Transcript Momentum and Collisions

Momentum and Collisions
Unit 6
Momentum- (inertia in motion)
• Momentum describes an object’s
motion
• Momentum equals an object’s mass
times its velocity
• p = mv
• Units: kg.m/s
• If both a truck and a roller skate are rolling down
a hill with the same speed which has more
momentum?
• If the truck is at rest and the roller skate is
moving, which has more momentum?
Both an 18-wheeler and a compact
car are traveling down the
highway at 60 mph, which has the
greatest momentum?
a. 18-wheeler
b. compact car
c. Both
d. Neither
• Impulse (also “change in momentum”)
occurs when a force is applied for a
time interval
• Impulse equals Force times time
• J = F∙ t
• Units are the same as momentum,
kg ∙m/s or may also be N∙s
Force and Impulse
J = F•t = p = mvf – mvi
Examples:
• golf club hitting a golf ball
• Baseball bat hitting a baseball
• car hitting a haystack
• Car hitting a brick wall
• To increase the momentum
of an object, apply the
greatest force possible for as
long as possible.
• A golfer teeing off and a
baseball player trying for a
home run do both of these
things when they swing as
hard as possible and follow
through with their swing.
Decreasing Momentum
• If you were in a car that was out of control and
had to choose between hitting a haystack or a
concrete wall, you would choose the haystack.
• If the change in momentum occurs over a long
time, the force of impact is small
• If the change in momentum occurs over a short time, the
force of impact is large.
•When hitting either the wall or the haystack and coming to
a stop, the change in momentum (or impulse) is the same.
•The same impulse does not mean the same amount of
force or the same amount of time.
•It means the same product of force and time.
•To keep the force small, we extend the time.
F, t, and p relationship
• When you extend the time, you reduce the force.
• Used for safety equipment and sports equipment
• A padded dashboard in a car is safer than a
rigid metal one.
• Airbags save lives.
• To catch a fast-moving ball, extend your hand
forward and move it backward after making
contact with the ball.
• p is the same; there is an inverse
relationship between force and time
Consider this!
• Compare the magnitude of force
required to stop a 70 kg
passenger moving at 25 m/s in
0.75 s (airbag) and 0.026 s
(dashboard)
• What is the advantage of airbags
in our cars?
Bouncing
Impulse is greater when bouncing occurs.
The force needed to cause an object to
bounce is greater than the force needed when
it does not bounce.
Ex. A glass bottle falls on your head. If it
breaks when it hits your head, the impulse
has ended.
If it bounces off your head, your head applies
a force to send it back up.
Stopping Times and Distances
• Depends on the impulse-momentum theorem and the
Work-KE theorem
• Be careful when distinguishing time and distances
– Time can be found using impulse-momentum theorem, distance
is found using work-KE theorem
• Larger velocities have larger KE
• Larger changes in KE mean more work needs to be
done to stop the object
• Work = Fd, more distance needed or more force needed
to stop faster moving objects
• Ex. 2x’s speed means 4x stopping distance
Conservation of momentum
• Law of Conservation of p: total momentum of an
isolated system is constant
• Momentum before must equal momentum after.
pai + pbi = paf + pbf
mavai + mbvbi = mavaf + mbvbf
• Where p is momentum, m is mass, and v is velocity.
The subscripts a and b are for different objects
involved and i and f are for initial and final.
• The total p of all objects interacting with
one another remains constant regardless
of nature of forces between objects
• Momentum is conserved in collisions
• Momentum is conserved for objects
pushing away from each other
• Consider a recoil situation:
• The momentum before firing is zero. After
firing, the net momentum is still zero because
the momentum of the cannon is equal and
opposite to the momentum of the cannonball.
For recoil or other situations where two objects are
together initially such as
• A bullet fired from a gun
• A boy on a skateboard who passes a basketball
• Two people on skateboards who push off of each
other
• A cannonball fired from a cannon
• Initial mass is the sum of the two masses
(ma+ mb) vabi = mavaf + mbvbf
• Pay attention to signs of velocity!!
Practice Problem
• A 65.0 kg ice skater moving to the right
with a velocity of 2.50 m/s throws a 0.150
kg snowball to the right with a velocity of
32.0 m/s relative to the ground.
• What is the velocity of the ice skater after
throwing the snowball? Disregard the
friction between the skates and ice
Collisions
Collision Types
• Elastic: two objects bounce apart after the
collision so that they move separately
• Perfectly inelastic: two objects stick
together after the collision so that their
final velocities are the same
• Inelastic: two objects deform during the
collision so that the total KE decreases,
but the objects move separately after the
collision
Inelastic Collisions
• In an inelastic collision between two freight cars,
the momentum of the freight car on the left is
shared with the freight car on the right.
• Assume perfectly inelastic collisions
where the objects stick together
• Final mass is the sum of the two
masses
mavai + mbvbi = (ma+ mb)vf
• Pay attention to signs of velocity!!
A cart moving at speed v collides with an
identical stationary cart on an airtrack, and
the two stick together after the collision. What
is their velocity after colliding?
a. v
b. 0.5 v
c. zero
d. –0.5 v
e. –v
f. need more information
Consider the skater problem
above
• A second skater initially at rest with a
mass of 60.0 kg catches the
snowball. What is the velocity of the
second skater after catching the
snowball in a perfectly inelastic
collision?
Elastic Collisions
• When objects collide without being permanently
deformed and without generating heat, the collision is an
elastic collision and the total KE remains constant
• After the collision the two objects move separately
• Colliding objects bounce perfectly in perfect elastic
collisions.
• The sum of the momentum vectors is the same before
and after each collision.
mavai + mbvbi = mavaf + mbvbf
Elastic Collisions
a. A moving ball strikes a ball at rest.
b. Two moving balls collide head-on.
c. Two balls moving in the same direction collide.
Practice Problem
• Two billiard balls each with a mass of 0.35
kg strike each other head-on. One ball is
initially moving left at 4.1 m/s and ends up
moving right at 3.5 m/s. The second ball
is initially moving to the right at 3.5 m/s.
• Find the final velocity of the 2nd ball
•
You tee up a golf ball and drive it down
the fairway. Assume that the collision of
the golf club and ball is elastic. When
the ball leaves the tee, how does its
speed compare to the speed of the golf
club?
a. Greater Than
b. Less than
c. Equal to