MomentumMomentumDefinition:Definition: MomentumMomentum = = massmass x x velocityvelocity

What has more momentum?What has more momentum?

1.1. a 25 kg artillery shell going 600 m/s,a 25 kg artillery shell going 600 m/s,

2.2. a 900 kg Honda Civic going 50 km/h.a 900 kg Honda Civic going 50 km/h.

vvHCHC = = 50 km/h50 km/h

The artillery shell has more momentum.The artillery shell has more momentum.

= = 13.9 m/s13.9 m/s

ppAA = = (25kg)(600m/s)(25kg)(600m/s) = = 15000 kg·m/s15000 kg·m/s

p = mvp = mv (kg(kg·m/s)·m/s)

ppHCHC = = (900kg)(13.9m/s)(900kg)(13.9m/s) = = 12500 kg·m/s12500 kg·m/s

ImpulseImpulseDefinition:Definition: ImpulseImpulse = = the change in momentumthe change in momentum

(caused by a force)(caused by a force)

ExampleExample::

1.1. A baseball of mass 600 g is thrown towards a batter at 30 m/s A baseball of mass 600 g is thrown towards a batter at 30 m/s and hit back towards the pitcher at 50 m/s. Find the impulse.and hit back towards the pitcher at 50 m/s. Find the impulse.

ΔΔp = mv - mvp = mv - mvoo = = (0.6)(-50) – (0.6)(30)(0.6)(-50) – (0.6)(30)

ΔΔp = mv - mvp = mv - mvoo

30 m/s30 m/s

-50 m/s-50 m/s

= = - 48- 48 kg·m/skg·m/s

The impulse applied to the baseball is 48The impulse applied to the baseball is 48 kg·m/s kg·m/s towards the pitcher.towards the pitcher.

Force & ImpulseForce & ImpulseFF = ma = ma

““Force = the rate of change of momentum”Force = the rate of change of momentum”

FF = m ( = m (v – vv – voo))

ΔΔtt

FF = = mv – mvmv – mvoo

ΔΔtt

FF = = ΔΔpp ΔΔtt

In the previous problem, the bat is in contact with the ball In the previous problem, the bat is in contact with the ball for 0.2 seconds. Find the average force.for 0.2 seconds. Find the average force.

FF = = ΔΔpp ΔΔtt

= = - 48 kg- 48 kg·m/s·m/s 0.2s0.2s

= = - 240 kg- 240 kg·m/s·m/s22

= = - 240 N- 240 N

240 N of force towards the pitcher.240 N of force towards the pitcher.

ExampleExample::

2.2. Rambo fires his AK-48 machine gun. This gun fires 100 bullets per Rambo fires his AK-48 machine gun. This gun fires 100 bullets per minute (each bullet = 175g). Find the average recoil force. The minute (each bullet = 175g). Find the average recoil force. The muzzle velocity is 950m/s.muzzle velocity is 950m/s.

FF = = ΔΔpp ΔΔtt

= = ppff – p – poo

ΔΔtt

ΔΔt t == 60s60s

ppoo == 00

ppff = = mvmv = = 100 (0.175 x 950)100 (0.175 x 950) = = 16600 kg16600 kg·m/s·m/s

FF == 16600 - 016600 - 0 60 60

== 280 N280 N

Note:Note: ΔΔp = Fp = FΔΔtt

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