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<p><strong>Chapter 9 Linear Momentum And Collisions</strong></p>

<p><strong>Introduction:</strong></p>

<p>-A reason given why the concept of work, energy and the work-energy theorem
are valuable are for dealing with computation with what kind of forces? <span
id="ans">Nonconstant </span></p>

<p>-Can physical systems evolve randomly considering energy? <span id="ans">No.
It can only change in a ways that conserve energy.</span></p>

<p></p>

<p><strong>9.1 Linear Momentum:</strong></p>

<p>-What is momentum? Is it vector or scalar? <span id="ans">Product of mass
and velocity. Vector</span></p>

<p>-How is momentum different from the kinetic energy? <span id="ans">Momentum
: vector, KE scalar, mv vs 0.5mv^2</span></p>

<p></p>

<p><strong>9.2 Impulse and Collisions:</strong></p>

<p>-How are momentum and force connected? <span id="ans">Force changes velocity
and hence the momentum.</span></p>

<p>-On what factors does the amount of change of the object's motion depend?
<span id="ans">Magnitude of force and time interval over which the force is
applied</span>. </p>

<p>-What is impulse? Is it a vector or scalar? <span id="ans">product of force
and time interval. vector</span>. </p>

<p>-Which equation tells how impulse is related to the average force and time
interval? <span id="ans">Equation 9.5</span> </p>

<p>-Do you need to know details of the force to calculate impulse or just the
average force? <span id="ans">Often just the average force, IF you know the
time interval.</span> </p>

<p>-Which equation tells how impulse is related to the mass and change in
velocity? <span id="ans">Equation 9.6</span></p>

<p>-The Example 9.1 shows a rare complicated case where the functional form
F(t) of a non-constant force is explored. It is a good demonstration of why we
prefer to use impulse/momentum instead of the force. It also provides a good
visual reminder (Fig. 9.8) of how the average of a function relates to the
actual functional form, [In this case how the average force relateds to F(t)]
</p>

<p>-Two different expressions of impulse (Equation 9.5 and Equation 9.6) can be
combined to find out unknown varible from known variables. Look at how the
average force experienced by the driver during a collision is calculated from
the known values of time of impact and speed of car in Example 9.2. Why is the
seat belt and airbag important? </p>

<p>-What does the impulse-momentum theorem state? <span id="ans">The change in
momentum is equal to the impulse.</span> </p>

<p>-Problem solving strategy for impulse-momentum theorem. Equate two
expressions (Equation 9.5 and Equation 9.6) for impulse to solve desired
quantity. </p>

<p>-Which equation is another form of Newton's second law of motion expressed
in terms of momentum? <span id="ans">Equation 9.9</span> </p>

<p></p>

<p><strong>9.3 Conservation of Linear Momentum:</strong></p>
<!-- <p>Why can't the two equal but opposite forces in Newton's third law be
canceled?

<p><span id="ans">Two forces are applied to different
objects.</span> </p>

</p> -->

<p>-What is the law conservation of linear momentum? <span id="ans">Total
momentum of a closed system is conserved or constant.</span> </p>

<p>-What is a conservation law? <span id="ans">If the value of a physical
quantity is constant in time, the quantity is conserved.</span> </p>

<p><span id="prob">-NOTE: In Figure 9.14 the caption momentum labels/subscripts
has an inconsistency with the figure (p2 vs p3)</span> </p>

<p>-What are the requirements for momemtum conservation? <span id="ans">i) Mass
of the system must remain constant during interaction--remember, you can choose
what's in the system and what's not . ii) The net external force on the system
must be zero.</span> </p>

<p>-What is a system?<span id="ans">collection of objects in whose motion is
under consideration.</span> </p>

<p>-How is a closed system (isolated system) defined?<span id="ans">system
obeying above requirements.</span> </p>

<p><span id="comm"></span>-Problem-solving strategy for conservation of
momemtum. First, identify closed sytem and equate the momentum of system before
and after "event". </p>

<p>-How is the final velocity of two carts sticking together after collision
calculated in Example 9.6 using the conservation of momentum? </p>

<p>-Example 9.7: Note in this example as opposed to the previous falling phone
example, the system considered is actually the Earth + Ball. Thus the gravity
acting on the ball, is not an external force. Ignoring gravity from e.g. the
Sun. </p>

<p></p>

<p><strong>9.4 Types of Collision:</strong></p>

<p>-What other type of "interaction" is discussed besides a collision which is
"One to Many"? <span id="ans">an explosions</span> </p>

<p>-Many to One: NOTE: an inelastic collision is defined by Kinetic Energy NOT
being conserved--it does not NEED to be Many to One or One to Many, although
these cases are automatically inelastic</p>

<p>-How does the book define a perfectly inelastic collision?<span
id="ans">Final KE zero. colliding particles stick and remain motionless.</span>
</p>

<p><span id="prob">-NOTE: Usually a <em>perfectly</em> inelastic collision is
just defined by the objects all sticking together in the final configuration:
they may still be moving -- the change in KE in that case is still maximal, as
one can always move in a frame of reference moving at constant velocity with
the final config of stuck together objects--which means in that frame of
reference it's at rest.</span> </p>

