Momentum and Impulse: Lesson 3

It`s not how fast you are going: it is how fast you stop

To reduce the impact force, increase the stopping distance or increase the stopping time

( )F t m v

constant

0fv

( ) 27.778 /

(0.10 ) 100 ( 27.8 / )27800 arg ,

f iF t m v v v v m s

F s kg m sF N very l e force exerted onto body result death

What if the driver wears a seatbelt and the car has an airbag? The airbag inflates in 3/100 s so the driver comes to rest in 1.0 s. Determine the impact force now.( )

(1.0 ) 100 ( 27.8 / )

2780 ,

F t m v

F s kg m s

F N less impact force more likely for driver to survive

Eg) The driver of a car has a mass of 100 kg. The car is travelling at 100 km/h. Impact The driver is not wearing a seat belt. It takes 0.10s for the driver to impact onto a concrete wall and stopDetermine the impact force on the driver.

Concrete floor

Very short stopping distance

-High impact forceF(up)

foam

Greater stopping distance, less impact force

ball

ball

If you increase the stopping distance or increase the stopping time, there is less impact force resulting in less injury being sustained

Definition: in an isolated system the total momentum before a collision or interaction is equal to the total momentum after the collision

Total momentum remains constant

Isolated system – is a condition in which there is no exchange of matter of energy

Collision – interaction or contact of two or more objects during a short period of time

Conservation of pmomentum before momentumafter

before afterp p

1. Recoil ProblemsEg) A 500 kg cannon fires an 800 g shell at a

velocity of 700 east. Determine the recoil velocity of the cannon.

AfterBefore

' ' ' '1 1 2 2 1 1 2 2

'1

'1

'1

'11

0 0 500 ( ) .800 (700 / )

0 500 ( ) 560 /

560 / 500 ( )

1.12 /

before afterp p

cannon shell cannon shell

m v m v m v m v

kg v kg m s

kg v kgm s

kgm s kg v

v m s

Eg) A 500 kg cannon fires an 800 g shell at a velocity of 700 east. Determine the recoil velocity of the cannon.

1 1 2 2

1

1

1

500 ( ) 0.800 (700 / )500 ( ) 560 /

1.12 / '

west eastp pcannon shellm v m vkg v kg m skg v kgm s

v m s negative because it s west

Eg) A bomb bursts into two fragments, X and Y. Fragment X has a mass of 0.50 kg and is directed at 240 m/s left. Fragment Y has a mass 3.5 times that of X and moves in the opposite direction. Determine the velocity of Fragment Y.

1 1 2 2

2

2

0.80 (240 / ) 3.5(0.80 )( )69 /

left rightp p

x ym v m v

kg m s kg vv m s