Chapter 7: Work and Energy. Work Energy Work done by a constant force (scalar product) Work done by a varying force (scalar product & integrals) Kinetic Energy. Work-Energy Theorem. Forms of Mechanical Energy. CONSERVATION OF ENERGY. Work by a Baseball Pitcher.
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Work done by a constant force
(scalar product)
Work done by a varying force
(scalar product & integrals)
Work-Energy Theorem
Work and Energy
Work and Energy
CONSERVATION OF ENERGY
Work and Energy
Work and Energy
A baseball pitcher is doing work on
the ball as he exerts the force over
a displacement.
v1 = 0
v2 = 44 m/s
Work and Energy
Work done by several forces
Work(W)
How effective is the force in moving a body ?
Both magnitude (F) and directions (q ) must be taken into account.
W[Joule] = ( F cos q ) d
Work and Energy
Example:Work done on the bag by the person..
Special case: W = 0 J
a) WP = FP d cos ( 90o )
b) Wg = m g d cos ( 90o )
Nothing to do with the motion
Work and Energy
A 50.0-kg crate is pulled 40.0 m by a
constant force exerted (FP = 100 N and
q = 37.0o) by a person. A friction force Ff =
50.0 N is exerted to the crate. Determine
the work done by each force acting on the
crate.
Work and Energy
F.B.D.
WP = FP d cos ( 37o )
Wf = Ff d cos ( 180o)
Wg = m g d cos ( 90o)
WN = FN d cos ( 90o)
180o
d
90o
Work and Energy
WP = 3195 [J]
Wf = -2000 [J] (< 0)
Wg = 0 [J]
WN = 0 [J]
180o
Work and Energy
Wnet = SWi
= 1195[J] (> 0)
Work and Energy
Wnet= Fnet d = ( m a ) d
= m [ (v2 2 – v1 2 ) / 2d ] d
= (1/2) m v2 2 – (1/2) m v1 2
= K2 – K1
Work and Energy
A car traveling 60.0 km/h to can brake to
a stop within a distance of 20.0 m. If the car
is going twice as fast, 120 km/h, what is its
stopping distance ?
(a)
(b)
Work and Energy
(1)Wnet = F d(a) cos 180o
= - F d(a) = 0 – m v(a)2 / 2
- Fx (20.0 m) = -m (16.7 m/s)2 / 2
(2) Wnet = F d(b) cos 180o
= - F d(b) = 0 – m v(b)2 / 2
- Fx (? m) = -m (33.3 m/s)2 / 2
(3)F & m are common. Thus, ? = 80.0 m
Work and Energy
Work and Energy
Satellite in a circular orbit
Does the Earth do work on the satellite?
Work and Energy
B
2
Work and Energy
Forces on a hammerhead
Forces
Work and Energy
S
S23
Fn
Work and Energy
FS
Spring Force
(Restoring Force):
The spring exerts its force in the
direction opposite
the displacement.
FP
x > 0
Natural Length
x < 0
FS(x) = - k x
Work and Energy
FS
FP
FS(x) = - k x
Natural Length
x2
W = FP(x) dx
x1
W
Work and Energy
Work and Energy
lb
W = F||dl
la
Dl 0
Work and Energy
A person pulls on the spring, stretching it
3.0 cm, which requires a maximum force
of 75 N. How much work does the person
do ? If, instead, the
person compresses
the spring 3.0 cm,
how much work
does the person do ?
Work and Energy
x2 = 0.030 m
WP = FP(x) d x = 1.1 J
x1 = 0
Work and Energy
A person pulls on the spring, stretching it
3.0 cm, which requires a maximum force
of 75 N. How much work does the spring
do ? If, instead, the
person compresses
the spring 3.0 cm,
how much work
does the spring do ?
Work and Energy
x2 = -0.030 m
WS = FS(x) d x = -1.1 J
x1 = 0
Work and Energy
A 1.50-kg block is pushed against a spring
(k = 250 N/m), compressing it 0.200 m, and
released. What will be the speed of the
block when it separates from the spring at
x = 0? Assume mk =
0.300.
FS = - k x
(i) F.B.D. first !
(ii) x < 0
Work and Energy
(a) The work done by the spring is
(b) Wf = - mkFN (x2 – x1) = -4.41 (0 + 0.200)
(c) Wnet = WS+ Wf = 5.00 - 4.41 x 0.200
(d) Work-Energy Theorem: Wnet=K2 – K1
4.12 = (1/2) mv2 – 0
v = 2.34 m/s
x2 = 0 m
WS = FS(x) d x = +5.00 J
x1 = -0.200 m
Work and Energy
Work along a path
(Path integral)
Work around any closed path
(Path integral)
Mechanical Energy Conservation
Energy Conservation
y
Near the Earth’s surface
l
(Path integral)
Energy Conservation
y
Near the Earth’s surface
(Path integral)
dl
Energy Conservation
Wg < 0 if y2 > y1
Wg > 0 if y2 < y1
The work done by the gravitational
force depends only on the initial and
final positions..
Energy Conservation
Wg(ABCA)
=Wg(AB) +
Wg(BC) +
Wg(CA)
=mg(y1 – y2) +
0 +
mg(y2- y1)
= 0
C
B
dl
A
Energy Conservation
Energy Conservation
Wg = 0 for a closed path
The gravitational force is a conservative force.
Energy Conservation
(Path integral)
- μmg L
L depends on the path.
LB
Path B
Path A
LA
Energy Conservation
The work done by the friction force
depends on the path length.
The friction force:
(a) is a non-conservative force;
(b) decreases mechanical energy of the system.
Wf = 0 (any closed path)
Energy Conservation
A 1000-kg roller-coaster car moves from
point A, to point B and then to point C.
What is its gravitational potential energy
at B and C
relative to
point A?
Energy Conservation
Wg(ABC) =Wg(AB) + Wg(BC)
=mg(yA- yB) + mg(yB - yC)
= mg(yA - yC)
y
B
A
dl
B
C
A
Energy Conservation
Work and Energy
Power
Work and Energy
The Burj Khalifa is the largest
man made structure in the world
and was designed by Adrian
Smith class of 1966
thebatt.com Febuary 25th