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Momentum can be defined as "mass in motion."
All objects have mass; so if an object is moving,
then it has momentum
Momentum depends upon the variables mass and
velocity. In terms of an equation, the momentum
of an object is equal to the mass of the object times
the velocity of the object.
Momentum (p) = mass • velocity
momentum is directly proportional to an object's
mass and directly proportional to the object's
velocity.
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Momentum is a vector quantity
The direction of the momentum vector is the
same as the direction of the velocity of the
object
https://www.youtube.com/watch?v=y2Gb4N
Iv0Xg
Determine the momentum of a ...
a. 60-kg halfback moving eastward at 9 m/s.
b. 1000-kg car moving northward at 20 m/s.
c. 40-kg freshman moving southward at 2 m/s.
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A. p = m*v = 60 kg*9 m/s
p = 540 kg•m/s, east
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B. p = m*v = 1000 kg*20 m/s
p = 20 000 kg•m/s, north
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C. p = m*v = 40 kg*2 m/s
p = 80 kg•m/s, south
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A car possesses 20 000 units of momentum.
What would be the car's new momentum if ...
a. its velocity was doubled.
b. its velocity was tripled.
c. its mass was doubled (by adding more
passengers and a greater load)
d. both its velocity was doubled and its mass was
doubled.
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A. p = 40 000 units (doubling the velocity will
double the momentum)
B. p = 60 000 units (tripling the velocity will
triple the momentum)
C. p = 40 000 units (doubling the mass will
double the momentum)
D. p = 80 000 units (doubling the velocity will
double the momentum and doubling the mass
will also double the momentum; the combined
result is that the momentum is doubled twice quadrupled)
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The more momentum that an object has, the
harder that it is to stop.
To stop an object, it is necessary to apply a
force against its motion for a given period of
time.
As the force acts upon an object for a given
amount of time, the object's velocity is
changed; and therefore, the object's momentum
is changed.
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an unbalanced force always accelerates an
object - either speeding it up or slowing it
down
If the force acts opposite the object's motion, it
slows the object down. If a force acts in the
same direction as the object's motion, then the
force speeds the object up.
Either way, a force will change the velocity of
an object. And if the velocity of the object is
changed, then the momentum of the object is
changed.
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F = m • a (Newton’s second law)
F = m • ∆v / t
If both sides of the above equation are
multiplied by the quantity t, a new equation
results.
F • t = m • ∆v
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F • t = m • ∆v
the force times the time equals the mass times
the change in velocity.
the quantity Force • time is known as impulse
Impulse = Change in momentum
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In a collision, an object experiences a force for a specific
amount of time that results in a change in momentum.
The result of the force acting for the given amount of
time is that the object's mass either speeds up or slows
down (or changes direction). The impulse experienced
by the object equals the change in momentum of the
object. In equation form, F • t = m • Δ v.
In a collision, the impulse experienced by an object is
always equal to the momentum change.
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Vector Diagram
Greatest velocity change?
Greatest acceleration?
Greatest momentum change?
Greatest Impulse?
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a. The velocity change is greatest in case B. The
velocity changes from +30 m/s to -28 m/s. This is
a change of 58 m/s (-) and is greater than in case A
(-15 m/s).
b. The acceleration is greatest in case B.
Acceleration depends on velocity change and the
velocity change is greatest in case B (as stated
above)
c. The momentum change is greatest in case B.
Momentum change depends on velocity change
and the velocity change is greatest in case B (as
stated above).
d. The impulse is greatest in case B. Impulse
equals momentum change and the momentum
change is greatest in case B (as stated above).
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Velocity-Time Graph
Greatest velocity change?
Greatest acceleration?
Greatest momentum change?
Greatest Impulse?
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a. The velocity change is greatest in case A. The v
changes from +5 m/s to -3 m/s. This is a change of
8 m/s (-) and is greater than in case B (-4 m/s).
b. The acceleration is greatest in case A.
Acceleration depends on velocity change and the
velocity change is greatest in case A (as stated
above).
c. The momentum change is greatest in case A.
Momentum change depends on velocity change
and the velocity change is greatest in case A (as
stated above).
d. The impulse is greatest in case A. Impulse
equals momentum change and the momentum
change is greatest in case A (as stated above).
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Ticker Tape Diagram
Greatest velocity change?
Greatest acceleration?
Greatest momentum change?
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a. The velocity change is greatest in case B. In each case
the initial velocity is the same. In case B, the object
rebounds in the opposite direction with a greater speed
than in case A. This is equivalent to a change from +10
m/s to -5 m/s; whereas, case A has a change from +10
m/s to -2 m/s.
b. The acceleration is greatest in case B. Acceleration
depends on velocity change and the velocity change is
greatest in case B (as stated above)
c. The momentum change is greatest in case B.
