Physics 2211, Spring 2005

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Physics 2211 Lecture 14

• Reference frames and relative motion

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Inertial Reference Frames

• A Reference Frame is the place from which you
  measure.
• -- its where you nail down your (x,y,z) axes!
• An Inertial Reference Frame (IRF) is one that is
  not accelerating.
• We will consider only IRFs in this course.
• Valid IRFs can have fixed velocities with respect
  to each other.
• More about this later when we discuss forces.
• For now, just remember that we can make
  measurements from different vantage points.

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Newtons Principle of Relativity

• Principle of Relativity (from Newton in 1600s)
• The motion of bodies included in a given space
  are the same among themselves whether that space
  is at rest or moves uniformly forward in a
  straight line.

• Newtons Principle of Relativity Restated
• The laws of mechanics (Newtons Laws) are
  invariant (the same) in all inertial
  (non-accelerating) reference frames(IRFs).
• OR
• Absolute uniform motion (or absolute rest)
  cannot be detected.

• Impact Experiments (e.g., dropping a ball,
  period of a pendulum, two objects colliding) in a
  boxcar moving with constant velocity will have
  the same results as the same experiments in a
  boxcar at rest.

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Example(relative motion)

• Kim is sitting on a train moving at 20 m/s. She
  is throwing a ball straight up and is catching it
  at the same place she threw it. The ball is in
  the air 1.5 s. Joe is standing on the ground by
  the railroad tracks and watches Kim as she throws
  the ball.
• What is the initial speed of the ball and how
  high does it go
• as seen by Kim?
• as seen by Joe?

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Example

• The ball moves vertically in the IRF attached to
  the train (Kims IRF)

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Example

• But suppose the train is moving to the right in
  the IRF attached to the ground (Joes IRF).

• From the grounds IRF, the balls motion exhibits
  projectile motion.

Galilean velocity transformation
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Example

• The initial velocity as see my Joe is

• Magnitude of initial velocity (initial speed)

• Angle above the horizontal

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Example

• Recall x and y components of motion are
  independent

• Therefore, vertical (y) motion is the same both
  in both IRFs

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What is relative?
To talk about A relative to B is to redefine B
to be zero. If I weight 230 lbs and my
girlfriend weighs 120 lbs then my weight relative
to hers is 110 lbs. It is the same as to say
what would be my weight if hers was zero. Her
weight relative to mine is 110 lbs. In both
cases you subtract the value of the reference.
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The idea a relative also applies to position. To
talk about the position of point A relative to
point B is to make the location of point B the
origin of a new coordinate system. If A is
located at (-3,7) and B is located at (8,-5),
what is the location of A relative to B? It is
a vector from B to A.
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Lastly relative applies to velocities. If ship A
is sailing east at 20 knots and ship B is sailing
north at 24 knots, what is the velocity of ship A
as seen from ship B?
Ship B sees ship A sail away with a speed of 31
knots towards the southeast.
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How to solve relative velocity problems.
Nearly all relative velocity problems involve
three vectors. Do the following (1) Draw the
picture (2) It is critically important to
understand which vector is the sum of the
other two. (3) solve for unknown quantity by
either vector arithmetic or trigonometry
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Example 1
An airplane files north in air that is moving
towards the southeast (its called wind). The
sum is what an observer on the ground sees.
VP/A is what the velocity of the plane would
be if the air were still. look for air
speed or velocity in still air VA/G is what
the velocity of the air would be if the ground
were still, which it is.
VP/G is the sum of VP/A and VA/G It is what
the observer on the ground sees.
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Example

• What is the boats velocity with respect to the
  shore if the boat crosses in the shortest
  possible time?

• Time to cross the river is given by the distance
  travel (as measured on the shore) divided by the
  speed of the boat (as measured on the shore)

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Example
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Example
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Example 2

• You are swimming across a 50m wide river in which
  the current moves at 1 m/s with respect to the
  shore. Your swimming speed is 2 m/s with respect
  to the water. You swim across in such a way that
  your path is a straight perpendicular line across
  the river.
• How many seconds does it take you to get across
  ?

50 m
2 m/s
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• The time taken to swim straight across is
  (distance across) / (vy )

• Since you swim straight across, the sum of the
  vectors must be in the y-direction.

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A small airplane cruises at a speed of 240 km/hr
in still air. The pilot files directly from Mega
City to Smallville which lies 100 km directly
north of Mega City. The wind the day of the
flight is 80 km/hr towards the southeast. What is
the time of the flight?
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Assume that Houston, Texas is 400 km directly
southeast of Dallas and a flight between those
two cities is scheduled to take 45 min. If the
wind is 120 km/hr to the west, what must the
airspeed of the plane be to arrive exactly on
time?
To arrive on time the plane must have a net
velocity of 533 km/hr SE. Solve the problem with
vector artihmetic.