Transcript PHYSICS

WORK, ENERGY &
MOMENTUM
WORK & KINETIC ENERGY
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Work, W: using a force, F, to displace
an object a distance, d
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unit: Joule
W = Fd
(1 J = 1 Nm)
W = (Fcosq)d
W=0
WORK & KINETIC ENERGY
d
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Work done by any force: W = Fdcosq
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can be positive, negative, or zero
q
F
Ex: sled sliding down a hill
gravity does positive work
friction does negative work
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normal force does no work
d
WORK & KINETIC ENERGY
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Power, P: the
time rate at which
work is done
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Lift
Thrust
Drag
P = W/t
unit: Watt, W
(1 W = 1 J/s)
(1 J/s = 1 Nm/s)
Weight
english unit:
horsepower, hp
(1.00 hp = 746 W)
P = Fv
WORK & KINETIC ENERGY
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Kinetic Energy, K: energy of motion
Energy: the ability to do work
2
 K = ½mv
 unit: Joule
 scalar quantity – amount only – direction
doesn’t matter
 can only be zero or positive – never
negative
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WORK & KINETIC ENERGY
WORK & KINETIC ENERGY
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Work/Energy Theorem: net work done
on an object is equal to the total change
in kinetic energy of the object
Wnet = Kf – Ki
2
2
 Fnetdcosq = ½mvf – ½mvi
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WORK & KINETIC ENERGY
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Net work determines the change in an
object’s motion
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positive work = increase in kinetic energy (speed up)
 Ex: throwing a ball
negative work = decrease in kinetic energy (slow down)
 Ex: catching a ball
zero work = no change in kinetic energy
 Ex: weightlifting
PHYSICS
UNIT 4: ENERGY &
MOMENTUM
POTENTIAL ENERGY &
CONSERVATION
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Potential Energy, U: energy of position
 Gravitational PE: energy of position due to
gravity force
 U = mgh
g
 h: height, measured from origin
(reference point)
 unit: Joule, J
 Scalar Quantity - can be positive, zero, or
negative depending on choice of origin
POTENTIAL ENERGY &
CONSERVATION
pendulu
m:
UK
KU
the
amount
POTENTIAL ENERGY &
CONSERVATION
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Conservation of Mechanical Energy: a
system's total mechanical energy (K+U)
stays constant if there is no friction
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Ki + Ui = Kf + Uf
However, if there is friction, some K will be
turned into other energy forms - heat, sound,
etc.
Ki + Ui = Kf + Uf + Wlost
 mechanical energy is not conserved
 total energy is still conserved
Cons. Of Energy
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Example: a Mass
in Free Fall
Ki + Ui = Kf + Uf
2
 ½mvi + mghi =
½mvf2 + mghf
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POTENTIAL ENERGY &
CONSERVATION
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Example: a Mass on a Horizontal Spring
Ki + Ui = Kf + Uf
2
2
2
2
½mvi + ½kxi = ½mvf + ½kxf
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POTENTIAL ENERGY &
CONSERVATION
PHYSICS
UNIT 4: ENERGY &
MOMENTUM
QUIZ 4.1
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Joe throws a ball straight up into the air,
and catches it on the way back down.
(a) Draw a graph showing the kinetic
energy of the ball throughout its flight.
(b) Draw a graph showing the
gravitational potential energy of the ball
throughout its flight. (c) Draw a graph
showing the total energy of the ball
PHYSICS
UNIT 4: ENERGY &
MOMENTUM
QUIZ 4.2
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(a) Tell what kinds of energy a pole
vaulter has at each of the four points
labeled on the picture above (point 4 is
just before hitting the mat)
(b) After the pole vaulter hits the mat,
his total energy is zero. Where did all
PHYSICS
UNIT 4: ENERGY &
MOMENTUM
QUIZ 4.3
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A roller coaster car, mass 500 kg, starts
from rest at the top of a hill 30 m above
147,000
J
ground level.
Ignore
friction. (a) What
147,000 energy
J
is the car’s potential
at the top
m/s car’s kinetic
of the hill? (b) What 24.2
is the
energy at the bottom of the98,000
hill?J (c)
How fast will the car be going at the
bottom of the hill? (d) What is the car’s
PHYSICS
MOMENTUM
MOMENTUM & IMPULSE
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Momentum, p: amount of “umph" an
object has (Inertia in Motion)
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= mv
unit p : kg m/s
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vector quantity - includes direction
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+2 kgm/s
–2 kgm/s
MOMENTUM & IMPULSE
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Impulse, J: A
force that acts
over a duration
of time.
J = Ft
 unit: kg m/s
or
Ns
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MOMENTUM & IMPULSE
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Impulses cause a change in momentum.
This is known as the Impulse-Momentum
Theorem.
It is analogous to the Work-Energy Theorem.
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FΔT = Δp = pf – pi = mvf -mvi
unit: kg m/s or N s
force of impact, F = -pi/t
 to decrease force of impact, decrease p (decrease v
i
before impact) or increase t (catching an egg; stunt
falling; air bags)
Practice
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A 2000 kg car going 30 m/s hits a
brick wall and comes to rest.
(a) What is the car’s initial
momentum? 60,000 kg m/s
(b) What is the car’s final
0 kg m/s
momentum?
(c) What impulse does the wall give
-60,000 kg m/s
to the car?
(d) If the impact takes 0.5 seconds,
-120,000 N
what force is exerted on the car?
MOMENTUM & IMPULSE
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Bouncing vs. Sticking in an impact
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ex: a 1000 kg car going +10 m/s hits a wall
J = pf-pi
sticking: pi = +10,000 kgm/s, pf = 0
J = –10,000 kgm/s
bouncing: pi = +10,000 kgm/s, pf = – 10,000
kgm/s
J = –20,000 kgm/s
bouncing off at impact has up to twice the force
of sticking
MOMENTUM & IMPULSE
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Law of Conservation of Momentum:
total momentum of a system of objects
is constant if no outside forces act
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mivi = mfvf
 if mass increases, velocity decreases (and
vice versa)
COLLISIONS
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inelastic collision: objects collide and
stick (or collide and deform)
momentum is conserved, kinetic energy is
not
BEFORE = AFTER
 m v + m v = Mv
(M = m1 + m2)
1 1
2 2
f
 be sure to include + or – for velocity’s
direction
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COLLISIONS
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propulsion or explosion: total initial
momentum is zero; separated pieces
receive equal & opposite momentums,
so total final momentum is zero
0 = m1v1f + m2v2f or m1v1f = –m2v2f
 ex: rocket propulsion, gun recoil
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COLLISIONS
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Ex: A 4 kg rifle fires a 0.050 kg bullet,
giving the bullet a final velocity of 300
m/s east. What is the recoil velocity of
the rifle?
COLLISIONS
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elastic collision: objects collide and
bounce off with no loss of energy
both momentum and kinetic energy are
conserved
BEFORE = AFTER
 m v
1 1o + m2v2o = m1v1f + m2v2f
2 + ½m v 2 = ½m v 2 + ½m v 2
 ½m v
1 1o
2 2o
1 1f
2 2f
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Useful Equations
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p = mv
J = pf – pi = Ft
m1v3 = –m2v4
m1v1 + m2v2 = Mv3
m1v1 + m2v2 = m1v3 + m2v4