Transcript Kinematics - Plain Local Schools

Kinematics – Relative Motion
http://www.aplusphysics.com/courses/honors/kinematics/honors_relative.html
Unit #2 Kinematics

Objectives and Learning Targets
 Resolve a vector into perpendicular components:
both graphically and algebraically.
 Solve problems involving changing frames of
reference and relative velocities.
Unit #2 Kinematics
Relative Motion
 You may have heard about the topic of relativity in either of
Einstein’s Theories, but what is it?
 The concept of relative motion or relative velocity is all about
understanding frame of reference. A frame of reference can be
thought of as the state of motion of the observer of some event.

For example, if you’re sitting on a lawn chair watching a train travel
past you from left to right at 50 m/s, you would consider yourself in
a stationary frame of reference. From your perspective, you are at
rest, and the train is moving. Further, assuming you have
tremendous eyesight, you could even watch a glass of water sitting
on a table inside the train move from left to right at 50 m/s.
Unit #2 Kinematics
Relative Motion
 An observer on the train itself, however, sitting beside the table
with the glass of water, would view the glass of water as remaining
stationary from their frame of reference. Because that observer is
moving at 50 m/s, and the glass of water is moving at 50 m/s, the
observer on the train sees no motion for the cup of water.
 This seems like a simple and obvious example, yet when you take a
step back and examine the bigger picture, you quickly find that all
motion is relative. Going back to our original scenario, if you’re
sitting on your lawn chair watching a train go by, you believe you’re
in a stationary reference frame. The observer on the train looking
out the window at you, however, sees you moving from right to
left at 50 m/s.
Unit #2 Kinematics
Relative Motion

Even more intriguing, an observer outside the Earth’s atmosphere
traveling with the Earth could use a “magic telescope” to observe you
sitting in your lawn chair moving hundreds of meters per second as the
Earth rotates about its axis. If this observer were further away from the
Earth, he or she would also observe the Earth moving around the sun at
speeds approaching 30,000 m/s. If the observer were even further away,
they would observe the solar system (with the Earth, and you, on your
lawnchair) orbiting the center of the Milky Way Galaxy at speeds
approaching 220,000 m/s. And it goes on and on.

According to the laws of physics, there is no way to distinguish between
an object at rest and an object moving at a constant velocity in an
inertial (non-accelerating) reference frame. This means that there really
is no “correct answer” to the question “how fast is the glass of water on
the train moving?” You would be correct stating the glass is moving 50
m/s to the right and also correct in stating the glass is stationary
Unit #2 Kinematics
Relative Motion
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Imagine you’re on a very smooth airplane, with all the window shades
pulled down. It is physically impossible to determine whether you’re flying
through the air at a constant 300 m/s or whether you’re sitting still on the
runway. Even if you peeked out the window, you still couldn’t say whether
the plane was moving forward at 300 m/s, or the Earth was moving
underneath the plane at 300 m/s.

As you observe, how fast you are moving depends upon the observer’s
frame of reference. This is what is meant by the statement “motion is
relative.” In order to determine an object’s velocity, you really need to
also state the reference frame (i.e. the train moves 50 m/s with respect to
the ground; the glass of water moves 50 m/s with respect to the ground;
the glass of water is stationary with respect to the train.)
Unit #2 Kinematics
Relative Motion

Most of the time the Earth and the objects traveling on it will be our
frame of reference.

Imagine you’re in a canoe race, traveling down a river. It could be
important to know not only your speed with respect to the flow of the
river, but also your speed with respect to the riverbank, and even your
speed with respect to your opponent’s canoe in the race.

In dealing with these situations, you can state the velocity of an object
with respect to its reference frame. For example, the velocity of object A
with respect to reference frame C would be written as vAC. Even if you
don’t know the velocity of object A with respect to C directly, by finding
the velocity of object A with respect to some intermediate object B, and
the velocity of object B with respect to C, you can combine your velocities
using vector addition to obtain:
Unit #2 Kinematics
1-D Sample Problem

Question: A train travels at 60 m/s to the east
with respect to the ground. A businessman
on the train runs at 5 m/s to the west with
respect to the train. Find the velocity of the
man with respect to the ground.
Unit #2 Kinematics
1-D Sample Problem

Question: A train travels at 60 m/s to the east
with respect to the ground. A businessman
on the train runs at 5 m/s to the west with
respect to the train. Find the velocity of the
man with respect to the ground.
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Answer: First determine what information
you are given. Calling east the positive
direction, you know the velocity of the train
with respect to the ground (vTG=60 m/s). You
also know the velocity of the man with
respect to the train (vMT=-5 m/s). Putting
these together, you can find the velocity of
the man with respect to the ground.
Unit #2 Kinematics
2-D Sample Problem

Question: The president’s airplane, Air Force
One, flies at 250 m/s to the east with respect
to the air. The air is moving at 35 m/s to the
north with respect to the ground. Find the
velocity of Air Force One with respect to the
ground.
Unit #2 Kinematics
2-D Sample Problem
 Question: The president’s airplane,
Air Force One, flies at 250 m/s to the
east with respect to the air. The air is
moving at 35 m/s to the north with
respect to the ground. Find the
velocity of Air Force One with respect
to the ground.
 Answer: In this case, it’s important to
realize that both vPA and vAG are twodimensional vectors. You can find vPG
by vector addition.
Unit #2 Kinematics
2-D Sample Problem

Drawing a diagram can be of tremendous assistance in solving this problem.

Looking at the diagram, you can easily solve for the magnitude of the velocity
of the plane with respect to the ground using the Pythagorean Theorem.

You can find the angle of Air Force One using basic trig functions. Therefore,
the velocity of Air Force One with respect to the ground is 252 m/s at an
Unit #2 Kinematics
angle of 8° north of east.