A small particle of mass m is initially moving in the x direction with speed u0

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 F=k/(r^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 U ? 0 as r ? ?.

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.

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 F=k/(r^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. Find the potential energy due to the force, assuming U ? 0 as r ? ?. 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.

Explanation / Answer

a)
if the two particles have charges q1 and q2

F = k*q1*q2/r^2

we know.,

U = -dF/dr

= -k*q1*q2*(-1/r)

= k*q1*q2/r



b) Ui + ki = uf + kf

0 + 0.5*m*uo^2 = k*q1*q2/r + 0.5*m*v^2


k*q1*q2/r = 0.5*m*(u0^2-v^2)


==> r = k*q1*q2/(0.5*m*(uo^2-v^2))

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