Download AP B Chapter 7

Linear Momentum
Momentum
Linear Momentum of a body is defined as the
product of its mass and its velocity.
 Momentum symbol, ρ (rho), = mv.
 Since velocity is a vector, momentum is also a
vector with its direction being that of the object’s
velocity.
 Units of momentum are derived: kg*m/s
 A fast moving car has more momentum than a
slower moving car of the same mass and a heavy
truck has more momentum than a light car at the
same speed.

Enter Force
A force is required to change the momentum
of an object. Forces can increase, decrease,
or change direction of an object’s
momentum.
 ΣF=Δρ/Δt. The rate of change of momentum
is equal to the net force applied. ΣF= the net
force on the object.
 Δρ is the change in
Momentum and Δt is the
Time interval for the
change.

Deriving force changing momentum

Recall from Newton’s second law: ΣF=ma,
and
 mv  mv0
v
F 
=ma


t

t
m
t
Because a = Δv/Δt we arrive at F=ma. We
have dealt with changes in velocity, but it is
important to note that sometimes MASS can
change, such as a rocket in takeoff burning
fuel!
Conservation of Momentum

Under certain circumstances, momenta is a
conserved quantity. Consider certain types
of collisions…
Changes in momenta
Although the momenta of each ball changes as a
result of the collision, the total momenta of the
system remains constant. This is found by the
sum of the individual momenta.
 m1v1 + m2v2= m1v1’ + m2v2’
 Momentum before = momentum after
 This is a general Law of Conservation of
Momentum and applies for the SYSTEM involved.

Collisions and Impulse
From Newton’s 2nd law: Fnet = rate of change in
momentum (Δρ/Δt) therefore, in a collision a force
exerted over a period of time (Impulse) changes
the momentum of an object (Δmv).
 FΔt = Δρ Impulse = change in momentum
 In a collision, the force between objects is
generally NOT constant. It is often sufficient to
approximate the average force over that time
interval. Ft This impulse is the area under the
curve of a F vs. t graph.

Conservation of Energy and
Momentum in collisions

When objects collide, we can compare energy
before and after collisions. If no damage is done
and no heat is produced, the collision is
considered elastic and the total KE is conserved
as well as the total momentum.
( 1   2 )before  ( 1   2 ) after

At the atomic level, this is common. On the
“macro” level, elastic collisions are rare as thermal
energy, sound, & other forms are produced.
Energy conservation of collisions
The total energy in a collision is ALWAYS
conserved, even when Kinetic energy is not.
 Collisions where KE is NOT conserved are
considered inelastic collisions. These tend
to convert KE to other forms of energy (often
thermal) so we write:

KE1  KE2  KE  KE
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