Transcript Momentum - Mr. Shaffer at JHS

Chapter 7
Momentum
In golfing or in baseball – why is the follow through of the swing so
important in hitting the LONG BALL?
By definition:
Momentum = mass x velocity
(speed)
momentum (p) = mv
What is Momentum measured in?
A) Newtons
B) kg m/s
C) m/s²
D) Joules
The momentum of a 6 kg bowling ball going 6 m/s down
the alley. How much momentum does the ball have?
A bowler throws the same ball down the alley at the same
velocity, but the ball strikes a wall at the end and recoils back
towards you at 2 m/s. What is the change in momentum?
WHY?
Would it hurt more getting hit from
the boxer with the gloves on or the
gloves off?
A) Gloves on
B) Gloves off
Impulse = Change in Momentum
If momentum changes – what does not have to
change?
A) Mass
B) Velocity
C) Time
When things change momentum, most of the time the object is changing its
Velocity, and not its mass. Think about it… while walking down the hallway, if
Wanted to change your momentum, would you change your mass or your speed?
So…
If you change your velocity, you are ACCELERATING – if you are accelerating
Some FORCE must be happening – it all goes back to Newton’s 2nd law (F = MA)
The greater the force, the greater the acceleration (change in
velocity), the greater the momentum.
The amount of time Force is applied is very
important to IMPULSE (change in momentum)
Impulse = Force x time interval
Change in velocity = Force x time
Δmv = FΔt
(this equation is just a modification of F=ma)
Increasing momentum:
Apply the greatest force possible for the longest time possible
Why is a follow through so important in a golf swing?
Δmv = FΔt
If you have a strong follow through, the ball and the golf club
Are in contact with each other longer. That teeny weeny little
Bit of extra contact time gives a longer golf shot.
A .2 kg baseball is pitched going 20 m/s and is
hit by a batter where the ball is going 50 m/s
off the bat. What is the impulse applied to the
ball by the bat? .2(20) + .2(50) = 14 kg m/s
If the bat is in contact with the ball for
.016 sec, how much average force did the
bat apply to the ball?
14 kg m/s = F (.016 sec)
F = 875 N
Conservation of Momentum
The momentum before = momentum after a collision
mv = mv
An 1500 kg SUV going 10 m/s hits a 5,000 kg bus going
6 m/s, and lock up together. What is the speed of the
locked up SUV and Bus?
mvbefore = mvafter
1500kg(10m/s) + 5000kg(6m/s) = mvbefore
(1500kg+5000kg) vsuv/bus = mvafter
45,000 kg m/s = 6500 kg v
V = 6.9 m/s
A 60kg skater pushes a shopping car of mass
20 kg. The shopping car takes off moving at
3 m/s, what is the recoil
speed of the skater?
mvbefore = mvafter
0
= (60 kg) v + (20 kg)(3 m/s)
vskater= 60 kg m/s / 60 kg = 1 m/s
Elastic Collisions – total KE before collision is
equal to total KE after.
Inelastic collision – total KE before collision is
not equal to total KE after.
A ) Elastic B) Inelastic
A ball of clay is thrown against the wall and
sticks.
A person jumping on a trampoline
In elastic collisions: mvbefore = mvafter
½ mv2before = ½ mv2after
A ball of mass .250 kg moving at 5 m/s collides
head on with a heavier ball (.8kg) that is at
rest. What are the velocities of the ball if it is
a completely elastic collision?
vf1 = (m1 – m2) v01
(m1 + m2)
vf2 = ( 2 m1 ) v01
m1 + m2
mvbefore = mvafter
½ mv2before = ½ mv2after
m1v1 + m2v2 = m1vf1 + m2vf2
Vf1 = -2.62 m/s
vf2 = 2.38 m/s
Ballistic Pendulum
Ballistic pendulums are used to find the
speed of bullets. A block of wood (2.5
kg) hangs from a pendulum. A fired
bullet (.01 kg) hits the wood with speed
v01 and lodges itself in the wood. The
pendulum swings upward .65 m as a
result of the collision. What is the speed
of the bullet before it struck the wood?
m1v01 = (m1 + m2) vf
V01 = (m1 + m2) vf
m1
We need vf
With the pendulum, the KE of the bullet/block at the
bottom will equal the PE at the top of the swing
KEat bottom = Peat top
½ mv2f = mgh for m, it is equal to the bullet+block
Vf = 2gh
V01= 896 m/s
2 Dimensional collisions
Collisions in 2 dimensions is the same as 1D
collisions except that you need to find the x
and y components of the velocities.
V01 = .9m/s
M1 = .15 kg
Vf1=
50o
Ɵo
V02 = .54 m/s
M2 = .26 kg
35o
Vf2 = .7 m/s
X component: m1v01 + m2v02 = m1vf1 + m2vf2
.15kg(.9 m/s sin 50o) + (.26 kg) .54m/s = .15(vf1) + .26 kg(.7m/s cos 35o)
solving for vf1 = .63 m/s
Y component: m1v01 + m2v02 = m1vf1 + m2vf2
..15kg(-.9m/s
cos 50o) + .26kg(0 m/s) = .15kg(vf1) + .26kg(-.7 sin 35o)
solving for vf1 = .12 m/s
V01 = .9m/s
M1 = .15 kg
Vf1=
.64 m/s
50o
Ɵo
.63 m/s
V02 = .54 m/s
M2 = .26 kg
a2+b2 = c2
.632 + .122 = vf12
vf1 = .64 m/s
.12 m/s
35o
Ɵ= tan-1(.12/.63)
Vf2 = .7 m/s
Ɵ = 11o
Center of Mass
An objects center of mass is a point that represents
the average location for the total mass of the
object.
(the cm does not always have to be within the confines of the object)
m1x1 + m2x2
Center of mass xcm = m1 + m2
Find the center of mass for the planetary system below:
X1= 5
M1 = 5
Center of mass
38.3
x2= 40
m2 = 100
Center of Mass Experiment
1. Stand 2 ft (your own feet) away
from a wall
2. Place a chair between you and
the wall
3. Lean over, with your head
against the wall and grab the
seat of the chair
4. Lift up the chair and stand up
straight without moving your
feet.
5. Using your clicker
A) You did it
B) No you didn’t