Transcript Momentum-Impulse-Collisions - juan

Momentum & its Conservation
Unit 4
What is momentum?
• “Mass in motion”- objects at rest have no
momentum
• A vector quantity in units of kg ∙ m/s
• Symbolized by a lower case “p”
• ∆p = mass x change in velocity
• Objects with large p have either a large
mass or a high velocity
• Objects with small p have either a small
mass or a small velocity
It takes an impulse to change
momentum….
• A force acting over a given time will
change an object’s momentum
• An unbalanced force always accelerates an
object…speeding it up or slowing it down
Impulse-Momentum Theorem
• From Newton’s 2nd law: F = m a
• Substituting v/t for a we get F = m Δv/t or
F t = m Δv
• The product F x t is called the impulse (J)
which results in a change in momentum
(Δp)
• The impulse (J) causes and is equal to the
change in momentum (Δp).
Impulse-momentum Theorem
• FΔt = mΔv
• In a collision, an object experiences a force
for a specific amount of time which results
in a change in momentum (speeding up or
slowing down).
• Momentum is conserved…any change in
p by one object is balanced by the change
in p in the other object.
Self-Check
Elastic Collisions
• A collision in which the total momentum
of the two objects is conserved, while the
individual momenta of each object
changes.
• Δp are always equal, but in opposite
directions from Newton’s 3rd law.
• Moving R (or east) is noted
as positive
• Moving L (or west) is noted
Elastic Collisions
• Force and time are
inversely proportional
• A force applied over a
greater time will minimize
the effect of the force
• A force applied over a
shorter time will maximize
the effect of the force
Elastic Collisions
• Examples: padded dashboards, “riding
the punch,” nylon ropes in rock climbing,
follow-through in bat & racket sports
Elastic Collisions
• Momentum and Kinetic Energy Are
Conserved in an Elastic Collision
Elastic Collisions
Self-Check
• While driving down the road, a firefly
strikes the windshield of a bus and makes a
quite obvious mess in front of the face of
the driver. This is a clear case of Newton's
third law of motion. The firefly hit the bus
and the bus hits the firefly. Which of the
two forces is greater: the force on the firefly
or the force on the bus?
Self-Check
• For years, space travel was believed to be impossible
because there was nothing that rockets could push
off of in space in order to provide the propulsion
necessary to accelerate. This inability of a rocket to
provide propulsion in space is because ...
• a. space is void of air so the rockets have nothing to push
off of.
• b. gravity is absent in space.
• c. space is void of air and so there is no air resistance in
space.
• d. ... nonsense! Rockets do accelerate in space and have
been able to do so for a long time.
Self-Check
•
Many people are familiar with the fact that a rifle recoils
when fired. This recoil is the result of action-reaction force
pairs. A gunpowder explosion creates hot gases that
expand outward allowing the rifle to push forward on the
bullet. Consistent with Newton's third law of motion, the
bullet pushes backwards upon the rifle. The acceleration of
the recoiling rifle is ...
• a. greater than the acceleration of the bullet.
• b. smaller than the acceleration of the bullet.
• c. the same size as the acceleration of the bullet.
Elastic Collisions
• pf - pi = 0 since momentum is conserved
and objects bounce apart with no loss of
energy.
pa + pb = p’a + p’b
mava + mbvb = m’av’a + m’bv’b
• The momenta of the two objects before the
collision must be equal to the momenta of
the two objects after the collision.
• The object with the smaller mass
experiences the greatest change in velocity.
Practice Problem
• In a physics lab, 0.500-kg cart (Cart A) moving
rightward with a speed of 92.8 cm/s collides with
a 1.50-kg cart (Cart B) moving leftward with a
speed of 21.6 cm/s. The two carts stick together
and move as a single object after the collision.
Determine the post-collision speed of the two
carts.
Practice Problem
• A 25.0-gram bullet enters a 2.35-kg watermelon
and embeds itself in the melon. The melon is
immediately set into motion with a speed of 3.82
m/s. The bullet remains lodged inside the melon.
What was the entry speed of the bullet?
(CAUTION: Be careful of the units on mass.)
•
Inelastic Collisions
• When objects collide, some mechanical
energy is transformed into heat energy and
is dissipated.
• Common inelastic collisions occur when
objects stick together or are deformed (cars
colliding or bullet hitting a target) or when
they start out stuck together and then
separate (firing of the bullet from a gun).
Inelastic collisions
• The masses of each object remains the
same, but they share a common velocity
either before or after the event.
• There is no rebounding effect.
• mava + mbvb = (ma + mb) vf
• (ma + mb) vi = mava + mbvb
• When the two objects
are stuck together,
they have the same
velocity.
Practice Problem
• During a goal-line stand, a 75-kg fullback moving
eastward with a speed of 8 m/s collides head-on
with a 100-kg lineman moving westward with a
speed of 4 m/s. The two players collide and stick
together, moving at the same velocity after the
collision. Determine the post-collision velocity of
the two players.
Practice Problem
• A 3000-kg truck moving rightward with a speed
of 5 km/hr collides head-on with a 1000-kg car
moving leftward with a speed of 10 km/hr. The
two vehicles stick togetherand move with the same
velocity after the collision. Determine the postcollision velocity of the car and truck.