Chapter 9Momentum &

Its Conservation

Determining Impulse

F = maa = v/t

ThusF = mv/t or

Ft = mv

Impulse•The product of a force times the amount of time

the force is applied.

•Ft

Determining Momentum

v = vf – vi

thus

mv = mvf – mvi

Momentum (p)•The product of mass

times velocity

•p = mv

Change in Momentum

p = mv

Ft = mv•Impulse = momentum

change

Ft = mv = mvf - mvi

= pf - pi

The Equation below is called the Impulse-

Momentum Theorem

Ft = 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, p & v:

A force of 75 N is applied to a 5.0 kg

object for 15.0 seconds. Calculate: impulse, p & v:

A 250 kg sled is accelerated from 6.0 m/s to 18 m/s over

120 s. Calculate: a, pi, pf, p, & impulse

A 150 g ball pitched at 40.0 m/s is batted in the

opposite direction at 40.0 m/s. Calculate: p,

& 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: p & F on

the man.

Calculate the momentum change when a 100.0 kg

block accelerates for 10.0 s down a 37o 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. block = 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. block = 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 kg ball bounced at a 30o

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.