Download Momentum - Red Hook Central Schools

Linear Momentum
&
Impulse
Define Linear Momentum = product
of objects mass x velocity
A measure of how hard it is to stop an
object.
It is like a quantity of motion.
How is it different from inertia?
Momentum (p) depends on:
mass & velocity of object.
p = mv
m in kg
v in m/s
Units are … kg m no name.
s
Momentum is a
Vector Quantity
Same direction as velocity
All Energy KE too is a scalar
Change in momentum
occurs any time an object changes
velocity (speed or direction).
Momentum Change &
Newton’s 2nd Law
•
•
•
•
F = ma
F = m(Dv/Dt)
FDt =mDv
m (vf - vi) for const mass.
FDt = Dp Impulse direction is same as F.
 Dp = Change in momentum
Equations of Momentum Change
• Impulse J = change momentum.
• J =FDt = Dp pf – pi.
 Dp = mvf – mvi
• for velocity change with constant mass can
factor out mass you can write,
• m (vf - vi) or mDv.
Increased force & contact time on
object give greatest Dp = mDv.
The more time in contact, the less
force needed to change p.
The quantity FDt (or Ft) is called
impulse (J).
Impulse (J) is the momentum change.
It has the same units.
kg m
s
or
Ns
1. A bus driving east hits a mosquito flying west.
Compare the impacts of each on the bus and the bug:
•
•
•
•
•
•
Time of impact
Force
Impulse
Dp
Acceleration
Damage done.
Changing momentum: bringing objects to rest
with impulse.
• Catch the egg without breaking vs dropping
on ground.
• Fall from building onto cement vs. airbag.
Same impulse,
more time = less
force.
2. Find the change in momentum of a 1 kg
mass which is dropped and hits the floor with
a velocity of 8 m/s. It bounces back up with 6
m/s.
• Dp = m Dv.
• = 1 kg( - 8 m/s – 6 m/s)
• - 14 Ns
• Stand on a skateboard catch a ball and bring
it to rest or let it bounce off?
• Bouncing causes bigger impulse than
absorbing or giving with the motion.
Graphs
Force N
Constant force F - t graph:
Dp /Impulse is area under curve
FDt.
3. Non-Constant Force
Force vs. time graph. The area under the curve =
impulse or Dp change in momentum.
• How much impulse is each box on the graph?
• 5 Ns.
4. What is the change in velocity imparted to
the 0.8 kg object below?
IB Style Question
5. Water is poured from 0.5 m onto a pan balance at
30 L/min. Assume vf of water = 0. rWat = 1 kg/L.
• 1. Estimate the velocity of the water
upon hitting the pan. (Assume the
stream starts from rest).
• 2. Estimate the mass of water hitting
the pan each second.
• 3. Assuming the water’s velocity after
hitting the pan goes to zero, estimate
the reading on the pan balance in
grams.
• v2 = 2as.
• v2 = 2(10)(0.5) =
• v = 3.2 m/s
• Mass water/sec,
• 30 L / 60 s x 1 kg/ L = 0.5 kg/sec so in 1 second
0.5 kg mass arrives at the pan balance.
• Water changes momentum FDt = mDv.
• The force on the balance = mDv/t,
• (0.5kg)(3.2 m/s)/ 1 s = 1.6 N
• = 160 grams.
Hwk Kerr.
• Pg 72 # 6-7
Newton’s First Law
• Object at rest or constant velocity has not
Fnet. Upward = Downward.
Newton’s
rd
3
Law
• Object A exerts Force F, on object B, then
object B exerts equal but opposite force on
A.
• F a,b = - F b,a.
Conservation Momentum particle interaction
N3
• FAB = - FBA.
• FDt = mDv
• mDva = - mDvb.
t
t
• Contact time, t, is the same they cancel.
• m (vfa – via ) = - m (vfb – vib )
• Expand and rearrange, collect vi on one
side, vf on the other.
• S pi = Spf (Conservation of momentum).
Conservation of Momentum
• If no external force acts on a closed
system, the total momentum within the
system remains unchanged even if objects
interact.
• Momentum can be transferred between
objects.
What is a system?
• Two or more objects that interact in
motion. One may transfer part or all of
its momentum to the other(s).
• Common examples: collisions,
explosions.
6. Bounce a ball off the floor
• Did the momentum of the ball change?
• Was conservation of momentum obeyed?
• What happened to the momentum?
• How much momentum was gained by Earth?
• The ball’s mass is 0.25-kg. It’s initial speed was 5.0 m/s, and
its final speed was 3.0 m/s.
• What was the change in velocity of Earth due to the collision?
(mass Earth = 6.0 x 1024 kg.)
• The impulse on the ball:
• 0.25 (8 m/s) = 2.0 Ns.
•
•
2.0 Ns = mDv
Dv = 2 Ns / 6 x 1024 kg
To Calculate:
SPbefore =
Spafter
m1v1 + m2v2 = m1fv1f + m2fv2f
• v1 and v2 velocities for objects
one and two.
• m1 and m2 masses of objects
One Ball transfers all its momentum.
Conservation of Momentum Calc’s
• Total momentum before = total after
interactions.
• The direction of the total momentum is
conserved as well.
• Collisions.
• Explosions
• Pushing apart.
Elastic & Inelastic Collisions
Elastic: no KE (velocity) lost (to heat, light,
sound etc.) Usu. Involves objects that don’t make
contact.
KE before = KE aft.
Inelastic: involves greatest loss of KE (velocity).
Often objects stick together.
Recoil: objects initially at
rest explode or push apart
Recoil illustrates conservation
of momentum where initial and
final momentum = 0.
0 = p1 + p2.
7. On July 4th my family likes to shoot off fireworks.
One rocket was shot straight up, climbed to a height 18m and exploded into hundreds of pieces in all directions
at its highest point.
Thinking about conservation laws, think about the
rocket at its highest point just before & just after it
explodes:
How does the rocket’s momentum compare before &
after the explosion?
How does its KE compare before & after the explosion?
Throw a ball off the wall.
• How is momentum conserved?
• What is the system?
Systems, External & Internal Force
• If system is single astronaut, then external force
applied by astronaut 2, momentum not conserved –
it changes.
• If system is 2 astronauts, then the force is internal
and total momentum is conserved.
State Newton 3
• If 2 objects interact, the force exerted by on
object A by object B (Fa,b), is equal in
magnitude but opposite in direction to the
force exerted on object B by object A, (-Fb,a).
1. A lamp of weight W is suspended by a wire fixed
to the ceiling. With reference to Newton’s third law
of motion, the force that is equal and opposite to W
is the:
•
•
•
•
A.
B.
C.
D.
tension in the wire.
force applied by the ceiling.
force exerted by the lamp on the Earth.
force exerted by the Earth on the lamp
2. A student is sitting on a chair. One force that is
acting on the student is the pull of gravity.
According to Newton’s third law, there must be
another force which is:
•
•
•
•
A.
B.
C.
D.
the upward push of the chair on the student.
the downward force on the student.
the downward push of the chair on Earth.
the upward force on Earth.
3. What is the reaction force for the following:
A 0.5 kg bird glides above the earth’s surface.
It’s wings push down on the air with its
weight, 5-N, so:
How can anything have Fnet and accelerate?
• Acceleration is caused by the Fnet on a single
object. It is the sum of all the forces.
• Action/Reaction occurs for different objects.
Hwk in Kerr
• pg 72 # 8 – 9 Show work.
• IB set momentum .