The work done is proportional to the difference in the height from the ground, which means that
W=mg(h2-h1), which is also the difference in the potential energy of Spiderman.
The difference in height is: l-l cos 60=12-12 cos 60=6 m.
[Solution redacted by the Mentors]
kq^2/(2x+l)^2=mgμ
(2x+l)^2=kq^2/(mgμ)=25
2x+l=5
x=5-l/2=1.5 m
kq^2/l=2mv^2/2+kq^2/(2x+l)+2mgμx
mv^2=kq^2/l-kq^2/(2x+l)-2mgμx=0.0405 J
v^2=0.0405/m=4.5
v=2.12 m/s which is wrong. The velocity must be 0.67 m/s.
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I only could calculate the distance travelled by each body, by making the difference between the initial and final electric potential work equal to the work of friction done by the 2 bodies.
When the first electron has the known initial velocity the second electron is at rest (not moving) at a long unknown distance between them. And I think that when they will get the closest possible to each other they will still be moving, thus both having kinetic energy. So no, I don't think they...
I tried to make the kinetic energy of the first electron equal to the electric potential work.
mv^2/2=ke^2/d
We have to solve for the minimum distance between them: d=2ke^2/mv^2=5.05*10^-10 m
The force is: F=ke^2/d^2=9*10^-10 N, which is not correct.