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26 May 2010

Elevator question #1: Forces on the student

The poll question to the right asks only for the downward forces acting on the student.  For the purposes of our discussion, let's first consider ALL forces acting on the student.

It is important to focus only on the forces acting directly on the student himself.  Forces that act on the elevator, on the scale, or on the building are utterly irrelevant to this question. 

So, we begin with earth's gravity.  We know the earth applies a downward force on the student.  That downward force is generally called the student's weight.

Since there are no electric or magnetic fields here (and, if you're really going to be a lawyer about it, since we're not dealing directly with a nucleus), any other forces on the student require contact with the student.  What else is touching the student?  Only the platform scale.  And since he's standing on the scale, that scale must push upward. 

What about the "normal force?"  A normal force is defined as the contact force of a surface pushing perpendicular to that surface.  Because the scale provides a surface for the student to stand on, the upward force of a platform scale *is* a normal force... on a free body diagram, a label of "Fn" or "N" rather than "Fscale" would be completely correct.  Just recognize that when we apply Newton's second law, whatever value we find for the normal force is the reading on the scale.

What about the force of the student pushing down on the scale?  Well, that force certainly exists... but that force does not act on the student.  In order for Newton's Laws to work, we must consider only the forces that act ON the student, not forces exterted BY him.

What about the force of the cable attached to the elevator, or the elevator's weight?  Isn't the entire elevator accelerating, not just the person?  Yes... but we must choose a single object for the purpose of using Newton's second law.  Had we chosen the entire elevator with the person inside, then there would be an upward tension from the cable, and a downward weight.  But we were asked about forces acting on the person, not the elevator. Newton's second law applies just fine to the person alone, even though the elevator exists. 

And as for the "force of motion" or the "force of acceleration"... these things do not exist. A force must be attributed to some agent pushing or pulling, either through contact or through a gravitational (or electric or magnetic) field.  Sure, forces can cause acceleration, but the "force of acceleration" is not a meaningful or correct phrase.

Next, I'm going to ask about the MOTION of the elevator... stay tuned.

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