forces on the person;
Tension, T, upward
Normal force of the elevator floor on the person, N, upward
person weight, Mg, downward
forces on the elevator;
Tension, T, upward
Normal force of the person on the elevator floor, N, downward
elevator weight, mg, downward
(c) a = 0.5 m/s^2 upward
T + N  Mg = Ma
T  N  mg = ma

2T (M+m)g = (M+m)a
2T = (M+m)(g+a) = (100 kg)(10.5 m/s^2) = 1050 N
T = 525 N
using the net force equation on the person
N = M(g+a)  T = (70 kg)(10.5 m/s^2)  525 N = 210 N
(d) N = 300 N
T + N  Mg = Ma
(T  N  mg = ma)

2N  Mg + mg = Ma  ma
2N  (Mm)g = a(Mm)
[2N  (Mm)g]/(Mm) = a
[600 N  400 N]/(40 kg) = 5 m/s^2
