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Linear Mom
entum
5-1 Linear Momentum
Linear Momentum, p – defined as mass x velocity
The unit is kg·m/s
A quantity used in collisions
So a small object with a large velocity could have the same momentum as a large object with a small velocity
vmp
9-1 Linear Momentum
5.2 Momentum and Newton’s Second Law
Newton’s Second Law is
This is only true for objects with a constant mass
The original form of the equation was
This statement is true even if the mass varies
amF
5.2 Momentum and Newton’s Second Law
t
pF
5.3 Impulse
A baseball player hits a pitch
Bat delivers an impulse
We actually only
consider average force
Impulse is define as
5.3 Impulse
ptF
An increase in time produces a decreases in force
A decrease in time produces an increase in force
5.3 Impulse
Airbag
5.4 Conservation of Linear Momentum
If no net external force is applied to a system
Then momentum is conserved
5.4 Conservation of Linear Momentum
pp
0
External Forces will result in a change in momentum, so no conservation
1.Force added in
2.Force removed
5.4 Conservation of Linear Momentum
Shuttle Launch
5.5 Inelastic Collisions
Inelastic collision – momentum is conserved, but energy is lost
Momentum is conserved
5.5 Inelastic Collisions
pp
0
BBAABBAA vmvmvmvm 00
Completely (or perfectly) Inelastic collision – two objects collide and stick together
5.5 Inelastic Collisions
vmmvmvm BABBAA )(00
Example: On a touchdown attempt, a 95 kg running back runs toward the end zone at 3.75 m/s. A 111kg linebacker moving at 4.10 m/s meets the runner in a head on collision. If the two players stick together what is their velocity immediately after the collision?
5.5 Inelastic Collisions
smv
v
48.0
)11195()10.4)(111()75.3)(95(
vmmvmvm BABBAA )(00
If the collision occurs in two dimensions
We need to consider the x
and y axis separately
5.5 Inelastic Collisions
xBABBAA vmmvmvmxx
)(00
yBABBAA vmmvmvmyy
)(00
Then we use vector addition to calculate the magnitude and velocity.
5.5 Inelastic Collisions
x
y
yx
v
v
vvv
1
22
tan
Example: A 950kg car traveling east at 16m/s collides with a 1300 kg car traveling north at 21 m/s. If the collision is completely inelastic, what is the magnitude and direction of the cars’ velocity after the collision?
5.5 Inelastic Collisions
smv
v
x
x
/76.6
)1300950()0)(1300()16)(950(
smvx /76.6
smv
v
y
y
/1.12
)1300950()21)(1300()0)(950(
smvy /1.12
x
y
yx
v
v
vvv
1
22
tan
o
smv
8.6076.6
1.12tan
9.131.1276.6
1
22
xBABBAA vmmvmvmxx
)(00
yBABBAA vmmvmvmyy
)(00
5.6 Elastic Collisions
Elastic collision – two objects collide and bounce apart
Elastic Collisions
Momentum is conserved
Kinetic energy is conserved too
5.5 Elastic Collisions
BBAABBAA vmvmvmvm 00
2212
212
212
21
00 BBAABBAA vmvmvmvm
A 10 kg car moving at 2 m/s runs into a 5 kg car that is parked. What is the velocity of each car after the collision?
5.5 Elastic Collisions
BBAABBAA vmvmvmvm 00
2212
212
212
21
00 BBAABBAA vmvmvmvm
BA vv 510)0)(5()2)(10( BA vv 51020
2212
212
212
21 )5()10()0)(5()2)(10( BA vv 2222 )5()10()0)(5()2)(10( BA vv 22 51040 BA vv
A 10 kg car moving at 2 m/s runs into a 5 kg car that is parked. What is the velocity of each car after the collision?
5.5 Elastic Collisions
BA vv 51020
22 51040 BA vv
BA vv 5.2
22 5)5.2(1040 BB vv
A 10 kg car moving at 2 m/s runs into a 5 kg car that is parked. What is the velocity of each car after the collision?
5.5 Elastic Collisions
BA vv 5.2 22 5)5.2(1040 BB vv
22 5)4225(.1040 BBB vvv 22 540205.240 BBB vvv
BB vv 205.70 2
A 10 kg car moving at 2 m/s runs into a 5 kg car that is parked. What is the velocity of each car after the collision?
Confirm
5.5 Elastic Collisions
BB vv 205.70 2
sm
Bv 67.2
BA vv 51020 )67.2(51020 Av sm
Av 67.0
22 51040 BA vv 1.40)67.2(5)67.0(10 22
5.7 Center of Mass
The point where the system can be balanced in a uniform gravitational field
Uniform objects
center of mass is in the
center
5.7 Center of Mass
Motion of CM
Center of mass ofTriangle
Center of mass is not always in the object
Objects balance if supported at their center of mass
5.7 Center of Mass