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Chapter 9. Momentum & Its Conservation. Determining Impulse. F = ma a = D v / D t. Thus. F = m D v / D t or F D t = m D v. Impulse. The product of a force times the amount of time the force is applied. F D t. Determining Momentum. D v = v f – v i thus m D v = m v f – m v i.

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chapter 9

Chapter 9

Momentum & Its Conservation

determining impulse
Determining Impulse

F = ma

a = Dv/Dt

slide3

Thus

F = mDv/Dt or

FDt = mDv

impulse
Impulse
  • The product of a force times the amount of time the force is applied.
  • FDt
determining momentum
Determining Momentum

Dv = vf – vi

thus

mDv = mvf – mvi

momentum p
Momentum (p)
  • The product of mass times velocity
  • p = mv
f d t m d v
FDt = mDv
  • Impulse = momentum change
a 750 kg car is traveling east at 180 km hr calculate the magnitude direction of its momentum
A 750 kg car is traveling east at 180 km/hr. Calculate the magnitude & direction of its momentum.
slide12

A 250 kg car is traveling east at 360 km/hr. Calculate the magnitude & direction of its momentum.

slide13

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.

a force of 25 n is applied to a 5 0 kg object for 5 0 seconds calculate impulse d p d v
A force of 25 N is applied to a 5.0 kg object for 5.0 seconds. Calculate: impulse, Dp & Dv:
slide15

A force of 75 N is applied to a 5.0 kg object for 15.0 seconds. Calculate: impulse, Dp & Dv:

slide17

A 150 g ball pitched at 40.0 m/s is batted in the opposite direction at 40.0 m/s. Calculate: Dp, & impulse

slide18

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.

slide19
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
Conservation of Momentum
  • In a closed system, momentum is conserved
  • pf = pi or p1 = p2
slide21

Conservation of Momentum

  • In collisions, momentum is conserved
  • (p1 + p2)b = (p1 + p2)a
slide22

Book Notation of Momentum

(p1 + p2)b = (p1 + p2)a

(pA + pB)1 = (pA + pB)2

pA1 + pB1 = pA2 + pB2

slide23

Book Notation of Momentum

pA1 + pB1 = pA2 + pB2

mAvA1 + mBvB1 =

mAvA2 + mBvB2

slide24

Collision Momentum

mAvA + mBvB =

mAvA’ + mBvB’

slide25

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:

slide26

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.

slide27

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.

slide28

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.

slide29

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.

slide30

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.

slide31

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.

slide32

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
Explosion Momentum
  • The momentum before the explosion must = the momentum after the explosion.
  • The momentum before the explosion = 0
slide34

Explosion Momentum

  • pA = pB
  • pB = 0 thus
  • pA = 0
slide35

Explosion Momentum

  • The summation of all parts after the explosion = 0
slide36

Explosion Momentum

mAvA + mBvB + etc = 0

slide40

A 500.0 Mg cannon fired a 150 kg projectile at 1500.0 m/s. Calculate the recoil velocity of the gun.

slide41

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.

slide42

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

slide43

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

slide45

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.

slide46

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.

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