Momentum change depends on velocity change and
the velocity change is greatest in case B (as stated
above).
d. The impulse is greatest in case B. Impulse equals
momentum change and the momentum change is
greatest in case B (as stated above)
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force and time are inversely proportional; for
the same mass and velocity change, a tenfold
increase in the time of impact corresponds to a
tenfold decrease in the force of impact
mass and force are directly proportional; for
the same time and velocity change, a fivefold
increase in the mass corresponds to a fivefold
increase in the force required to stop that mass
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https://www.youtube.com/watch?v=r8E5dU
nLmh4
https://www.youtube.com/watch?v=yUpiV2I
_IRI
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A 5kg object has a velocity of 8m/s due east.
An unbalanced force acts on the object for 3s
causing it to decrease to 2m/s due east.
Determine the magnitude and direction of the
unbalanced force.
J=∆P
Ft=m∆V
F=-10kg*m/s2 or -10N
west
and direction is to the
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Newton's third law : for every action there is an
equal and opposite reaction
In a collision between two objects, both objects
experience forces that are equal in magnitude and
opposite in direction.
Such forces often cause one object to speed up
(gain momentum) and the other object to slow
down (lose momentum).
The magnitude of the force is equal but the
acceleration of an object is dependent upon both
force and mass so, if the colliding objects have
unequal mass, they will have unequal
accelerations as a result of the contact force that
results during the collision.
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Consider the collision between a moving seven ball
and an eight ball that is at rest in the sport of table
pool. When the seven ball collides with the eight
ball, each ball experiences an equal force directed in
opposite directions. The rightward moving seven
ball experiences a leftward force that causes it to
slow down; the eight ball experiences a rightward
force that causes it to speed up. Since the two balls
have equal masses, they will also experience equal
accelerations. In a collision, there is a force on both
objects that causes an acceleration of both objects;
the forces are equal in magnitude and opposite in
direction. For collisions between equal-mass objects,
each object experiences the same acceleration.
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For a collision occurring between object 1 and
object 2 in an isolated system, the total momentum
of the two objects before the collision is equal to
the total momentum of the two objects after the
collision
the momentum lost by object 1 is equal to the
momentum gained by object 2
The Force is equal and opposite and the time is the
same therefore the impulse is equal but opposite
and therefore momentum is equal but opposite
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A collision in a closed system, the change in
momentum for each mass has the same
magnitude but opposite direction.
Law of conservation of momentum: the total
momentum of the objects in a closed system is
constant.
Pbefore = Pafter
A large truck and a Volkswagen have a headon collision.
a. Which vehicle experiences the greatest force of
impact?
b. Which vehicle experiences the greatest
impulse?
c. Which vehicle experiences the greatest
momentum change?
d. Which vehicle experiences the greatest
acceleration?
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a, b, c: the same for each.
Both the Volkswagon and the large truck
encounter the same force, the same impulse,
and the same momentum change
d: Acceleration is greatest for the
Volkswagon. While the two vehicles
experience the same force, the acceleration is
greatest for the Volkswagon due to its smaller
mass.
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A 3000-kg truck moving with a velocity of 10
m/s hits a 1000-kg parked car. The impact
causes the 1000-kg car to be set in motion at 15
m/s. Assuming that momentum is conserved
during the collision, determine the velocity of
the truck immediately after the collision.
Before Collision
After Collision
Truck
3000 • 10 = 30 000
3000 • v
Car 0
1000 • 15 = 15 000
Total
30 000
30 000
3000*v + 15 000 = 30 000
3000*v = 15 000
v = 5.0 m/s
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A 0.150-kg baseball moving at a speed of 45.0
m/s crosses the plate and strikes the 0.250-kg
catcher's mitt (originally at rest). The catcher's
mitt immediately recoils backwards (at the
same speed as the ball) before the catcher
applies an external force to stop its momentum.
If the catcher's hand is in a relaxed state at the
time of the collision, it can be assumed that no
net external force exists and the law of
momentum conservation applies to the
baseball-catcher's mitt collision. Determine the
post-collision velocity of the mitt and ball.
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0.15 kg • v + 0.25 kg • v = 6.75 kg•m/s
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0.40 kg • v = 6.75 kg•m/s
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v = 16.9 m/s
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A 1kg cart A is initially at rest on a frictionless
air track. A .20kg cart B is moving to the right
at 10m/s. Cart B collides with cart A causing
cart A to move to the right at 3 m/s.
Determine the velocity of cart B after the
collision.
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P after = P before
VBf = -5m/s