USC2001 Energy Lecture 3 Classical Relativity

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USC2001 Energy Lecture 3 Classical Relativity

• Wayne M. Lawton
• Department of Mathematics
• National University of Singapore
• 2 Science Drive 2
• Singapore 117543

Email matwml_at_nus.edu.sg Tel [phone]
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FALLING OBJECT SEEN FROM THE GROUND
Lecture 1 described the motion of a falling
object as seen from the ground. The height h is a
function of t.
The velocity is also a function of time.
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FALLING OBJECT SEEN FROM AN ELEVATOR
How does the motion appear from an elevator that
is moving with a uniform speed w ?
Question What is the height of the object seen
by an observer who measures it relative to the
elevator floor ?
Answer
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FALLING OBJECT SEEN FROM AN ELEVATOR
How does the motion appear from an elevator that
is moving with a uniform speed w ?
Question What is the height of the elevator
floor as a function of time?
Answer
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FALLING OBJECT SEEN FROM AN ELEVATOR
How does the motion appear from an elevator that
is moving with a uniform speed w ?
Question What is the velocity of the object
relative to the elevator ?
Answer
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FALLING OBJECT SEEN FROM AN ELEVATOR
How does the motion appear from an elevator that
is moving with a uniform speed w ?
Question What is the potential energy of the
object relative to the elevator ?
Answer
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FALLING OBJECT SEEN FROM AN ELEVATOR
How does the motion appear from an elevator that
is moving with a uniform speed w ?
Question What is the kinetic energy of the
object relative to the elevator ?
Answer
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FALLING OBJECT SEEN FROM AN ELEVATOR
How does the motion appear from an elevator that
is moving with a uniform speed w ?
Question What is the total energy of the object
relative to the elevator ?
Answer
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COLLISIONS
A collision is an isolated event in which two or
more bodies exert relatively strong forces on
each other for a relatively short time
Collisions range widely in scale. Meteor Crater
in Arizona (1200m wide by 200m deep), alpha
particle bouncing off a nitrogen nucleus, tennis
ball in contact with a racquet for 0.004s
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ELASTIC COLLISIONS
We will restrict our attention to systems that
are closed (no mass leaves or enters) and
isolated (no net external forces act on the
bodies within the system)
A collision between two bodies is elastic if
their total kinetic energy is conserved (same
before and after the collision). Although real
world collisions are inelastic, many are
approximately elastic. Completely inelastic
collisions occur when the colliding bodies stick
to each other and kinetic energy is transferred
into heat.
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CONSERVATION OF ENERGY RELATIVE TO ALL OBSERVERS
Consider the 1-dim elastic collision of two
objects
Since kinetic energy is conserved relative to an
observer moving with velocity w
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CONSERVATION OF MOMENTUM
Consider the 1-dim elastic collision of two
objects
Question What is momentum and why is it
preserved?
Answer Momentum is mass times velocity. Expanding
both sides of the preceding equation yields an
equality between two quadratic polynomials in
the variable, the coefficients of the linear
terms are equal therefore
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ANALYTIC GEOMETRY PICTURE
The ellipse and line intersect in two points
that describe the velocity pairs before and after
collision, these points have coordinates
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TUTORIAL 3

• If a falling object attains maximal height above
• the Earths surface at time T when will it
  appear
• to reach a maximal altitude with respect to an
• elevator that moves with constant velocity w ?

2. Conservation of total energy with respect to
an observer on the ground does not imply that an
object moves since a stationary object does not
change its energy. Prove that if the total energy
is constant for every observer moving with
constant velocity then the objects moves
according to
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TUTORIAL 3
3. Use the preceding two equations to show that
and
4. Solve these equations to show that
5. Show that two hockey pucks with identical
mass colliding elastically along a line exchange
velocities.