Momentum and
Conservation of Momentum
Which do you think has more momentum?
Momentum
• Momentum is a measure of how hard it is to
stop or turn a moving object.
• What characteristics of an object would make it
hard to stop or turn?
Momentum
• Since momentum is a measure of how difficult
it is to stop or turn a moving object, it is a
function of the object’s mass and velocity.
• p = mv
Sample Problem
• Calculate the momentum of a 65-kg sprinter
running east at 10 m/s.
Sample Problem
• Calculate the momentum of a system composed of a 65-kg
sprinter running east at 10 m/s and a 75-kg sprinter running
north at 9.5 m/s.
Change in momentum
• Like any change, change in momentum is
calculated by looking at final and initial
momentums.
• Dp = pf – pi
– Dp: change in momentum
– pf: final momentum
– pi: initial momentum
Wording
dilemma
• In which case is the
magnitude of the
momentum change
greatest?
• In which case is the
change in the
magnitude of the
momentum
greatest?
Law of Conservation of Momentum
• If the resultant external force on a system is
zero, then the vector sum of the momentums
of the objects will remain constant.
•
SPbefore = SPafter
Sample problem
• A 75-kg man sits in the back of a 120-kg canoe that is at
rest in a still pond. If the man begins to move forward in
the canoe at 0.50 m/s relative to the shore, what happens
to the canoe?
External versus internal forces
• External forces: forces coming from outside the
system of particles whose momentum is being
considered.
– External forces change the momentum of the system.
• Internal forces: forces arising from interaction of
particles within a system.
– Internal forces cannot change momentum of the system.
An external force in golf
The System
• The club head exerts
an external
impulsive force on
the ball and changes
its momentum.
• The acceleration of
the ball is greater
because its mass is
smaller.
An internal force in pool
• The forces the balls
exert on each other
are internal and do
not change the
momentum of the
system.
• Since the balls have equal
masses, the magnitude of
their accelerations is
equal.
The System
Explosions
• When an object separates suddenly, as in an
explosion, all forces are internal.
• Momentum is therefore conserved in an explosion.
• There is also an increase in kinetic energy in an
explosion. This comes from a potential energy
decrease due to chemical combustion.
Recoil
• Guns and cannons “recoil” when fired.
• This means the gun or cannon must move
backward as it propels the projectile forward.
• The recoil is the result of action-reaction force
pairs, and is entirely due to internal forces. As the
gases from the gunpowder explosion expand,
they push the projectile forwards and the gun or
cannon backwards.
Sample problem
• Suppose a 5.0-kg projectile launcher shoots a 209
gram projectile at 350 m/s. What is the recoil
velocity of the projectile launcher?
Sample Problem
• An exploding object breaks into three fragments. A 2.0 kg
fragment travels north at 200 m/s. A 4.0 kg fragment travels east
at 100 m/s. The third fragment has mass 3.0 kg. What is the
magnitude and direction of its velocity?