Question

3. Consider a two-dimensional region (say, the - v plane), in which a particle (mans m)
experiences a force-field, characterised by potential energy
U(r) = -Uo Ir so
U (r) = 0 Ir > a
where Uo > 0 and r- xi + vj (see Fig. 2). 2 The particle approaches the well from 1 =
with velocity -voi (vo > 0), energy E - mv/2 and angular momentum L = l k, where
<> 0.3
(a) Identify all conserved dynamical quantities associated with the motion of this particle
(1 MARK)
(b) Determine the condition on l such that the particle will eventually enter the potential
well (1 MARK).
4. In problem 3 above, consider specific values l = mvoa/V2 and U, =
mvooE/2.
(a) Determine the velocity of the particle, immediately AFTER it enters the well, in plane
polar coordinates (1 MARK).
(b) Use the relevant conservation laws (refer to 3 (a) above) to express the radial speed r in
terms of the radial coordinate r (2 MARKS).
(c) By solving the equation in (b) or otherwise (show details), determine the time T it takes
for the particle to escape from the well (2 MARKS).​

Answer 1

Answer:

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