[Borodog]

I started with energy conservation, since the negative work done by friction is equal to the positive work done by the torque due to the friction. So after a displacement x:

mgx sinq = (7/10) mv^2

Differentiating with respect to time:

mgv sinq = (7/5) mva

a = (5/7)g sinq

Newton's 2nd Law:

Fnet_x = mg sinq - F_f = ma = (5/7) mg sinq

(2/7) mg sinq = F_f = mu mg cosq

tanq = (7/2)mu = 7/4

In general, for a round object of moment of inertia I = cmr^2,

slope = tanq = (1 + 1/c) mu

Which is a neat formula.