2.4 understanding momentum

Chapter 2 Forces and Motion

2.4 Understanding Momentum


• http://www.youtube.com/watch?v=T9lehHxv-C8

http://www.youtube.com/watch?v=T9lehHxv-C8

http://www.youtube.com/watch?v=T9lehHxv-C8


• Every moving object has momentum.• Momentum can be thought as the

tendency of an object to keep on moving with the same speed in the same direction.

• Momentum and inertia are quite connected. (momentum only found in moving object)

• Momentum often indicates the difficulty a moving object has in stopping. A fast-moving car has more momentum than a slower one of the same mass.

2.4 Understanding MomentumDifference between

INERTIA and MOMENTUM Inertia it is the tendency of body to resist

any change in its motion. Eg: A body at rest will be at rest until a force has been applied ........... mass is measure of inertia

Momentum product of mass and velocity, so for deciding momentum velocity also plays a role. Eg: It is easier to stop a cycle rather than a massive car ......... it has the same tendency as inertia

2.4 Understanding Momentum• If an object is moving in a straight

line, we say that it has linear momentum.

• The amount of linear momentum of the object depends on its mass and velocity.

We define linear momentum as the product of mass and velocity:Momentum = mass x velocity

p = mvWhere m = mass and v =

velocity

kg m s-1

orN s


• Momentum is a vector quantity, the direction of the momentum is the same as the direction of the velocity.

Momentum = mass x velocityp = mv

Where m = mass and v = velocity

kg m s-1

orN s

2.4 Understanding MomentumExampleA billiard ball A of mass 0.5 kg is moving from left to right with a velocity of 2 m s-1 while another billiard ball B of equal mass is moving from right to left with the same speed.


Negative sign shows the object is moving in opposite direction.


http://www.youtube.com/watch?v=qNou0xg3_cY

Principle of Conservation of Momentum




The principle of conservation of momentum states that the total momentum in a closed system is

constant, if no external force acts on the system, that is, the momentum of all objects before

a collision equals the momentum of all objects after a collision.



The principle of conservation of momentum is true for the following: a) Collision of two objects –elastic collision–inelastic collision

b) Explosion



http://phet.colorado.edu/sims/collision-lab/collision-lab_en.html





A collisionThe total momentum of the objects before a collision equals that after the collision.

An explosionThe sum of the

momentums remains as

zero after an explosion.



Elastic CollisionsPrinciple of Conservation of Momentum


Elastic CollisionsPrinciple of Conservation of Momentum

•Momentum is conserved.•Total energy is conserved.•Kinetic energy is conserved.

22112211 vmvmumum


Car A of mass 1000 kg moving at 20 m s-1 collides with Car B of mass 1200 kg moving at 10 m s-1 in the same direction. If the Car B is shunted forwards at 15 m s-1 by the impact, what is the velocity, v, of the Car A immediately after the crash?


2.4 Understanding MomentumPrinciple of Conservation of Momentum

1-B

A

1-B

1-A

B

A

s m 15

?s m 10

s m 20

kg 1200kg 1000

v

vu

u

mm

1-A

A

A

A

BBAABBAA

s m 14

14000100018000100032000

)15(12001000)10(1200)20(1000

v

vvv

vmvmumum


Inelastic CollisionsPrinciple of Conservation of Momentum


Inelastic CollisionsPrinciple of Conservation of Momentum

•Momentum is conserved.•Total energy is conserved.•Kinetic energy is not conserved.the total kinetic energy after the collision is less than the total kinetic energy before the collision.

vmmumum )( 212211


A truck of mass 1200 kg moving at 30 m s-1 collides with a car of mass 1000 kg which is travelling in the opposite direction at 20 m s-1. After the collision, the two vehicles move together. What is the velocity of both vehicles immediately after collision?


2.4 Understanding MomentumPrinciple of Conservation of Momentum

?s m 20

s m 30

kg 1000

kg 1200

1-car

1-lorry

car

lorry

vu

u

m

m

1-

carlorrycarcarlorrylorry

s m 27.7

220016000)10001200()20(1000)30(1200

)(

v

vv

vmmumum


ExplosionMeans the separation of objects which are initially at rest. Before explosion both

object stick together and at rest. After collision, both object move at opposite direction


2211

22110collisionsafter momentum total collisions before momentum total

vmvmvmvm


Example

A rifle of mass 5.0 kg fires a bullet of mass 50 g with a velocity of 20 m s-1. Calculate the recoil velocity. Explain why the recoil velocity of a rifle is much less than the velocity of the bullet.


http://www.youtube.com/watch?v=rY3H5a_gHAc





Solution

1-bullet

bullet

1- rifle

rifle

s m 0

g 50 s m 0

kg 5

u

mu

mBefore fire

1-bullet

bullet

rifle

rifle

s m 80

g 50 ?

kg 5

v

mvmAfter fire

1-rifle

rifle

rifle

rifle

rifle

rifle

bulletbulletrifleriflebulletbulletriflerifle

s m 8.05445

)80(05.05)80(05.050)80(05.05)0(05.0)0(5

v

v

vv

vv

vmvmumum


M(gun) x V(gun) = M(bullet) x V(bullet)

B I G x small = small x B I G

Since the bullet and the gun should have opposite and equal momentum, the velocity

of the bullet is much greater since the mass is much smaller.

Solution


Example

2.4 Understanding MomentumApplication of Conservation of

Momentum

Rockets


Momentum

Water Rockets


Momentum

CO2 car


Conserved = maintain at a constant overall

total.



Closed system = the sum of

external forces acting on the system is zero


2.4 understanding momentum

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