a. 850 N is the minimum force needed to get the machine/player system moving, which means this is the maximum magnitude of static friction between the system and the surface they stand on.
By Newton's second law, at the moment right before the system starts to move,
• net horizontal force
∑ F[h] = F[push] - F[s. friction] = 0
• net vertical force
∑ F[v] = F[normal] - F[weight] = 0
and we have
F[s. friction] = µ[s] F[normal]
It follows that
F[weight] = F[normal] = (850 N) / (0.67) = 1268.66 N
where F[weight] is the combined weight of the player and machine. We're given the machine's weight is 200 N, so the player weighs 1068.66 N and hence has a mass of
(1068.66 N) / g ≈ 110 kg
b. To keep the system moving at a constant speed, the second-law equations from part (a) change only slightly to
∑ F[h] = F[push] - F[k. friction] = 0
∑ F[v] = F[normal] - F[weight] = 0
so that
F[k. friction] = µ[k] F[normal] = 0.56 (1268.66 N) = 710.45 N
and so the minimum force needed to keep the system moving is
F[push] = 710.45 N ≈ 710 N
