(x) represents the function of the particle's velocity, what does the integral of f(x) represent?