Energy in the two-magnet system, experiment with coasting car (also in systems > toy cars and magnets)

Substituting a = F_net  / m into the fourth equation of motion leads to the definitions of work and kinetic energy, and the work-kinetic energy theorem.  Substituting a = F_net / m into the second equation of motion leads to the definitions of impulse and momentum, and the impulse-momentum theorem.

The energy to push the magnets together came from the Cheerios I theoretically ate for breakfast (note the energy conversion is only about 15% efficient).

The work done by the force I exerted goes into the potential energy of the magnet system.  When I release the car, the energy is mostly transformed into KE, though some is lost to friction before the magnetic force becomes insignificant. 

When the system is first released the magnitude of the force of repulsion between the two magnets exceeds that of the frictional force, and the car accelerates forward.  The magnetic force decreases as the separation increases.  At a certain point the magnitude of the magnetic force has fallen to the extent that it is equal to the magnitude of the frictional force, at which point the net force on the car and hence its acceleration is zero.  Beyond this point the frictional force exceeds the magnetic force and the acceleration of the system becomes negative, so that the KE reaches its maximum at the point where the two forces are equal and opposite.  (University Physics students should be able to explicitly relate this to the First Derivative Test).  The car will then slow in response to the frictional force, its KE being gradually depleted as the car does work against friction.  The car eventually comes to rest.

• Biochemical energy was transformed to PE.
• PE was mostly transformed to KE (the rest doing work against friction).
• KE was depleted in order for the car to do work against friction.
• In the end the biochemical energy was dissipated to the surroundings, almost all in the form of thermal energy (friction heats things up, and those things then cool to (very nearly) the ambient temperature).

Units of force and work (also in Concepts > units and dimensional analysis)

F_net = m a.  So the unit of a force is the product of a mass unit and an acceleration unit.

Units of mass include grams, slugs, kilograms and many others.  Units of acceleration (being units of distance divided by squared units of time) include meters / second^2, miles / hour^2, (miles/hour) / second, kilometers / year^2 and many others. 

Possible units of force would therefore include gram * meters / second^2, slug * kilometers / year^2, etc..

• The SI unit of force is the kilogram * meter / second^2.
• This is the force required to accelerate a 1 kg mass at 1 meter / second^2.
• This unit is given its own name.  1 kg m/s^2 = 1 Newton.

The work done by frictional force, for a given interval, is

• `dW = Fave_frict * `dx

The unit of work is therefore equal to the product of the unit of force and the unit of displacement.

• In the case of your experiment from 0915, forces were typically expressed in milliNewtons, displacements in centimeters.  In this case work would be measured in milliNewton * cm.
• The SI units of force and displacement are Newtons and meters, so the SI unit of force is the product of these units, Newtons * meters.
• This unit is given a name.  1 Newton * meter = 1 Joule.
• Note that since 1 Newton is 1 kg * m / s^2, 1 Joule is 1 N * m = 1 kg m/s^2 * m = 1 kg m^2 / s^2.