Download File - DEHS Physics

Chapter 9: Linear Momentum &
Collisions
WICKED FACE PUNCH!!!
Coffee?
9.1 – Linear Momentum
• Linear momentum is defined as the product of
an objects mass (m) and velocity (v).
• Units = kg·m/s
• Momentum is a vector, with it’s direction in
the same direction as the velocity.
Change in Momentum
Initial p
Beanie Baby
Rubber Ball
Final p
Example 9.1
Riddle Me This…
Consider the following objects:
(1) an electron (m = 9.1 × 1031 kg, v = 5.0 × 107 m/s)
(2) the Hubble Space Telescope (m = 1.1 × 104 kg, v = 7.6 × 103 m/s)
(3) a snail (m = 0.02 kg, v = 0.0003 m/s)
(4) the largest super oil tanker (m = 1.5 × 108 kg, v = 2.0 m/s)
(5) a falling rain drop (m = 0.0002 kg, v = 9.5 m/s)
Which one of these objects requires the greatest change in momentum to
stop moving?
a) 1
b) 2
c) 3
d) 4
e) 5
ConcepTest 9.1 Rolling in the Rain
An open cart rolls along a
frictionless track while it is
raining. As it rolls, what
happens to the speed of the
cart as the rain collects in it?
(Assume that the rain falls
vertically into the box.)
a) speeds up
b) maintains constant speed
c) slows down
d) stops immediately
ConcepTest 9.1 Rolling in the Rain
An open cart rolls along a
frictionless track while it is
raining. As it rolls, what
happens to the speed of the
cart as the rain collects in it?
(Assume that the rain falls
vertically into the box.)
a) speeds up
b) maintains constant speed
c) slows down
d) stops immediately
Because the rain falls in vertically, it adds
no momentum to the box, thus the box’s
momentum is conserved. However,
because the mass of the box slowly
increases with the added rain, its velocity
has to decrease.
Follow-up: What happens to the cart when it stops raining?
9.2 – Momentum & Newton’s Second
Law
• Newton’s Second Law
• This version of Newton’s second law is only
valid when objects have constant mass!
• General version of Newton’s Second Law
9.3 - Impulse
Elastic vs Inelastic Collisions
• Elastic Collision
– Momentum is conserved.
– Kinetic Energy is conserved.
• Inelastic Collision
– Momentum is conserved.
– Kinetic Energy is NOT
conserved
9.3 - Impulse
• Impulse (I) is defined as the product of:
– Average force (Fav) applied to an object.
– Time duration (Δt) that force is being applied.
• Impulse is equal to the change in momentum.
(Momentum-Impulse Theorem)
9.3 Impulse
• SI Units for Impulse
N·s = kg·m/s
• Remember, Impulse is a vector!
9.3 - Impulse
• Therefore,
the same
change in momentum may
be produced by a large
force acting for a short time,
or by a smaller force acting
for a longer time.
9.3 - Impulse
Jumping For Joy
Jumping For Joy
Given Information
• Our contestant has a mass
of 72 kg.
• Jump results in an upward
speed of 2.1 m/s.
Requested Information
(A) What is the impulse
experienced by the
contestant?
(B) What additional average
upward force does the
floor exert if the contestant
pushes down for 0.36
seconds during the jump?
9.4 – Conservation of Linear
Momentum
• Linear Momentum is a conserved quantity.
• Formally: if the net force acting on an object is
zero, its momentum is conserved.
Internal vs External Forces
Internal Forces
• Act between objects within
the system.
• Come in action-reaction
pairs (aka Newton’s Second
Law)
• Always sum to zero.
• May change the momenta
of components within the
system, but the system’s
momentum does not
change.
External Forces
• May or may not sum to
zero.
• Only an external force can
change the moment of an
object.
9.4 – Conservation of Linear
Momentum
An example of internal forces moving components of a system:
Example 9-3
Given Information
• Person from canoe 1 pushes
on canoe 2 with a force of
46 N.
• Mass of canoe 1 &
occupants is 130 kg.
• Mass of canoe 2 &
occupants is 250 kg.
(pg 264-265)
Requested Information
• Find the momentum of
each canoe after 1.20
seconds of pushing.
9.5 – Inelastic Collisions
• Collision?
– Two or more objects strike each other.
– Fext is negligibly small.
• Inelastic Collisions
– Momentum is conserved.
– Kinetic Energy is NOT conserved.
• Completely Inelastic Collisions
– Objects stick together after collision.
Inelastic Collision in 1-D
Before
After
Example 9-5
Find the height the pendulum rises in terms of variables.
Inelastic Collisions in 2-D
• Must conserve momentum component by
component.
Example 9-6
• Given Information
–
–
–
–
m1 = 950 kg
v1i = 16 m/s
m2 = 1300 kg
v2i = 21 m/s
• Requested Information
– Find the speed and
direction of vehicles just
after collision. (Assume
completely inelastic).
9.6 – Elastic Collisions
• In elastic collisions
– Momentum is conserved
– Kinetic Energy is
conserved
Cons. Of Momentum
Cons. Of Kinetic Energy
Momentum rewritten…
Kinetic Energy rewritten…
Recall…
Rearrange…
Example 9-7
• Given Information
–
–
–
–
–
–
m1 = .130 kg
v1i = 1.11 m/s
m2 = .160 kg
v2i = 1.21 m/s
v2f = 1.16 m/s
Θ = 42°
• Requested Information
– v1f = ?
– Φ=?
9.7 – Center of Mass
• Center of mass of a
system is the point
where the system can
be balanced in a
uniform gravitational
field.
• “Average location of a
system’s mass.”
9.7 – Center of Mass
Xcm for multiple objects…
Ycm for multiple objects…
Motion of the Center of Mass
Velocity of the Center of Mass
• Acceleration of the Center
of Mass
• What is the result of a force
acting on the center of
mass?
Fnet,ext = Macm