Transcript Momentum

Reading Quiz - Momentum
1. Which is true? Conservation of the total
momentum of a system
___ 1. holds only when mechanical
energy is
conserved.
___ 2. holds for any system.
___ 3. follows from Newton’s second law.
___ 4. is equivalent to Newton’s third law.
2. A rocket is propelled forward by ejecting
gas at high speed. The forward motion is a
consequence of
___ 1. conservation of energy.
___ 2. conservation of momentum.
___ 3. both of the above.
___ 4. neither of the above.
3. The impulse delivered to a body by a
force is
___ 1. defined only for interactions of short
duration.
___ 2. equal to the change in momentum
of
the body.
___ 3. equal to the area under an F vs. x
graph.
___ 4. defined only for elastic collisions.
4. In an elastic collision
___ 1. energy is conserved.
___ 2. momentum is conserved.
___ 3. the magnitude of the relative
velocity is
conserved.
___ 4. all of the above
Linear Momentum
• The linear momentum p
of an object of mass m
moving with velocity v
is defined as: p  mv
• Note vector nature!
• Newton’s 2nd law can be
re-expressed as:
F  ma  p
t
Impulse
• Many forces are variable and
act for a short period of time
(as in collisions). A useful
quantity is the impulse I of
such a force:
I  Ft p
• Equivalent average force of
the impulsive force:
Ft  I
Conceptual Questions
1) Momentum is most closely related to
____ a) kinetic energy
____ b) potential energy
____ c) impulse
____ d) power
____ e) none of the above
2) An object that has momentum must also have
____ a) acceleration
____ b) impulse
____ c) kinetic energy
____ d) potential energy
3) Two equal-mass bullets traveling with the
same speed strike a target. One of the
bullets is rubber and bounces off, the other
is metal and penetrates, coming to rest in
the target. Which exerts the greater impulse
on the target?
____ a) the rubber bullet
____ b) the metal bullet
____ c) both exert the same
____ d) not enough information
____ e) none of these
Quantitative Questions
1) What effect on its momentum does doubling the
kinetic energy of a moving object have?
2) The head of a golf club is in contact with a 46
gram golf ball for 0.50 milliseconds, and as a
result, the ball flies off at 70 m/s. Find the
average force that was acting on the ball during
the impact.
Conservation of Linear Momentum
• The total momentum of a system composed
of many particles is simply the vector sum of
the individual momentum of each particle.
• An isolated system is one in which the only
forces present are those between the objects
of the system.
• It follows from Newton’s 3rd law that the
total momentum of an isolated system of
bodies remains constant.
Quantitative Problems
1) A 13 gram bullet traveling 230 m/s penetrates
a 2.0 kg block of wood and emerges going 170
m/s. If the block is stationary on a frictionless
surface when hit, how fast does it move after
the bullet emerges?
2) A spacecraft moving at 10 km/s breaks apart
into 2 pieces of equal mass, one of which
moves off at 4 km/s in a direction opposite to
the original direction. Find the speed and
direction of the other piece.
3) An astronaut outside an orbiting space craft
uses a pistol that ejects a gas in order to
maneuver in space. Suppose the astronaut in her
space suit have a total mass of 100 kg and the
pistol ejects 12 gm of gas per second at a speed
of 650 m/s. How long should the astronaut
operate the pistol in order to have a speed of 1
m/s?
Collisions
• Important: Momentum is always conserved in all
collisions! Not energy or kinetic energy!!
• Elastic collision - one where total kinetic energy
is conserved.
• Inelastic collision - one where total kinetic energy
is not conserved.
• Completely inelastic collision - one in which the
colliding bodies stick together after the collision.
Conceptual Question
1) In an elastic collision
____ a) momentum is conserved but not KE
____ b) KE is conserved but not momentum
____ c) momentum and KE are both conserved
____ d) neither momentum nor KE is conserved
Quantitative Problems
1) A pair of bumper cars collide elastically as one
approaches the other directly from the rear. One has
a mass of 450 kg and the other 550 kg. If the lighter
one approaches at 4.5 m/s and other is moving at 3.7
m/s, calculate (a) their velocities after the collision,
and (b) the change in momentum of each.
2) A 30 kg girl who is running at 3 m/s jumps on a
stationary 10 kg sled on a frozen lake. How fast
does the sled then move?
3) Two people, one of mass 75 kg and the other of
mass 60 kg, sit in a rowboat of mass 80 kg. With
the boat initially at rest, the two people, who have
been sitting at opposite ends of the boat 2.0 m
apart from each other, now exchange seats. How
far and in what direction will the boat move?
(Hint: it can be shown that the net force acting on
a system of particles equals the total mass times
the acceleration of the center of mass: F  Macm )
Collisions in Higher Dimensions
• When a collision between 2 objects is not head
on (called a glancing collision), the collision
becomes 2- or 3-dimensional.
• Since momentum is a vector quantity, for these
glancing collisions, each component of
momentum must be individually conserved:
p1x  p2 x  p1x  p2 x
p1 y  p2 y  p1y  p2 y
p1z  p2 z  p1z  p2 z
• If collisions are also elastic, then the total
kinetic energy is also conserved:
KE1  KE2  KE1  KE2
Conceptual Problem
Two identical balls moving with the same speed
towards each other along the x-axis suffer a
glancing collision. After the collision,
____ a) they bounce back and move along the xaxis.
____ b) they must necessarily stick together and
stop moving.
____ c) they can move off in any direction but
must have equal and opposite velocities.
____ d) not enough information is given.
Quantitative Problems
1) Two shuffleboard disks of equal mass, one
orange and the other yellow, are involved in a
perfectly elastic glancing collision. The yellow
disk is initially at rest and is struck by the orange
disk moving with a speed of 5 m/s. After the
collision, the orange disk moves along a
direction that makes an angle of 37 with its
initial direction of motion and the velocity of the
yellow disk is perpendicular to that of the orange
disk (after the collision. Determine the final
speed of each disk.
2) After a completely inelastic collision, two
objects of the same mass and same initial
speed are found to move away together at
half their initial speed. Find the angle
between the initial velocities of the objects.