Pp Conservation Of Momentum

Conservation of Momentum This is used whenever things collide or there is an explosion

Collisions can be .....

massive big

medium

small tiny

The facts : Momentum = mass x velocity p = m.v total of momentum beforebefore a collision is equal the The sum the momentum a collision is to equal total to themomentum sum of theafterwards momentum afterwards as long as no external forces act. m1 . u1 + m2 . u2 = m1 . v1 + m2 . v2 u = velocity before collision v = velocity after collision

After

Before

m1u1

mm2u1v2 1

m2v2

m1 . u1 + m2 . u2 = m1 . v1 + m2 . v2 u = velocity before collision v = velocity after collision

The weight of a skater acts down through her centre of gravity The reaction caused by the ice bending acts up where the skate touches the ice We can now forget about them as they are equal and opposite

Abigail is gliding towards Beatrice at 3 m/s. When they collide Abigail stops. What happens to Beatrice ? m20x. u m10x. v01 + m m . u31 + 40 402 v. v2 40 02 = 40 120 1 x 40 v = 120

3 m/s

40 kg

0 m/s

40 kg

= 3 m/s

Beatrice’s velocity afterwards = v

Now Abigail is gliding towards Beatrice at 4 m/s. When they collide Abigail and Beatrice partner up. What is their combined velocity after the collision? m20x. u02 = 40 m1 v. v1 80 m . u41 + 40 40 40 + vm 160 2 .vv2 1 x 80 v = 160

4 m/s

0 m/s

= 2 m/s

Afterwards v=?

40 kg

40 kg

Afterwards at 0.75 m/s toeach the right. Abigail and Beatrice Beatrice travels are gliding towards other What is Abigail’s velocity at 3 m/s and 2 m/s. Whatthen? is their total momentum ? 40 momentum x -2 = 120 –after No external forces 80 == 40 kg m/s Momentum = 40 x act 3 + so -

x 0.75 +10 40 = 40.v + 4030 40 v = 10

3 m/s

40 kg

= 0.25 m/s 2 m/s 0.75 m/s

v=?

40 kg

40 kg

40 kg

The full collision looks like this: m1 = m2 = 40 kg u1 = 3 m/s u2 = -2 m/s v1 = 0.75 m/s v2 = 0.25 m/s 40 x 3 + 40 x -2 = 40 x 0.75 + 40 *0.25 120

-

80

=

30

+

10

A thermal neutron travelling at 2 200 m/s strikes a stationary Uranium 235 nucleus and is absorbed. What is the velocity of the combination afterwards? m1 . u1 + m2 . u2 = m1 . v1 + m2 . v2 1 x 2 200 + 235 x 0 = 1 v + 235 v 2 200 = 236 v v = 2 200 / 236 = 9.32 m/s

A 10 kg cannon ball is fired by a 400 kg cannon. If the gun recoils at 2 m/s, how fast does the cannon ball leave the barrel? m1 . u1 + m2 . u2 = m1 . v1 + m2 . v2 10 x 0 + 400 x 0 = 10 v + 400 x 2 0 = 10 v + 800 10 v = - 800 v = - 800 / 10 = - 80 m/s

2 m/s

80 m/s

What is an external force? Reaction and action forces are on different object During the collision energy Is either put in or taken energy out For example in a car accident: If the engine is still driving the wheels, energy is put in If the brakes are on, energy is being taken out Both are external forces so the law does not work

So what is an internal force? Both the action and reaction are on the same object

Action

Reaction

= The law will work

Driver pulling on steering wheel

Friction on seat

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