Fundamentals of Physics
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Transcript of Fundamentals of Physics
2009 Physics 2111 Fundamentals of Physics Chapter 7 1
Fundamentals of Physics
Chapter 7 Kinetic Energy & Work1. Energy2. Work3. Work & Kinetic Energy4. Work Done by a Gravitational Force5. Work Done by a Spring Force6. Work Done by a General Variable Force7. Power
Review & SummaryQuestionsExercises & Problems
2009 Physics 2111 Fundamentals of Physics Chapter 7 2
Energy & Work
• Energy is conserved.• A new tool to solve problems.
221 vmEnergyKinetic
2
2
11:Unitss
mkgJoule
Energy comes in many forms:• Thermal, Chemical, Atomic, Nuclear Energies
• Descriptions of Energy:• Potential Energy (Chapter 7)• Kinetic Energy - motion of a massive object
2009 Physics 2111 Fundamentals of Physics Chapter 7 3
WOW!
August 10, 1972, a large meteorite skipped across the atmosphere.
JvmKE 14221 1050
bombsatomicWWIIMTKE 81.0
smv
kgm
15
104 6
2009 Physics 2111 Fundamentals of Physics Chapter 7 4
“Work”
• Work (W) is energy transferred to or from an object by means of a force acting on the object.
– Energy transferred to the object is positive work.– Stepping on the gas causes positive work to be done on a car.
– Energy transferred from the object is negative work.– Stepping on the brakes causes negative work to be done on a
moving car.
2009 Physics 2111 Fundamentals of Physics Chapter 7 5
Work & Kinetic Energy
Consider a force acting on an object constrained to move in the x-direction:
The force causes a change in kinetic energy; the force does work:
Units: 1 Joule = 1 kg (m / s)2 = (1 kg m / s2) m = 1 N m
dFdFWork x cos""
davv x220
2
Frictionless Wire
dFvmvm
damvmvm
davv
x
x
x
202
1221
202
1221
20
2 2
2009 Physics 2111 Fundamentals of Physics Chapter 7 6
A force acting on a particle moving along a curve:
work.no doesF
s
cos
FWork
sFWork
sFWork S
090coscos 0
velocity. thechangenot doesF
2009 Physics 2111 Fundamentals of Physics Chapter 7 7
“Work”
Work (W) is energy transferred to or from an object by means of a force acting on the object.
– A force does positive work when it has a vector component in the same direction as the displacement.
– A force does negative work when it has a vector component in the opposite direction as the displacement.
– A force does zero work when it is perpendicular to the displacement.
dFdFW cos
2009 Physics 2111 Fundamentals of Physics Chapter 7 8
Work – Kinetic Energy Theorem
2
1
2
1
s
s S
s
s S
S
dsamdsFW
dsFW
ds
dvv
dt
ds
ds
dv
dt
dvaS
v
v
s
sdvvmds
ds
dvvmW
0
2
1
KW
KKW
vmvmW
if
202
1221
Net Work Done = Change in Kinetic Energy
chain rule for derivatives
2009 Physics 2111 Fundamentals of Physics Chapter 7 9
Scalar (Dot) Product of Two Vectors
Commutative Law:
cosbaba
abba
zzyyxx babababa
2009 Physics 2111 Fundamentals of Physics Chapter 7 10
Example
Tipler p 157
s FWork
NmW
mNmNW
yFxFW yx
14
5423
2009 Physics 2111 Fundamentals of Physics Chapter 7 11
Example:
Cutnell p 160
sFWork net
Knet fgmF 025sin
kgm
v sm
58
6.30
NfK 70
202
12
21025sin vmvmsfgm fK
ms 57
sm
fv 19
vf = ?
2009 Physics 2111 Fundamentals of Physics Chapter 7 12
Work done by the forces on the box?
F N
d m
210
20
3
0
W F d
W F d N m J
F
F
cos ( )( ) cos( ) 210 3 20 6000
W N d
W N d W
N
N g
cos( )90 00
mg
F
N
2009 Physics 2111 Fundamentals of Physics Chapter 7 13
Object sliding on a frictionless floor
F F F F
F F F
F F F
net
net
net net net
x
y
x Y
1 20
30
20
30
2 2 2
50 35
50 35
sin cos
cos sin
Since v d is parallel to F W F dnet net0 0 , :
v0 0
W J153.
NF
NF
NF
0.10
00.4
00.3
3
2
1
Work = ?
2009 Physics 2111 Fundamentals of Physics Chapter 7 14
Work Done by the Gravitational Force
Going up:
The work done by the gravity force reduced the kinetic energy of the object.
dgmW
dgmW
dFW
0180cos
Going down:
The work done by the gravity force increased the kinetic energy of the object.
dgmW
dgmW
dFW
00cos
2009 Physics 2111 Fundamentals of Physics Chapter 7 15
Work Done Lifting & Lowering an Object
To raise an object to a new location, an applied force, F, must act to overcome the gravity force, Fg.
Consider a case where an object is at rest before and after the move.
Work- Energy Theorem:
Kf - Ki = Wa + Wg
But Kf = Ki = 0:
0 = Wa + Wg
Wa = - Wg
The work done by the applied force is the negative of the work done by the gravitational force.
Raising Lowering
dgmWa dgmWa The work done by the lifter.
2009 Physics 2111 Fundamentals of Physics Chapter 7 16
Pull with constant force F.
F
F ma
F mg ma
F m g
2 0
12
Is less energy expended or less work done when using a pulley (or other such device)?
F
F
F
2009 Physics 2111 Fundamentals of Physics Chapter 7 17
Pull with constant force F.
F
d2d
F ma
F mg ma
F m g
2 0
12
W F d
W m g d
( )( )2 W F d
W m g d
( )( )2
Same amount of work!
F
F
2009 Physics 2111 Fundamentals of Physics Chapter 7 18
An object accelerated downwards
Work Energy Theorem:
gMT
gMaMmgT
amF
43
4
Mg
T
aa
d
00 v
dgMWT 43
dgMWg dgMWnet 41
dgv
dgMvM
WKK net
21
412
21
0
0
a = g/4drops dWork by cord ?Work by gravity?Final velocity
2009 Physics 2111 Fundamentals of Physics Chapter 7 19
Work Done by a Spring Force
Compressing
Stretching
Relaxed
Hooke’s Law:
where k = spring constant (N/m)
The force varies linearly with displacement.
dkF
2009 Physics 2111 Fundamentals of Physics Chapter 7 20
Work Done by a Spring Force
Compressing
Stretching
Relaxed Work done by the spring force:
W F x dx
W k x dx k x
W k x k x
S x
x
S x
x
x
x
S i f
i
f
i
f
i
f
( )
12
2
12
2 12
2
W k x xS i 12
2 0( )
Hooke’s Law: dkF
Sa WW
2009 Physics 2111 Fundamentals of Physics Chapter 7 21
A block is dropped on a relaxed spring
W m g d
W k d
W W W
g
S
net g S
12
2
m g d k d mv 12
2 12
20
vk
md g d
v ms
2 2
35.
d
v
0v
ifnet KKW
m = 250 gk = 2.5 N/cmd = 12 cmWg ? Ws?v ?
2009 Physics 2111 Fundamentals of Physics Chapter 7 22
Work – Kinetic Energy Theorem with a Variable Force
W F x dx m a dx
a dxdv
dtdx
dx
dtdv v dv
W m v dv mv
W KE KE
S x
x
xx
x
x
x
x
v
v
f i
i
f
i
f
i
f
i
f
( )
12
2
2009 Physics 2111 Fundamentals of Physics Chapter 7 23
Problem
a x
ms
a x
ms
20
82 5
2 5
2 2.
.
W F x dx m x dx
W m x J
S x
x
x
x
i
f
i
f
( ) .
( )( ). .
2 5
10 8 8002 52
2
0
82 5
22
A 10 kg brick moves with the following variable acceleration; how much work is done on the brick in the first 8 seconds.
2009 Physics 2111 Fundamentals of Physics Chapter 7 24
Power
Power = time rate at which Work is done due to a Force.
SI Units: 1 Watt = 1 Joule / s = 1 N m / s
English Units: horsepower
1 hp = 550 ft lbs / s = 746 Watts
Work = Power x Time
1 kW hr = 3.6 x 106 J
dt
dWP
For a constant force:
vFdt
dFdP