Download ch9 Momentum

11/21/2011
Momentum
• Momentum: p = mv
• Units are kg(m/s): no derived units
• A vector quantity: same direction as velocity
Momentum and Collisions
Phy 121
v=2m/s
From Newton’s 2nd
Collisions
• Impulse: I=ΣF Δt
• Units are same as
momentum
• Impulse causes a
change in momentum
• What happens to ΣF
with
ΣF = ma
∆v
ΣF = m
∆t
ΣF ( ∆t ) = m( ∆v )
ΣF ( ∆t ) = mv2 − mv1
p= 3 kg (2m/s)
• Elastic
– Momentum is Conserved
– Kinetic Energy is Conserved
• Inelastic
– Momentum is Conserved
– Kinetic Energy is NOT Conserved
– Small Δt?
– Large Δt?
ΣF ( ∆t ) = ∆p
Graphs
• the impulse
• the final velocity if
initially at rest
• the final velocity if initial
velocity is –2.00 m/s.
Multiple Plans
• Draw a MD
Force vs Time for a Moving Cart
4.5
4
– What new motion
equation can you add?
3.5
3
Force (N)
A force is acting in the
x-direction on a 4.00kg particle. The force
varies in time and is
shown on the graph.
Find:
Problem Solving
2.5
• Draw a FBD
2
1.5
1
0.5
0
0
5
10
Time (sec)
15
20
– What new equation do
we have that relates
force and motion?
• A 0.500-kg football is
thrown toward the east
with a speed of 15.0
m/s. A stationary
receiver catches the ball
and brings it to rest in
0.020 0 s.
• What is the average
force exerted on the
receiver?
Ans: F avg = 375 N
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11/21/2011
Problem Solving: …..this way
Problem Solving: solve this way or…
Multiple Plans
• Draw a MD
Multiple Plans
• Draw a MD
– What new motion
equation can you add?
• Draw a FBD
x=0
t=0
v=15 m/s
– What new motion
equation can you add?
x=
t=
0
• Draw a FBD
a=
– What new equation do
we have that relates
force and motion?
– What new equation do
we have that relates
force and motion?
Impulse --- Momentum
equation
− nhand on football ∆t = m∆v
− nhand on football = ma x
Ans: F avg = 375 N
Ans: F avg = 375 N
Problem in 2-D
Collision
• Momentum always
conserved
– Do this first
– Remember it is a vector
• Kinetic Energy conserved in
elastic collision
– Check this next
Conservation of Momentum
A billiard ball moving at 5.00
m/s strikes a stationary
ball of the same mass.
After the collision, the first
ball moves at 4.2 m/s at an
angle of 30° with respect
to the original line of
motion.
• Find the velocity
(magnitude and direction)
of the second ball after
collision.
• Was the collision inelastic or
elastic?
Motion
Momentum
Momentum (x)
Momentum (y)
Mass 1: Initial
5 m/s
Mass 2: Initial
0 m/s
Mass 1: Final
4.2 m/s at 30°
Mass 2: Final
Conserve
Momentum
Conservation of Momentum
Assume 0.5 kg balls
Motion
Momentum
Momentum (x)
Momentum (y)
Mass 1: Initial
5 m/s
2.5 kgm/s to the
right
+2.5 kgm/s
0
Mass 2: Initial
0 m/s
0
0
0
Mass 1: Final
4.2 m/s at 30°
2.1 kgm/s at 30°
+2.1 cos30° =
1.82 kgm/s
+2.1 sin30° =
1.05 kgm/s
Mass 2: Final
unknown
Conserve
Momentum
px
py
2.5 + 0 = 1.82 + px
Px = +0.68
0 = 1.05 + py
Py=-1.05
Use pythagorean equation to get p=1.25 kgm/s @57 degrees below +x axis.
Use p=mv to get final vel of Mass 2: v=2.5 kgm/s @57 degrees below +x axis
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