Psuedoforces and Inertial Frames

Before starting let’s go over what inertial and accelerating frames of reference are. (If you need to review Newton’s Second Law/ Frames of Reference go here). Imagine that a person A is standing on the ground watching a person B get accelerated upwards in an elevator. Within the elevator is not only person B but also a box of mass M which is getting accelerated at the same rate as person B. (Fig 1).

Now let’s draw Free Body Diagrams of the box based on the two Frames of Reference: Person A and Person B .(Fig 2)

For Observer A we used Fnet = ma and declared up to be the positive direction. Hence we called normal force and acceleration positive in our formula and subtracted the negative mg. We got that the normal force should equal the mass of the block times gravity + the mass of the block times the acceleration of the block. This is an inertial frame of reference. The observer is not accelerating and Newtonian physics holds true, because if we measured the normal force in the elevator we would find it to be mg + ma.

However for Observer B we find that since the box is accelerating at the same rate as Person B the acceleration according to B is 0. And if we rearrange the equation N – mg = we get the normal force equaling gravity. This is WRONG. Observer A is correct and Observer B is not. The reason is because B was accelerating in a non inertial frame of reference.

Here is where psuedoforces come into play. If we add a psuedoforce to an accelerating frame of reference it will give correct results. Whichever way the body is moving, we would add the mass times acceleration in the opposite direction. For example in the elevator problem we would add a “fake force” to person B’s frame of reference so Fnet = ma would be N – mg – ma (negative force we just added) = 0. If we solve we will get that N = mg + ma even in person B’s frame of reference. Bingo! Now even if you are in an accelerating train you can calculate the forces acting on you with the addition of a few psuedoforces

A question I want to leave with is that Einstein put forth that gravity itself could be a psuedoforce. Think about how that is possible and if you can’t solve it google has plenty of answers. Thanks for reading!