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13 February 2016

Block sliding down a frictionless incline -- two different articulations of energy conversion.

A block of mass m is released from rest from the top of a frictionless incline a vertical distance h from the table underneath.  The incline is fixed to the tabletop.  Obviously the block speeds up as it moves to the bottom of the incline.  

In AP Physics 1, students will be asked carefully about energy conversion.  Depending on the system we consider, what are the "external" and "internal" forces?  How should we articulate the energy conversion that allows the block to speed up?

1. On one hand, consider the block alone.  It has zero kinetic energy to start, and some KE to end.   Thus, some force must have done work on the block.  (Since the we are considering the block alone, all forces acting on the block must be "external.")

The incline can't do work on the block -- the force of the incline on the block is perpendicular to the block's motion, so does no work.  The only work done on the block is from the force of the earth on the block -- gravity.  The amount of that work is the block's weight mg times the displacement parallel to the force's direction, i.e. the vertical displacement of the block h.  That work mgh is converted to the block's kinetic energy.  

2. Consider the block-earth system.  Now the earth cannot do work on the block-earth system because the earth is part of the system.  But the block-earth interaction produces a potential energy mgh at the beginning.  No work is done by external forces -- the only force external to the system is the force of the incline on the block, and that's perpendicular to the block's motion, and so can do no work.  The system loses mgh of potential energy, which is converted to kinetic energy of the block. 

1 comment:

  1. Hey Greg,

    This is a great question and is analogous to a few different questions that I have been discussing with physics teachers over the last month. First the kinetic energy of a system of particles can be written as the sum of the kinetic energy of center of mass and the sum of the kinetic energy associated with the motion of each particle relative to the center of mass, see this proof:

    So in the second case, gravity is an internal force, now internal forces CAN do work on a system of particles, however they can not cause the velocity of the center of mass of the system to change. So the work they do is by having the particles move relative to the center of mass. Therefore the mass and the earth both move, however the only one that is practically measurable is that of the mass.