A particle of mass m moves under the influence of a central force.The potential energy function is
V(r) = { Vo if r < a 0 if r > a
as illustrated in the figure. The initial position of the particleis (x,y) = (a/2, 0).
The initial velocity is (vx,vy) = (0, v0). Determine the finalvelocity. [Data: m = 1 kg; V0 = 10 J; v0 = 4.6 m/s.]
(A) What is the final speed?
(B) What is the final direction θ?
**HINT GIVEN**
Energy and angular momentum are conserved.
Express E and L in terms of the initial conditions. Express Eand L in terms of the coordinates when the particle passes the radius r = a. Set the energies equal, and theangular momenta equal. That yields two equations for two unknowns. The rest is just math.
