A small particle of mass m is initially moving in the x direction with speed u 0
ID: 2264924 • Letter: A
Question
A small particle of mass m is initially moving in the x direction with speed u0 toward a much larger particle, as pictured. Assume that the large particle is stationary, and the small particle starts very far away. The two particles have a
repulsive force between them that is of the form ?? = k/??2 , where r is the distance
between the two particles. This force between the two particles causes the smaller particle to be deflected, thereby changing its velocity in both direction and magnitude.
a. Find the potential energy due to the force, assuming ?? ? 0 as ?? ? ?.
b. Find the minimum distance rmin between the two particles and the speed v of the small particle when it is closest to the large particle.
(Please give detailed answer)
Explanation / Answer
a) work doen = potential energy
work done from infinty to x is int((k/r^2)dr from r = infinity to r = x
work = [-k/r] from r = infinty to r = x
work = k/x = potential energy
b) considering the larger mass doesnt move
work done by internal force = change in kinetic energy = change in potential energy
let minimum distance be x
work done from infinty to x is int((k/r^2)dr from r = infinity to r = x
work = [-k/r] from r = infinty to r = x
work = k/x
work = change in kinetic energy
k/x = 1/2*m*u*u
x = 2k/mu^2
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