FBD Diagram

Won't they be the same? In either frame the man accelerates so there must be a force in the direction of acceleration on the man to cause it to accelerate?

 

The force that is accelerating the train and passengers with respect to the earth has little to do with the force that is accelerating the passenger with respect to the earth

If the person is standing still with respect to the train, then that person must be accelerating with respect to the earth, at the same acceleration of the train with respect to the earth.

Now the use of non-inertial (accelerating) frames should be avoided like the plague except in certain problems such as this one, since it was asked, so you cannot avoid the question unless you choose not to answer it. FBD's in non-inertial frames require the use of pseudo forces (fictitious forces) and real forces. There is no acceleration of the passenger with respect to the train...since they are both accelerating together...so the real force F is balanced by the make-believe force F' = -ma, where 'a' is the acceleration with respect to the earth. Although they cancel, they both should be shown and properly marked, in the x direction. Fg and Fn still show in either case, since the pseudo force in that direction is 0, so those forces in the vertical direction result in the same FBD of forces in the y direction. Pseudo forces are not fun!:yuck: