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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

2

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:

5

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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