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Simple Problems in College Physics
2- 1 The first formula should be (mB.gsinβ-F)/mB= (F-mA.gsinα)/mA.

2-2 tangential acceleration a is variable acceleration,

Positive pressure n = fn = m (v 2/r)

Friction is resistance.

ma=-μN=-μm(v^2/R)

A =-μ (v 2/r), that is, dv/dt =-μ (v 2/r) separates variables and integrates them.

∫ dv/v 2 = ∫ (-μ/r) dt, and the integration limit is (v0-> v), (0-> t)

Integral result: V-T relation V = v0.r/(r+μ v0.t) (1).

According to the formula (1)ds/dt = v 0. r/(r+μv 0. t), separate variables and integrate.

∫ds=∫(v0。 R/(r+μ v 0.t)) dt, and the integral limit is (0-> s), (0->; t)

Integral result: s-t relation s = v0.r.ln (r+μ v0.t/r).

2-3 When I have time.