There are two neutral solid spheres of radius r with a seperation d
r< < d
They are supplied charges constantly such that dq/dx=n for 1st and dq/dt=-n for the 2nd sphere.
After what time will the spheres stop pure rolling?
assume masses to be M and coeff of friction to be k
What will be the distance traveled by the spheres during this time?
Edited teh question to make the diferential equation solvable :)
106As r<<<d
F = (nt)24Πεx2
f = kMg
in limiting case of pure rolling ,limiting friction will act and the rolling will be of forward slipping as v will increase while increase in angular velocity will have a constant magnitude
F-f = Ma .. (i)
and fr = 2Mr2α5 .. (ii)
=> f = 2Ma/5
=> a = 5F/7M and flim = 2F/7
=> kMg = 27(nt)24Πεx2
Conserving energy (neglecting grav potential energy)
2*(12Mv2(7/5)) = (nt)24Πεx2
hmm thinking wat to do now
62asish.. be careful.. you cant conserve energy..
electric field is varying.. it is not constant...
1since dq/dx=n ....q=nx
q^2=n^2 x^2
net force on body..................
k(n^2 x^2)/ x^2 - f
kn^2-f..........
i think instanteneously it will start pure rolling,as initial velocity is 0
(kn^2-f)/m=5f/2m(acm=ralpha)
f=2/7 k n^2
1it will never stop pure rolling as the net force acting on com is constant kn^2-f..............if fmax <2/7 k n^2........it will never do pure rolling........