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| Composition Setup |
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Decomposing a problem into parts, each amenable to solution using the S.I.M. |
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approach. |
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Typical Decompositions
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Time
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or
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Position
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A
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single
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body
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may
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undergo
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different
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interactions
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during
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different
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times
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or
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at
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different
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positions.
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For
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example,
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a
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car
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may
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travel
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at
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uniform
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velocity,
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then
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the
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driver
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may
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apply
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the
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brakes
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causing
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deceleration,
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then
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the
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car
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may
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collide
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with
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something,
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then
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come
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to
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a
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stop
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because
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the
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brakes
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are
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still
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applied.
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This
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example
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requires
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decomposition
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into
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four
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separate
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regions.
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There
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are
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three
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boundaries
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between
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the
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regions,
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and
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for
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each
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the
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position
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and
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velocity
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of
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the
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car
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are
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the
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same
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on
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each
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side
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of
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the
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boundary
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(but
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may
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change
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within
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each
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region
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due
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to
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the
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laws
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of
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motion
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or
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due
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to
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interactions
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specific
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to
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that
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region).
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In general,
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the
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boundaries
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between
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to
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regions
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may
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be
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specified
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on
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the
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basis
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of
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position
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or
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time.
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For
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example,
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a
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road
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may
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be
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covered
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with
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ice
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for
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20
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m
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(e.g.
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over
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a
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bridge)
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but
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have
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bare
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pavement
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beyond
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that.
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Or
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the
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driver
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may
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continue
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at
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constant
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speed
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for
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a
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second
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and
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then
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apply
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the
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brakes
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(irrespective
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of
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how
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far
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the
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car
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traveled
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in
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that
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time).
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Often
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the
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position
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and
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velocity
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are
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equal
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across
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the
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boundary,
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but
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sometimes
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one
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assumes
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that
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a
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quick
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event
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(such
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as
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a
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collision
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with
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a
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projectile)
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suddenly
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changed
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the
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velocity
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of
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the
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particle
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at
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a
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particular
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time
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or
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place.
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Systems
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If
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there
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are
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two
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bodies
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present
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it
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may
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be
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preferable
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to
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treat
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them
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separately,
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rather
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than
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one
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system.
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An
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example
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is
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a
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faster
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car
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that
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is
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overtaking
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a
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slower
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one.
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Until
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they
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collide,
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they
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will
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have
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different
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positions
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vs.
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time.
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Afterwards,
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they
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may
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have
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different
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positions
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vs.
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time,
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or
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they
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may
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stick
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together
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so
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they
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have
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the
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same
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position
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vs.
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time.