In an example problem from a book I’m using (David Morin’s Introduction to Classical Mechanics with Problems and Solutions), there is a system with a person and a pulley on top of a platform. The pulley is attached to the platform with a rod. The person is standing next to the pulley holding one end of the rope, and the other end of the rope goes up to a ceiling. An equation is given for the subsystem of the platform. The mass of the platform is M, the normal force from the pulley is $N_\mu$, and the force from the pulley’s rod is f.
The book says the total force on the platform is equal to
$F=Ma=-Mg+f+N_p$
I don’t understand this. First, am I correct in assuming that the “upward force” from the rod f is simply the normal force from the rod? Second, why would we count the normal forces from these objects instead of their weight on the platform? To me it seems that the normal forces from these objects are being exerted by the platform, not on the platform.
A second equation is given for the subsystem of the person. The mass of the person is m, the normal force from the platform is N, the mass of the platform is M, and the tension in the rope is T, with the equation given as
$F=ma=N-T-mg$
The third equation is for the subsystem of the pulley, with $\mu$ equal to the mass of the pulley, $f$ equal to the force from the rod, and $T$ equal to the tension in the string:
$F=\mu a=2T-f-\mu g$
Again, I am not sure why the force from the rod is negative here. Is that simply the weight of the rod? Why are we considering the weight of the rod on the pulley, while we considered the normal force from the rod on the platform?
