Download 9-Momentum and impulse

Momentum and
Impulse
Momentum
Momentum: the product of mass and
velocity
 Momentum is inertia in motion.
 Ex: a dog running down the street
 Equation: mv
=p
• p = momentum (kg*m/s)
• m = mass (kg)
• v = velocity (m/s)
• A more massive object has more p than
an object with less mass.
• An object at rest has no p (v = 0)
• If the p of an object changes, the m, v, or
both MUST change.
• If the v changes, then the object is
accelerating
• a produces F
• The greater the F, the greater Δv
 Which means a greater Δp
Check Your Understanding
Which has more momentum, a dog
running down the street or a large
semi truck parked on the side of the
road?
 The running dog has momentum. The
truck has no momentum because it is not
even moving.
Check Your Understanding
A 10 kg cart is rolling down the street at
10 m/s. What is the cart’s momentum?
p = ?
m = 10 kg
v = 10 m/s
mv = p
(10)(10) = p = 100 kg*m/s
Impulse
• The F sustained for a longer period of time
produces more ∆p.
• This relationship of F to t is called impulse.
Impulse:
product of force and time interval
during which the force acts.
 Impulse does NOT change in a collision
 Ex: a car colliding with another car
 Equation: J = F∆t
• J = impulse (N*s)
• F = force (N)
• ∆t = time (s)
• Impulse is equal to the change in
momentum.
 J = Δp
• In collisions, the amount of damage
depends on several things.
 One is the hardness of surfaces that connect.
 Two softer, more malleable objects will do
less damage than two harder, more rigid
objects.
• J does not change if an egg hits a more or
less malleable surface b/c the object’s
change in momentum would be the same
either way.
• J is the same for both
 the only thing that changes is the time interval
of impact.
• As the t increases, the F decreases.
 Ex: car crash with and without airbags,
landing on the ground with bent knees vs.
straight legged
Check Your Understanding
Why is falling on a floor with more give
(like a big fluffy pillow) less dangerous
than falling on a floor with less give
(like concrete or brick)?
Because the floor with more give allows a
greater time for an object to come to rest.
A greater time for a change in momentum
results in less force.
Check Your Understanding
When a dish falls, will the impulse be
less if it lands on carpet than if it lands
on hard floor?
No. The impulse would be the same for
either surface because the same
momentum change occurs for each. It is
the force that is less for the dish on the
carpet because of the greater time of
momentum change.
Conservation of Momentum
Law of Conservation of Momentum: In
the absence of an external force, the
momentum of a system remains
unchanged.


In the absence of an external force, the
momentum of a system remains
unchanged.
Ex: a gun will recoil when fired b/c the
momentum of the gun and bullet together
before the shot should equal the total
momentum of the bullet and the gun after
they have been shot.
• When a cannon is fired, according to
Newton’s 3rd, the ball has an equal but
opposite force to the cannon.
 Same thing with p (within the system of the
cannon and the ball)…the overall p before
and after do not change…ignoring friction.
• Remember p is vector quantity (magnitude
AND direction)
• If no net force or net J act on a system,
the momentum of that system cannot be
changed.
Check Your Understanding
When fighting fires, a firefighter must use
great caution to hold a hose which
emits large amounts of water at high
speeds. Why would such a task be
difficult?
The hose is pushing lots of water (large
mass) forward at a high speed. This
means the water has a large forward
momentum. In turn, the hose must have
an equally large backwards momentum,
making it difficult for the firefighters to
manage.
Check Your Understanding
A bomb is sitting at rest on the ground. It
explodes into 3 pieces with a mass of 5
kg, one moving at a speed of 3 m/s
east, the other moving at a speed of 5
m/s northwest, and the last moving at a
speed of 4 m/s south. What is the total
momentum of all 3 pieces after the
explosion?
Zero! The momentum before equals the
momentum after.
Collisions
• The collision of objects clearly shows the
conservation of p.
Net momentum before collision =
Net momentum after collision
• Two main types of collisions
 Elastic and inelastic
Elastic Collisions
Elastic collision: When objects
collide without being permanently
deformed or without generating heat
 The momentum from the first object is
transferred to the second object (or vice
versa).
 Ex: billiard balls (pool); Newton’s Cradle
Inelastic Collisions
Inelastic collisions: When colliding
objects become entangled or coupled
together, thereby generating heat or
disfigurement
 The net p before the collision equals the net
p after the collision
 Ex: car crashes, sports, bumper cars