From Earth to Space
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Transcript of From Earth to Space
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