Angular Velocity and Acceleration

PHYC 160
Conservation of
momentum, center of mass, rocket
propulsion
Lecture #23
Office Hours
I will be in RH 109 (Instructor Office) on
Tuesday, March 24th, 12-2 pm
Bring your questions!
Elastic collisions
• In an elastic collision, the
total kinetic energy of the
system is the same after the
collision as before.
• Figure 8.14 at the left
illustrates an elastic collision
between air track gliders.
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Inelastic collisions
• In an inelastic collision, the total kinetic
energy after the collision is less than before
the collision.
• A collision in which the bodies stick together
is called a completely inelastic collision (see
Figure 8.15 at the right).
• In any collision in which the external forces
can be neglected, the total momentum is
conserved.
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Q8.4
Two objects with different
masses collide and stick to
each other. Compared to
before the collision, the
system of two objects after
the collision has
A
B
A. the same total momentum and the same total kinetic energy.
B. the same total momentum but less total kinetic energy.
C. less total momentum but the same total kinetic energy.
D. less total momentum and less total kinetic energy.
E. not enough information given to decide
© 2012 Pearson Education, Inc.
Q8.6
Block A has mass 1.00 kg and block B has mass 3.00 kg. The
blocks collide and stick together on a level, frictionless surface.
After the collision, the kinetic energy (KE) of block A is
A. 1/9 the KE of block B.
B. 1/3 the KE of block B.
C. 3 times the KE of block B.
D. 9 times the KE of block B.
E. the same as the KE of block B.
© 2012 Pearson Education, Inc.
Q8.5
Two objects with different
masses collide and bounce
off each other. Compared to
before the collision, the
system of two objects after
the collision has
A
B
A. the same total momentum and the same total kinetic energy.
B. the same total momentum but less total kinetic energy.
C. less total momentum but the same total kinetic energy.
D. less total momentum and less total kinetic energy.
E. not enough information given to decide
© 2012 Pearson Education, Inc.
Q8.7
Block A on the left has mass 1.00 kg. Block B on the right
has mass 3.00 kg. The blocks are forced together,
compressing the spring. Then the system is released from rest
on a level, frictionless surface. After the blocks are released,
the kinetic energy (KE) of block A is
A. 1/9 the KE of block B.
B. 1/3 the KE of block B.
C. 3 times the KE of block B.
E. the same as the KE of block B.
© 2012 Pearson Education, Inc.
D. 9 times the KE of block B.
A two-dimensional collision
•
Two robots collide
and go off at
different angles.
•
Follow Example
8.6 using Figure
8.13 at the right.
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Some inelastic collisions
•
• Follow Example 8.7, which illustrates a
completely inelastic collision, and use
Figure 8.17 at the right.
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Cars are intended to have
inelastic collisions so the car
absorbs as much energy as
possible.
Q8.6
Block A has mass 1.00 kg and block B has mass 3.00 kg. The
blocks collide and stick together on a level, frictionless surface.
After the collision, the kinetic energy (KE) of block A is
A. 1/9 the KE of block B.
B. 1/3 the KE of block B.
C. 3 times the KE of block B.
D. 9 times the KE of block B.
E. the same as the KE of block B.
© 2012 Pearson Education, Inc.
The ballistic pendulum
•
•
Ballistic pendulums are
used to measure bullet
speeds.
Follow Example 8.8 and
Figure 8.18 at right.
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An automobile collision
•
Follow Example 8.9, in which two cars traveling at right
angles collide. See Figure 8.19 below.
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Elastic collisions
•
As Figures 8.22 and
8.23 show, the behavior
of the colliding objects
is greatly affected by
their relative masses.
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An elastic straight-line collision
•
Follow Example 8.10, referring to Figure 8.24 below.
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Neutron collisions in a nuclear reactor
•
Follow Example 8.11 using Figure 8.25 below.
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A two-dimensional elastic collision
•
Follow Example 8.12 using Figure 8.26 below.
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Center of mass of a water molecule
• Follow Example 8.13 which investigates a water molecule.
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Center of mass of symmetrical objects
• It is easy to find the center of mass of a
homogeneous symmetric object, as
shown in Figure 8.28 at the left.
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Motion of the center of mass
•
The total momentum of a system is equal to the
total mass times the velocity of the center of
mass.
•
The center of mass of the wrench in Figure 8.29
at the right moves as though all the mass were
concentrated there.
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Tug-of-war on the ice
• Follow Example 8.14, in which a tug-of-war occurs on
frictionless ice.
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External forces and center-of-mass motion
• When a body or collection of particles is acted upon by
external forces, the center of mass moves as though all the
mass were concentrated there (see Figure 8.31 below).
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Q8.9
A yellow block and a red rod are joined together. Each object is
of uniform density. The center of mass of the combined object is
at the position shown by the black “X.”
Which has the greater mass, the yellow block or the red rod?
A. the yellow block
B. the red rod
C. They both have the same mass.
D. not enough information given to decide
© 2012 Pearson Education, Inc.
Rocket propulsion
• As a rocket burns fuel, its mass decreases, as shown
in Figure 8.32 below.
• Follow Example 8.15 (Acceleration of a rocket).
• Follow Example 8.16 (Speed of a rocket).
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