Download Psc CH-09 Momentum

Chapter 9
Momentum &
Its Conservation
Determining Impulse
F = ma
a = Dv/Dt
Thus
F = mDv/Dt or
FDt = mDv
Impulse
•The product of a force
times the amount of time
the force is applied.
•FDt
Determining Momentum
Dv = vf – vi
thus
mDv = mvf – mvi
Momentum (p)
•The product of mass
times velocity
•p = mv
Change in
Momentum
Dp = mDv
FDt = mDv
•Impulse =
momentum
change
FDt = mDv
= mvf - mvi
= pf - pi
The Equation below is
called the ImpulseMomentum Theorem
FDt = pf - pi
A 750 kg car is traveling
east at 180 km/hr.
Calculate the magnitude
& direction of its
momentum.
A 250 kg car is traveling
east at 360 km/hr.
Calculate the magnitude
& direction of its
momentum.
A 250 kg car collides with
a 10.0 Mg shed & remains
in contact with the shed for
0.500 s. Calculate the force
of the collision & the
impulse imparted onto the
shed.
Drill: A force of 25 N
is applied to a 5.0 kg
object for 5.0
seconds. Calculate:
impulse, Dp & Dv:
A force of 75 N is
applied to a 5.0 kg
object for 15.0
seconds. Calculate:
impulse, Dp & Dv:
A 250 kg sled is
accelerated from 6.0
m/s to 18 m/s over
120 s. Calculate: a, pi,
pf, Dp, & impulse
A 150 g ball pitched at
40.0 m/s is batted in the
opposite direction at
40.0 m/s. Calculate: Dp,
& impulse
Drill: A 60.0 kg man
drives his car into a tree
at 25 m/s. The car
comes to rest in 0.20 s.
Calculate: Dp & F on
the man.
Calculate the momentum
change when a 100.0 kg
block accelerates for 10.0 s
o
down a 37 incline with a
frictional coefficient of
0.25
Conservation of Momentum
•In a closed system,
momentum is
conserved
•pf = pi or p1 = p2
Conservation of Momentum
• In collisions,
momentum is
conserved
•(p1 + p2)b = (p1 + p2)a
Book Notation of Momentum
(p1 + p2)b = (p1 + p2)a
(pA + pB)1 = (pA + pB)2
pA1 + pB1 = pA2 + pB2
Book Notation of Momentum
pA1 + pB1 = pA2 + pB2
mAvA1 + mBvB1 =
mAvA2 + mBvB2
Collision Momentum
mAvA + mBvB =
mAvA’ + mBvB’
A 200. Mg freight car
moving at 2.5 m/s
collides with the same
sized car at rest where
they remain connected.
Calculate vf:
A 125 g hockey puck
moving at 40.0 m/s is
caught in a glove by a
75 kg goalie. Calculate
vf of the goalie.
A 35 g bullet strikes a
2.5 kg stationary block
at 750 m/s. The bullet
exits the block at 350
m/s.Calculate vf of the
block.
A 250 g ball at 4.0 m/s
collides head on with a
1.0 kg ball 2.0 m/s. the
250 g ball bounced
backwards at 5.0 m/s.
Calculate vf of the other.
Drill: A 750 g ball at 4.0
m/s collides head on with a
1.0 kg ball 5.0 m/s. The
750 g ball bounced
backwards at 8.0 m/s.
Calculate vf of the other.
A 25 g ball at 40.0 m/s
collides head on with a
2.0 kg ball 2.0 m/s. the
25 g ball bounced
backwards at 50.0 m/s.
Calculate vf of the other.
A 250 g ball at 4.0 m/s
collides head on with a
2.0 kg ball 5.0 m/s. the
250 g ball bounced
backwards at 40.0 m/s.
Calculate vf of the other.
A 1.0 kg bat swung at
50.0 m/s strikes a 250 g
ball thrown at 40.0 m/s.
The bat continues at
10.0 m/s. Calculate vf of
the ball.
Explosion Momentum
• The momentum before the
explosion must = the
momentum after the explosion.
• The momentum before the
explosion = 0
Explosion Momentum
•pA = pB
•pB = 0 thus
•pA = 0
Explosion Momentum
•The summation of
all parts after the
explosion = 0
Explosion Momentum
mAvA + mBvB +
etc = 0
Explosion Momentum
with only 2 parts
mAvA + mBvB
=0
Explosion Momentum
with only 2 parts
mAvA = -mBvB
A 50.0 kg gun fired
a 150 g bullet at
500.0 m/s.
Calculate the recoil
velocity of the gun.
Drill: A 500.0 Mg
cannon fired a 150 kg
projectile at 1500.0 m/s.
Calculate the recoil
velocity of the gun.
A 250 g cart is connected
to a 1.5 kg cart. When
disconnected, a
compressed spring pushes
the smaller cart 4.0 m/s
east. Calculate the
velocity of the larger cart.
A 2.0 kg block is tied to a
1.5 kg block. When
untied, a compressed
spring pushes the larger
block 6.0 m/s east. mblock
= 0.25 Calculate: vi, a, t, d
for the smaller block
A 5.0 kg block is tied to a
2.0 kg block. When
untied, a compressed
spring pushes the larger
block 1.0 m/s east. mblock
= 0.20 Calculate: vi, a, t, d
for the smaller block
Two Dimensional
Collisions
A 5.0 kg ball moving at
40.0 m/s collides with a
stationary 2.0 kg. The 2.0
o
kg ball bounced at a 30
angle from the path at 50.0
m/s. Calculate vf of the
other.
A 2.0 kg ball is dropped from
a 14.7 m high ledge collides
with a stationary 10.0 kg ball
hanging at a height of 9.8 m.
The 2.0 kg ball bounced
straight up at 4.9 m/s.
Calculate vi, vf, & tair of the 10
kg ball.