PHYSICSPHYSICS

Further Mechanics

Andres IgeaFriday 19th October 2012

Further MechanicsFurther MechanicsLinear MomentumConservation of Linear MomentumTarget checkElastic and Inelastic Collisions in

one dimensionTarget checkTwo-dimensional collisionsApplicationsResources

Linear MomentumLinear MomentumThe linear momentum of a

particle of mass m and velocity v is defined as:

The linear momentum is a vector quantity. Its direction is along v.

vmp

Conservation of Linear Conservation of Linear MomentumMomentum

1, 2, 1, 2,

constant

or:

i f

i i f f

p p

p p

p p p p

Target checkTarget checkA 2kg marble travels to the right at

0.4 m/s, on a smooth, level surface. It collides head-on with a 6kg marble moving to the left at 0.2 m/s. After the collision, the 2 kg marble rebounds at 0.1 m/s.

Task: Find the velocity of the 6kg marble

after the collision. Why are the marbles so

heavy ?

Elastic and Inelastic Elastic and Inelastic Collisions in one dimensionCollisions in one dimensionMomentum is conserved in any

collision, elastic and inelastic.Mechanical Energy is only

conserved in elastic collisions.

Perfectly inelastic collision: After colliding, particles coalesce (stick together). There is a loss of energy.

Elastic collision: Particles bounce off each other without loss of energy.

Inelastic collision: Particles collide with some loss of energy (deformation), but don’t coalesce.

Perfectly inelastic collision of Perfectly inelastic collision of two particles two particles

Notice that p and v are are vector quantities

and, thus have a direction (+/-).

There is a loss in energy Eloss

fii

fi

vmmvmvm

pp

)( 212211

lossfii

flossi

Evmmvmvm

KEK

221

222

211 )(

2

1

2

1

2

1

Elastic collision of two Elastic collision of two particlesparticlesMomentum is conserved

Energy is conserved

ffii vmvmvmvm 22112211

222

211

222

211 2

1

2

1

2

1

2

1ffii vmvmvmvm

Target checkTarget check A bullet (m = 0.01kg) is fired into a block (0.1 kg) sitting

at the edge of a table. The block (with the embedded bullet) flies off the table (h = 1.2 m) and lands on the floor 2 m away from the edge of the table.

a.) What was the speed of the bullet?b.) What was the energy loss in the bullet-block collision?

vb = ?

h = 1.2 m

x = 2 m

Two-dimensional collisions Two-dimensional collisions

Two particles:Conservation of momentum:

1 1 2 2 1 1 2 2

i f

i i f f

p p

m v m v m v m v

Split into components:

, ,

1 1 2 2 1 1 2 2

, ,

1 1 2 2 1 1 2 2

x i x f

ix ix fx fx

y i y f

iy iy fy fy

p p

m v m v m v m v

p p

m v m v m v m v

ApplicationsApplicationsConservation of momentum: Rocket being launched into

space.

Rocket gains momentum in the upwards direction

The hot gases gain momentum in the downwards direction

ResourcesResourcesAQA Mechanics 1 book

EDEXCEL Physics A2 Textbook

www.physicsclassroom.com

www.nasa.gov

Thanks a lot for Thanks a lot for watchingwatching

Andres