Question

An electron of mass 9.1E-31 kg is released from rest at a distance of 7.1 E-10 m from a fixed electron. The force on the movable electron is given by the function F = 2.3E-28/r^2, where r is the distance between the electrons. Find the maximum velocity (in meters/second) of the moving electron after release.

^ we're supposed to use mechanical energy theorems to solve this problem.

Ive tried integrating the F(x) to find the total work, but our teacher didn't specify the distance the object travels, so its impossible to bound the integral.
Ideas?
Solutions? thanks!

Answer 1

integrate the repulsion force from the initial separation to infinity and you will get a finite energy change. Set that equal to the final maximum kinetic energy.

Answer 2

integrate with lower bound is 7.1 E-10
and upper bound is infinity.
Then use lim as Rmax approaches infinity, replace upper bound.

Then find velocity by:

Work = (1/2) * m * v^2
v^2 = 2 * Work / m

v = sqrt( 2 * Work / m ).

Answer for this problem: 843780