A5.0 kg dog sits on the floor of an elevator that is accelerating downward at 1.20 m/s^2 .?
a) what is the magnitude of the normal force of the elevator floor on the dog?

b) what is the magnitude of the force of the dog on the elevator floor?

A)
Upward force = Normal Force
Downward force = weight
Resultant force = ma

Resultant = Weight - Normal
1.2 x 5 = 1.2 x 9.81 - Fn
Fn = 5.77 N

B) 
The reactant force is equal to the force exerted by the dog, just in the opposite direction. Thus, the dog's force is also 5.77 N.