Download Work and Energy

Work and Energy
Physics
Mr. Day
Work
 Work
- the product of the magnitudes of
the component of a force along the
direction of displacement and the
displacement
W = F d
 Work
– Push a chair from rest to a velocity
 Not
Work
– Hold a book in the air
– Carry a chair across the room at a constant
velocity
Work (cont.)
 Work
is only done when the
components of a force are parallel to a
displacement
d
F
W=Fd
•All of the force is acting on the box
d
F
W = F d cos 
•Only the horizontal component of the
force does work
Sign Convention for Work
Visual Concept
F
Work (cont.)
d
• Examples
W = F d cos
d
W = F d cos
W = F d cos 90
W=0
F
d
F
F
d
W = F d cos
W = F d cos
W = F d cos 0
W= F d
Work (cont.)
 Units
–Fd=W
– N m = Joule (J)
 Work
is a scalar quantity
– Work can be positive or negative
• Positive Work - Force and displacement are in the
same direction
• Negative Work - Force and displacement are in
opposite directions
Work Defined
Video
EX: A 20.0 kg suitcase is raised 3.0 m above a
platform by a conveyor belt. How much work is
done on the suitcase
m = 20.0 kg
d = 3.0 m
W=Fd
W = (m a) d
W = (20.0 kg)(9.8 m/s2)(3.0 m)
W = 588 J
EX: A person drags a suitcase with a
100.0 N force at an angle of 60.0° for
200.0 m. How much work does she do?
F
d
F = 100.0 N
 = 60.0°
d = 200.0 m
W = F d cos 
W= (100.0 N)(200.0 m) cos 60°
W = 10,000 J
W = 1.0 X 104 J
Types of Energy
Video
Energy
 Kinetic
Energy - the energy of an object
due to its motion
– Depends on speed and mass
– KE = 1/2 m v2
– Units  Joules (J)
 Potential
Energy - energy associated
with an object due to its position
– Units  Joules (J)
Kinetic and Potential Energy
Video
Kinetic Energy
Visual Concept
EX: A 6.0 kg cat runs after a mouse at
10.0 m/s. What is the cat’s kinetic
energy?
mc = 6.0 kg
vc = 10.0 m/s
KEc = 1/2 mc vc2
KEc = 1/2 (6.0 kg)(10.0 m/s)2
KEc = 300 J
EX: If a .10 kg mouse runs as fast as the
cat, what is its kinetic energy?
mm = .10 kg
vm = 10.0 m/s
KEm = 1/2 mm vm2
KEm = 1/2 (.10 kg)(10.0 m/s)2
KEm = 5 J
EX: A 24 kg dog begins to chase the cat
and has the same kinetic energy as the
cat. What is the dog’s velocity?
md = 24 kg
KEd = 300 J
KEd = 1/2 md vd2
vd = √(2 Ked / md)
vd = √(2 (300 J) / 24 kg)
vd = 5.0 m/s
Potential Energy
 Gravitational
Potential Energy potential energy associated with an
object due to its position relative to
Earth or some other gravitational source
PEg = m g h
 Elastic
Potential Energy - the potential
energy in a stretched or compressed
elastic object
– Spring
– Rubber band
Potential Energy
Visual Concept
Elastic Potential Energy
 The
length of a spring when no external
forces are acting on it is called the relaxed
length
 PEe = 1/2 k x2
– PEe = 1/2 (spring constant)(distance stretched
or compressed)2
 Spring
constant - a parameter that
expresses how resistant a spring is to being
compressed or stretched
Elastic Potential Energy
Spring Constant
spring constant  stiff spring
 Low spring constant  flexible spring
k = F / d
 High
– Units  N / m
Spring Constant
Visual Concept
EX: When a 2.00 kg mass is attached to a
vertical spring, the spring is stretched 10.0 cm
so the mass is 50.0 cm above the table.
m = 2.00 kg
x = 10. cm = .10 m
h = 50.0 cm = .50 m
A. What is the gravitational potential energy
associated with the mass relative to the table?
m = 2.00 kg
x = 10. cm = .10 m
h = 50.0 cm = .50 m
PEg = mgh
PEg = (2.00 kg)(9.8 m/s2)(.50 m)
PEg = 9.8 J
B. What is the elastic potential energy if the
spring constant is 400.0 N/m?
m = 2.00 kg
x = 10. cm = .10 m
h = 50.0 cm = .50 m
k = 400.0 N/m
PEe = 1/2 k x2
PEe = 1/2 (400.0 N/m)(.10m)2
PEe = 2.00 J
C. What is the total potential energy of the
system?
m = 2.00 kg
x = 10. cm = .10 m
h = 50.0 cm = .50 m
k = 400.0 N/m
∑PE = PEg + PEe
∑PE = 9.8 J + 2.00 J
PEe = 11.8 J
Mechanical Energy
 There
are many types of energy
associated with a system
– Kinetic
– Gravitational potential
– Elastic potential
– Chemical
– Thermal
• Most can be ignored because they are
negligible or not relevant
Mechanical Energy
 Mechanical
energy - the sum of the
kinetic and all forms of potential energy
 ME = ∑KE + ∑PE
 All other forms of energy are classified
as non-mechanical energy
Conservation of Energy
 Conserve
means it remains the same
 Conservation of mechanical energy
MEi = MEf
∑KEi + ∑PEgi + ∑PEei = ∑KEf + ∑PEgf + ∑PEef
 In
the presence of friction, energy is “lost” to
heat energy
Niagara Falls and Energy
Transformation
Video
Conservation of Mechanical
Energy
Visual Concept
Energy of a roller coaster
As the roller coaster falls the energy is transformed
from potential energy to kinetic energy
 The energy is then transferred back into potential
energy, etc.