<p>-Notice that "Many to Many" does not AUTOMATICALLY imply that a collision is
elastic: Many-to-Many, including "2-to-2" can also be inelastic if the system
KE does not stay constant (energy can be inserted or removed in invisible ways
such as the collision inducing vibrations or rotations.) Example 9.13 is such a
case--which can be seen quickly by noting the 2nd equation given, the
ratio/relation of the i and f velocities--this can be easily used to calculate
KE before and after using, 1/2mv^2, which will not be equal. </p>

<p>-Problem solving strategy for collision. First, identify closed system. Use
conservation of momentum and kinetic energy (if elastic) to solve for unknowns.
</p>

<p><span id="comm">-</span>How are the two unknown variables (final velocities
of two colliding hockey pucks) calculated using the two equations (from
conservation of momentum and kinetic energy) in Example 9.11? </p>

<p><span id="comm"></span>-How are the conservation of momentum and the
work-energy theorem (work done by frictional force) used to analyze crash
between a truck and a car in Example 9.13? </p>

<p>-What experiment did Rutherford perform to put forward his model about the
structure of atom? <span id="ans">analyzed scattering of alpha particles with
gold foil with the help of conservation of energy and momentum.</span> </p>

<p><strong>9.5 Collisions in Multiple Dimension:</strong></p>

<p>-How are the force and momentum related in component form? <span id="ans">Fx
= dpx/dt, Fy = dpy/dt</span> </p>

<p>-How many equations are needed to express/solve momentum conservation in 2
Dimensions (see Eq 9.18) <span id="ans">Two</span> </p>

<p>-Note the steps in the problem-solving strategy for conservation of momentum
in two dimensions: especially that one of the first steps is to find the
compenents of each momentum or velocity as shown in the figure --this is
usual." : </p>

<p><span id="comm"></span>-How is the conservation of momentum in two
independent axes (X-axis and Y-axis) used to fjnd the velocity of combined
werckage due to collision of car and truck in Example 9.14? </p>

<p><strong>9.6 Center of Mass:</strong></p>

<p>-What is internal force? <span id="ans">Internal force: result of particles
of the system acting on other particles of the same system.</span> </p>

<p>-Is the internal force for any individual part of a system always zero? What
about the sum of all the internal forces? <span id="ans">No. Yes.</span> </p>

<p>-Do the internal forces cause to change the momentum of the system as a
whole (hint does it appear in Eq. 9.25)? <span id="ans">No</span> </p>

<p>-READING EXERCISE : Why can't you lift yourself in the air by standing in a
basket and pulling up on the handles? <span id="ans">upward pulling is the
internal force on the basket + you system</span> </p>

<p>-What is center of mass of an object? <span id="ans">Weighted average
position of the mass of extended object.</span> </p>

<p>-Eq 9.29 is the most important equation of this section: it defines the
center of mass. Note that it is a vector equation, as the center of mass is a
point, i.e. a position: which has components in each dimension, (2 equations in
2D...) </p>

<p>-Does there have to be actual mass at the center of mass of an object? If
not, give examples. <span id="ans">No. Eg; center of hollow sphere, doughnut.
</span> </p>

<p>-How are the masses and positions (3D co-ordinante
system) of three different objects solved independently in 3 differnt axes (X-,
Y and Z-axis) to find the center of mass of the whole system in Figure 9.27?
</p>

<p>-Problem-solving strategy for calculating the center of mass. First, find
out the positions of particles in a co-ordinate system (with one of the
particle in origin). Then, solve for the each components of center of mass
independently along the axes of co-ordinate system. </p>

<p>-What is the first of the two listed crucial things to keep in mind before
calculating the center of mass of any object? <span id="ans">i) You must define
your coordinate system </span> </p>

<p>-What equation tells you how to calculate the center of mass of a continuous
object? <span id="ans">Equation 9.34</span> </p>

<p>-Which equation shows conservation of momentum expressed in terms of center
of mass of the system? <span id="ans">Eqn 9.36- because M*v_cm is just same as
the sys momentum.</span> </p>

<p>-Does the velocity of the center of mass of a system changes in the absence
of external force? <span id="ans">No, it remains constant: combining with
previous question/answer, this implies sys momentum is constant</span> </p>

<p></p>

<p><strong>9.7 Rocket Propulsion:</strong></p>

<p>-How does the rocket accelerate? <span id="ans">by burning fuel and ejecting
the burned exhaust gas.</span> </p>

<p>-Is the relation between rocket's velocity amount of mass of fuel that is
burned linear or non-linear? <span id="ans">Non-linear dependence</span> </p>

<p>-Which equation tells how velocity changes as a function of fuel expended
and what is this equation called? <span id="ans">Equation 9.38 - the rocket
equation.</span> </p>

<p>-The problem-solving strategy of rocket propulsion will not be used
extensively in this course. </p>

<p>-Note how the thrust and acceleration of space craft are calculated in
Example 9.20. </p>

<p>-How does the rocket equation changes in presence of gravity? <span
id="ans">Equation 9.39</span></p>

<p></p>
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