Chapter 9 Momentum & Its Conservation

Determining Impulse F = ma a =  v/  t

Thus F = m  v/  t or F  t = m  v

Impulse The product of a force times the amount of time the force is applied. F  t

Determining Momentum  v = v f – v i thus m  v = mv f – mv i

Momentum (p) The product of mass times velocity p = mv

Change in Momentum  p = m  v

F  t = m  v Impulse = momentum change

F  t = m  v = mv f - mv i = p f - p i

The Equation below is called the Impulse- Momentum Theorem F  t = p f - p i

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 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, p i, p f,  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 kg block accelerates for 10.0 s down a 37 o incline with a frictional coefficient of 0.25

Conservation of Momentum In a closed system, momentum is conserved p f = p i or p 1 = p 2

Conservation of Momentum In collisions, momentum is conserved (p 1 + p 2 ) b = ( p 1 + p 2 ) a

Book Notation of Momentum (p 1 + p 2 ) b = ( p 1 + p 2 ) a (p A + p B ) 1 = ( p A + p B ) 2 p A1 + p B 1 = p A2 + p B 2

Book Notation of Momentum p A1 + p B 1 = p A2 + p B 2 m A v A1 + m B v B1 = m A v A2 + m B v B2

Collision Momentum m A v A + m B v B = m A v A ’ + m B v B ’

A 200. Mg freight car moving at 2.5 m/s collides with the same sized car at rest where they remain connected. Calculate v f :

A 125 g hockey puck moving at 40.0 m/s is caught in a glove by a 75 kg goalie. Calculate v f 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 v f 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 v f 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 v f 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 v f 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 v f 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 v f of the ball.

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

Explosion Momentum p A = p B p B = 0 thus p A = 0

Explosion Momentum The summation of all parts after the explosion = 0

Explosion Momentum m A v A + m B v B + etc = 0

Explosion Momentum with only 2 parts m A v A + m B v B = 0

Explosion Momentum with only 2 parts m A v A = -m B v B

A 50.0 kg gun fired a 150 g bullet at m/s. Calculate the recoil velocity of the gun.

Drill: A Mg cannon fired a 150 kg projectile at 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: v i, 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: v i, 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 30 o angle from the path at 50.0 m/s. Calculate v f 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 v i, v f, & t air of the 10 kg ball.