# Chapter 9 - PowerPoint PPT Presentation

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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

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## Chapter 9

Momentum & Its Conservation

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

Dv = vf – vi

thus

mDv = mvf – mvi

### Momentum (p)

• The product of mass times velocity

• p = mv

Dp = mDv

### FDt = mDv

• Impulse = momentum change

### 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.

### 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

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.

### 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.

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.

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 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.