Impulse and Momentum AP Physics 1.
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Transcript of Impulse and Momentum AP Physics 1.
AP Physics 1
Impulse and Momentum
Momentum
Momentum
The product of a particle’s mass and velocity is called the momentum of the particle:
Momentum is a vector, with units of kg m/s. A particle’s momentum vector can be decomposed into
x- and y-components.
Slide 9-21
The cart’s change of momentum px is
A. –20 kg m/s.B. –10 kg m/s.C. 0 kg m/s.D. 10 kg m/s.E. 30 kg m/s.
QuickCheck 9.1
Slide 9-22
The cart’s change of momentum px is
A. –20 kg m/s.B. –10 kg m/s.C. 0 kg m/s.D. 10 kg m/s.E. 30 kg m/s.
QuickCheck 9.1
px = 10 kg m/s (20 kg m/s) = 30 kg m/s
Negative initial momentum because motion is to the left and vx < 0.
Slide 9-23
Impulse
Impulse = MomentumConsider Newton’s 2nd
Law and the definition of acceleration
Units of Impulse: Units of Momentum:
Momentum is defined as “Inertia in Motion”
NsKg x m/s
Impulse is the AreaSince J=Ft, Impulse is the AREA of a Force vs.
Time graph.
Impulse During a Collision
A large force exerted for a small interval of time is called an impulsive force.
The figure shows a particle with initial velocity .
The particle experiences an impulsive force of short duration t.
The particle leaves with final velocity .
Slide 9-26
Conservation of Momentum
Collisions
A collision is a short-duration interaction between two objects.
The collision between a tennis ball and a racket is quick, but it is not instantaneous.
Notice that the right side of the ball is flattened. It takes time to compress the ball, and more time
for the ball to re-expand as it leaves the racket.
Slide 9-24
Atomic Model of a Collision
Slide 9-25
How about a collision?Consider 2 objects speeding
toward each other. When they collide......
Due to Newton’s 3rd Law the FORCE they exert on each other are EQUAL and OPPOSITE.
The TIMES of impact are also equal.
Therefore, the IMPULSES of the 2 objects colliding are also EQUAL
21
21
2121
)()(JJFtFt
ttFF
How about a collision?If the Impulses are equal
then the MOMENTUMS are also equal!
22221111
222111
2211
21
21
)()(
oo
oo
vmvmvmvmvvmvvm
vmvmppJJ
22112211 vmvmvmvm
pp
oo
afterbefore
A mosquito and a truck have a head-on collision. Splat! Which has a larger change of momentum?
A. The mosquito.
B. The truck.
C. They have the same change of momentum.
D. Can’t say without knowing their initial velocities.
QuickCheck 9.8
Slide 9-60
A mosquito and a truck have a head-on collision. Splat! Which has a larger change of momentum?
A. The mosquito.
B. The truck.
C. They have the same change of momentum.
D. Can’t say without knowing their initial velocities.
QuickCheck 9.8
Momentum is conserved, so pmosquito + ptruck = 0.Equal magnitude (but opposite sign) changes in momentum.
Slide 9-61
Momentum is conserved!The Law of Conservation of Momentum: “In the
absence of an external force (gravity, friction), the total momentum before the collision is equal to the total momentum after the collision.”
smkgpsmkgpsmkgp
smkgp
smkgp
smkgmvp
total
car
truck
totalo
caro
otrucko
/*3300/*18005.4*400
/*15003*500
/*3300
/*800)2)(400(
/*2500)5)(500(
)(
)(
)(
Several Types of collisionsSometimes objects stick together or blow apart.
In this case, momentum is ALWAYS conserved.
2211)(
022011
2211022011
vmvmvmvmvmvmvmvmvmvm
pp
totalototal
totaltotal
afterbefore
When 2 objects collide and DON’T stick
When 2 objects collide and stick together
When 1 object breaks into 2 objects
Elastic Collision = Kinetic Energy is ConservedInelastic Collision = Kinetic Energy is NOT Conserved
Collisions and Explosion
ExampleA bird perched on an 8.00 cm tall swing has a mass of 52.0 g, and the base of the swing has a mass of 153 g. Assume that the swing and bird are originally at rest and that the bird takes off horizontally at 2.00 m/s. If the base can swing freely (without friction) around the pivot, how high will the base of the swing rise above its original level?
How many objects due to have BEFORE the action?
How many objects do you have AFTER the action?
12
swing
swing
ToT
AB
v
vvmvmvm
pp
)2)(052.0()153.0()0)(205.0( )(1
2211
-0.680 m/s
6.19)68.0(
2
21
22
2
)(
hgv
mghmv
UKEE
o
o
swingswingo
AB
0.024 m
Example Granny (m=80 kg) whizzes around the rink with a velocity of 6 m/s. She suddenly collides with Ambrose (m=40 kg) who is at rest directly in her path. Rather than knock him over, she picks him up and continues in motion without "braking." Determine the velocity of Granny and Ambrose.How many objects do I have before the collision?
How many objects do I have after the collision?
2
1
T
T
TToo
ab
vv
vmvmvmpp
120)0)(40()6)(80(2211
4 m/s
Momentum in Two Dimensions
Momentum is conserved only if each component of is conserved:
The total momentum is a vector sum of the momentaof the individual particles.
Slide 9-86
Collisions in 2 DimensionsThe figure to the left shows
a collision between two pucks on an air hockey table. Puck A has a mass of 0.025-kg and is moving along the x-axis with a velocity of +5.5 m/s. It makes a collision with puck B, which has a mass of 0.050-kg and is initially at rest. The collision is NOT head on. After the collision, the two pucks fly apart with angles shown in the drawing. Calculate the speeds of the pucks after the collision.
vA
vB
vAcos
vAsin
vBcosvBsin
Collisions in 2 dimensions
vA
vB
vAcos
vAsin
vBcosvBsin
)37cos)(050(.)65cos)(025(.0)5.5)(025.0( BA
xBBxAAoxBBoxAA
xox
vvvmvmvmvm
pp
BA vv 040.00106.01375.0
AB
AB
BA
yBByAA
yoy
vvvv
vv
vmvm
pp
757.00227.00300.0
)37sin)(050.0()65sin)(025.0(0
0
Collisions in 2 dimensions
AB vv 757.0
smvv
vvvv
A
A
AA
AA
/84.204845.01375.0
03785.00106.01375.0)757.0)(050.0(0106.01375.0
BA vv 040.00106.01375.0
smvB /15.2)84.2(757.0