Energy is a sling shot
It starts with elastic potential energy
 It quickly transfers into kinetic energy
 As the height increases it transfers into gravitational
energy
 As it falls the energy transfers into kinetic energy

EX: A small 10.0 g ball is held to a slingshot that
is stretched 6.0 cm. The spring constant of the
band on the slingshot is 2.0 X 102 N/m.
A. What is the elastic potential energy of the
slingshot before it is released
m = 10.0 g = .0100 kg
x = 6.0 cm = .06 m
k = 2.0 X 102 N/m
PEe = 1/2 k x2
PEe = 1/2 (2.0 X 102 N/m)(.06 m)2
PEe = .36 J
B. What is the kinetic energy of the ball just after
the slingshot is released?
MEi = MEf
∑KEi + ∑PEgi + ∑PEei = ∑KEf + ∑PEgf + ∑PEef
∑PEei = ∑KEf
.36 J = ∑KEf
C. What is the balls speed at the instant it
leaves the slingshot?
KEf = 1/2 m v2
v = √ (2KEf / m)
v = √(2(.36 J) / (.01 kg))
v = 8.5 m/s
D. How high would the ball travel if it were shot
directly upward?
MEi = MEf
∑KEi + ∑PEgi + ∑PEei = ∑KEf + ∑PEgf + ∑PEef
∑KEi = ∑PEgf
.36 J = ∑PEf
PEf = mgh
h = PEf / mg
h = .36 J / ((.01 kg)(9.8 m/s2))
h = 3.7 m
Work and Energy
 Work-kinetic
energy theorem - the net
work done on an object is equal to the
change in the kinetic energy of the
object
 Wnet = ∆ KE
 Wfriction = ∆ ME
Work Kinetic Energy Theorem
Visual Concept
Potential Energy is transferred into Kinetic Energy
 Next the change in the Kinetic Energy is equal to the
net work

Stopping Distance

If an object
has a
higher
kinetic
energy,
more work
is required
to stop the
object
Ex: On a frozen pond, a person kicks a 10.0 kg
sled, giving it an initial speed of 2.2 m/s. How far
does it travel if the coefficient of kinetic friction
between the sled and the ice is .10?
vi
W = ∆KE
µk = Fk / FN
F d = KEf - KEi Fk = µk (-mg)
µk (-mg) d = 1/2 m vf2 - 1/2 m vi2
µk (-mg) d = - 1/2 m vi2
m = 10.0 kg
d = (- 1/2 m vi2) / µk (-mg)
vi = 2.2 m/s
d = (- 1/2 (10.0 kg) (2.2 m/s)2) /
vf = 0 m/s
(.10 (-10.0 kg) (9.8 m/s2))
µk = .10
d = 2.47 m
EX: A 10.0 kg shopping cart is pushed
from rest by a 250.0 N force against a
50.0 N friction force over 10.0 m distance.
m = 10.0 kg
vi = 0
Fp = 250.0 N
Fk = 50.0 N
d = 10.0 m
FN
Fp
Fk
Fg
A. How much work is done by each force
on the cart?
Wg = 0
WN = 0
Wp = Fp d cos 
Wp = (250.0 N)(10.0 m)cos 0
Wp = 2500 J
Wk = Fk d cos 
Wk = (50.0 N)(10.0 m)cos 180
Wk = -500 J
B. How much kinetic energy has the cart
gained?
Wnet = ∆KE
Wp + Wk = KEf - KEi
2500 J + -500 J = KEf - 0
KEf = 2000J
C. What is the carts final speed?
KE = 1/2 m v2
v = √((2KE)/(m))
v = √((2(2000 J))/(10.0 kg))
v = 20 m/s
Power
 Power
- the rate at which energy is
transferred
P = W / ∆ t
– Units  J / s  watt (w)
 Since
P = W / ∆ t and W = F d;
– P = F d / ∆ t  P = F (d / t)
–P=Fv
 Horsepower
is another unit of power
– 1 hp = 746 w
Power Defined
Video
Power
Visual Concept
EX: A 100.0 N force moves an object 20.0
m in 5.0 s. What is the power?
F = 100.0 N
d = 20.0 m
F = 100.0 N
d = 20.0 m
t = 5.0 s
P = F (d / t)
P = 100.0 N (20.0 m / 5.0 s)
P = 400 w
EX: Two horses pull a cart. Each exerts a
250 N force at a 2.0 m/s speed for 10.0
min.
Fh1 = 250 N
Fh2 = 250 N
v = 2.0 m/s
v = 2.0 m/s
∆ t = 10.0 min
F = 250 N
= 600 s
F = 250 N
A. Calculate the power delivered by the
forces.
Ph1 = Fh1 v
Ph1 = (250 N)(2.0 m/s)
Ph1 = 500 w
Ph2 = Fh2 v
Ph2 = (250 N)(2.0 m/s)
Ph2 = 500 w
∑P = Ph1 + Ph2
∑P = 500 w + 500w
∑P = 1000 w
B. How much work is done by the two
horses?
P=W/∆t
W=P∆t
W = (1000 w)(600 s)
W = 6.0 X 105 J
Work Cited
 Sources
– www.classroomphysics.com
– www.clipart.com
– Holt Physics
– United Streaming