past hw solutions are available at hw website. http ...kenahn/07spring/ka_lecture9_part1.pdf ·...
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HW #7 due : March 23, Friday, tomorrow
Past HW solutions are available at HW website.
http://geocities.com/kenahn7
Good news: We will curve!
Ch.7, Kinetic Energy and WorkCh.7, Kinetic Energy and Work
So far, we learned
Motion: Ch.2, Ch.4
Vector, Units: Ch.1, Ch.3
Force: Ch.5, Ch.6 (+circular motion)
During the next 3 weeks, we learn
Energy and Work : Ch.7, Ch.8
Ch.8, Potential Energy and Conservation of EnergyCh.8, Potential Energy and Conservation of Energy
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3
(Joule)Note:
2
mJ kg m N m
s= ⋅ ⋅ = ⋅
Fast flying baseball:
4
Why ? It’s good that
K = ½ …It’s good that
2 21, not ......
2K mv mv=
Why ?
v vs. x:
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What is so special about
F x∆ = (Force) (Displacement) ?
Example: Gravitational force & Projectile motion
Force increases Kinetic energy in this case.
Why do we need displacement?
Does force always increase kinetic energy?
A ball thrown up
Gravitational forceDisplacement
0v
v
If the displacement is opposite to the force,the kinetic energy decreases!
Both Force & Displacement are important!
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Why ?
v vs. x:
“Work”, W, in 1D
Work in 2D and 3DWork in 2D and 3D
What if force and displacement are perpendicular?
Example: Uniform circular motion
netF�
netF�
netF�
No change in “magnitude” of velocity � No kinetic energy change � No work, sorry !
(Velocity does change, because the “direction” changes.)
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Force
Displacement
positive work
Force
Displacementnegative work
Force
Displacement
zero work
Work vs.Disp.-Force angle Cos!
Force and Displacement with an angle
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Work done by a constant force
cosW Fd F dθ= ≡��
i
Scalar (dot) product (Ch.3, Sec.8)
Force
Displacementθ
Note: cosF θ is component of force along displacement
cosd θ is component of displacement along force
magnitude(+)
Work–kinetic energy theorem
cosW Fd F dθ= ≡��
iIf work is done on an object,
kinetic energy, , changes by
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Scalar(dotScalar(dot) product) product
, ( )A B B A A B C A C B C= + = +� � � � � � �� � � �
i i i i i
Work Done by a Gravitational Force
Work done by gravitational force
Change in kinetic energy:
Tomato thrown upward
Lifting/lowering an object
Wg > 0Wg < 0
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A tomato thrown up
d
0v
v
gF mg=Gravitational force
= -mgd
Work done by gravitational force
2 20
1 1
2 2f iK K mv mv= − = −
A tomato falling down
d
0v
vgF mg=
Gravitational force
= mgd
Work done by gravitational force
2 20
1 1
2 2f iK K mv mv= − = −
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m
h
cosLifter LifterW F d θ=Work done by weightlifter on weight:
= mgh
Work done in lifting an objectWork done in lifting an object
LifterF mg=
LifterF mg=
Work done by gravity on weight:
cosg gW F d θ= = -mgh
Net work
Lifter gW W= +
f iK K= −
If multiple forces are applied on an object,
1F�
2F�
3F�
d�
Displacement
iv fv
1 2 3
1 2 3 1 2 3
2 2
( ...)
... ...
1 1
2 2
total net
f i f i
W F d F F F d
F d F d F d W W W
K K mv mv
= = + + +
= + + + = + + +
= − = −
� �� � � �
i i
� � �� � �
i i i
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Example (Somewhat related to HW#9-Prob.1)
Frictionless surface
30Oθ =
F=T = 10 N
2 kg
a. Find the forces on the box.
d = 5 m
b. Find the work by each force.
c. Find the total work
d. If initial velocity is zero, what is the final velocity?
rope
Homework Help!!
Analyze the motion in two parts.
Velocity at right edge is initial velocity for projectile motion.
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See Sample Prob 6-1, studied during class.
Two blocks moving together � Treat like big one block
Ah…tough one
Focus on upper block.
Net force on it shouldbe the static friction.
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See Sample Prob 6-8
PeriodPeriod
Angular velocity2
T
πω =
Velocity2
r
v rT
π ω= =
Tension and Gravitational force acting on the ball.
Net force should be centripetal force, pointing horizontally to the center of circle.
PeriodPeriod
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HW #7 due : March 23, Friday, tomorrow
Past HW solutions are available at HW website.
http://geocities.com/kenahn7
Good news: We will curve!
More HW help: Physics Learning Center
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