conservation of momentum (in 1d) sph4u. newton’s 3 rd law the force b exerts on a the force a...
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Conservation of Momentum (in 1D)
SPH4U
Newton’s 3rd Law
The force B exerts on A
The force A exerts on B
Newton’s 3rd Law
Newton’s 3rd Law
Note that the time for the interaction must be the same.
Newton’s 3rd Law
Newton’s 3rd Law
BA
BBAA
BB
AA
BBAA
ABBA
pp
vmvm
t
vm
t
vm
amam
FF
The Law of Conservation of Momentum
During an interaction between two objects (where there is no external net force), the change in momentum of the first object is equal in magnitude but opposite in direction to the change in momentum of the second.
Conservation and Impulse: Example
A rubber bullet R and a metal bullet M of equal mass strike a target with the same speed. The metal bullet comes to rest inside the target while the rubber bullet bounces back.
Which exerts a greater impulse on the target?
Conservation and Impulse: Example
A rubber bullet R and a metal bullet M of equal mass strike a target with the same speed. The metal bullet comes to rest inside the target while the rubber bullet bounces back.
Which exerts a greater impulse on the target?
R
Conservation and Impulse: Example
A rubber bullet R and a metal bullet M of equal mass strike a target with the same speed. The metal bullet comes to rest inside the target while the rubber bullet bounces back.
Which exerts a greater impulse on the target?
R – changing the momentum from [fwd] to [back] requires a greater impulse than changing momentum from [fwd] to zero.
Conservation of Momentum
Conservation of Momentum
“Primes” denote the velocity after interaction: v’=v2
Conservation of Momentum
Conservation of Momentum
BBAABBAA
BBBBAAAA
BBBAAA
BBAA
vmvmvmvm
vmvmvmvm
vvmvvm
vmvm
''
''
''
The Law of Conservation of Momentum (Version 2)
During an interaction between two objects (where there is no external net force), the total momentum of the system after is equal to the total momentum of the system before.
BBAABBAA vmvmvmvm ''
Conservation: Example 1
A baseball of mass m leaves a pitching machine off mass M (where M includes the mass of the ball m) with a speed v.
What is the recoil speed of the machine after shooting the baseball?
Conservation: Example 1
A baseball of mass m leaves a pitching machine off mass M (where M includes the mass of the ball m) with a speed v.
What is the recoil speed of the machine after shooting the baseball?
Note that total momentum before is zero.
Conservation: Example 1
Conservation: Example 1
mM
mvv
mvvmM
vmMmv
mM
mM
mM
)(
0)(
Conservation: Example 1
mM
mvv
mvvmM
vmMmv
mM
mM
mM
)(
0)(
Since the question asks for the (positive) speed, we would express this as:
mM
mv
Conservation: Example 2
A student of mass 75 kg is standing on a stationary raft of mass 55 kg. The student then moves toward one end of the raft at a speed of 2.3 m/s [N] relative to the water. Neglecting fluid friction, what is the velocity of the raft relative to the water?
Conservation: Example 2
i.e., 3.1 m/s opposite the direction of motion of the student
sm
r
sm
r
r
ssr
ssrr
rrss
v
kg
kgv
m
vmv
vmvm
vmvm
1.3
55
)3.2)(75(
''
''
0''
Conservation: Example 2
sm
r
sm
r
r
ssr
ssrr
rrss
v
kg
kgv
m
vmv
vmvm
vmvm
1.3
55
)3.2)(75(
''
''
0''
And the velocity of the raft relative to the student is 2.3 m/s + 3.1 m/s [back]
More Practice
Textbook Questions:• p. 243 #5, 6, 7• p. 245 #7
http://www.youtube.com/watch?v=r8E5dUnLmh4