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Chapter 5 – WORK and ENERGY
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5.2 MECHANICAL ENERGY
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ENERGY = ability to do WORK
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ENERGY = ability to do WORK
the energy of an object that is due to the
object’s motion
KINETICPOTENTIALthe energy
associated with an object
because of its position, shape,
or condition
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KINETIC ENERGY
A cart:mass = mforce =
constantSo a =
constant
Δx
Wnet = F ∙ dWnet = F ∙ ΔxWnet = m ∙ a
∙ Δx
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KINETIC ENERGY
Δx
Wnet = m ∙ a ∙ Δx
Wnet = ½ mvf2 – ½
mvi2
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KINETIC ENERGY depends on SPEED and MASS
KINETIC ENERGY = KE = Ek =
Wnet = ½ mvf2 – ½
mvi2
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KINETIC ENERGY depends on SPEED and MASS
KINETIC ENERGY = KE = Ek =
Wnet = ½ mvf2 – ½ mvi
2 = ΔKE = ΔEk
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WORK – KINETIC ENERGY THEOREM
Net work = change in kinetic energy
Wnet = ½ mvf2 – ½
mvi2 Wnet = KEf – KEi
Wnet = ΔKE
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KINETIC ENERGY = KE = Ek =
UNITS = Joules
KINETIC ENERGY depends on SPEED and MASS
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WORKSHEET EXAMPLEA 6.0 kg cat runs after a mouse at
10 m/s. What is the cat’s kinetic
energy?
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WORKSHEET EXAMPLEA 6.0 kg cat runs after a mouse at
10m/s. What is the cat’s kinetic
energy?KE = 300 J
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Wnet = 4.1975 x 104 J = 4.2 x 104 J
Wnet = ½ mvf2 – ½ mvi
2 = ΔKE
Wnet = 7.2 x 10-2 J
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EXAMPLEOn a frozen pond, a person kicks a 10.0 kg sled, giving it an initial speed of 2.2 m/s.
How far does the sled move if the coefficient of kinetic friction between
the sled and the ice is 0.10?
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EXAMPLEOn a frozen pond, a person kicks a 10.0 kg sled, giving it an initial speed of 2.2 m/s.
How far does the sled move if the coefficient of kinetic friction between
the sled and the ice is 0.10?GIVEN
?UNKNOWN
?FBD?
mass = 10.0 kgvi = 2.2
m/svf = 0.0
m/sμk = 0.10
d = Δx = ??
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EXAMPLEmass = 10.0 kgvi = 2.2
m/svf = 0.0
m/sμk = 0.10
d = Δx = ??Wnet = F ∙ d
Net Wnet is due to Ff, so…
Wnet = Ff ∙ d
-½ mvi2 = μk ∙ m ∙ g ∙ dd = 2.5 m
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WORKSHEET EXAMPLEHow much net work is needed to
accelerate a 1000.0 kg car from 20.0 m/s to 30.0 m/s
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WORKSHEET EXAMPLEHow much net work is needed to
accelerate a 1000.0 kg car from 20.0 m/s to 30.0 m/s
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HOMEWORKWorksheetProblems: Practice B
Practice C
19
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POTENTIAL ENERGY
gravitational
elastic
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POTENTIAL ENERGYthe energy associated with an object
because of its position, shape, or condition
It is stored energy
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POTENTIAL ENERGYDepends on the properties of an
object and its interactions with its environment
It is stored energy
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GRAVITATIONAL POTENTIAL ENERGYIs the energy of an object due to the
objects position relative to a gravitational source
i.e. energy stored in an object due to its position relative to the Earth’s
gravitational field
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GRAVITATIONAL POTENTIAL ENERGYi.e. energy stored in an object due to
its position relative to the Earth’s gravitational field
Potential energy
Kinetic energy
Where did the KE come from?
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GRAVITATIONAL POTENTIAL ENERGYi.e. energy stored in an object due to
its position relative to the Earth’s gravitational field
Potential energy
Kinetic energy
GRAVITATIONALPOTENTIAL
ENERGY
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GRAVITATIONAL POTENTIAL ENERGYi.e. energy stored in an object due to
its position relative to the Earth’s gravitational field
Ep = PEg = Ug = m ∙ g ∙ h UNITS =
JoulesREMEMBER:a. free – fall acceleration = constant
(near the E’s surface) for PEg to be valid
b. It is relative (because measuring the height is arbitrary)
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TRUE or FALSE?Suppose I throw a volleyball from a second floor roof (A), and it lands on the first floor
of an adjacent building (B)…
If the height is measured from the ground (C),
PEg is zero.
PEg = m∙g∙h
If the height is measured from the 1st floor (B),
PEg is zero.
TRUE
FALSE
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Can You Have a Negative PE?
If YES, give an example
If NOT, explain why.
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Can You Have a Negative PE?
You could bring a textbook from a table height to a zero – level (ground) –
performing a negative work
If yes, give an example
If not, explain why.
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Can you have an object with a positive PE relative to one point and negative PE to another point at the same time?
If YES, give an example
If NOT, explain why.
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A textbook which is 0.5 m below a table (negative PE relative to the
table)
If yes, give an example
If not, explain why.
A textbook which is 0.5 m above the ground (positive PE relative to
the table)
Can you have an object with a positive PE relative to one point and negative PE to another point at the same time?
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m = 25 kg
h = 6 m
Potential energy doubles
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ELASTIC POTENTIAL ENERGYIs the energy of available for use when a deformed elastic object
(spring, bungee cord…) returns to its original position
PEelastic = ½ kx2
x
PEelastic = ½ spring constant ∙ (distance compressed/stretched)2
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k = SPRING CONSTANTMeasures how easy is to compress or
stretch a spring
SMALL k LARGE kVery flexible
Easy to stretch
Very stiffDifficult to
stretch
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WHAT IS THE UNIT OF k?
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WORKSHEET EXAMPLEA 70.0 kg stuntman is attached to a bungee cord with an
unstretched length of 15.0 m. He jumps off a bridge spanning a river from a height of 50.0 m. When he finally
stops, the cord has a stretched length of 44.0 m. Treat the stuntman as a point mass, and disregard the weight
of the bungee cord and air resistance. Assuming the spring constant of the bungee cord is 71.8 N/m,
WHAT IS THE TOTAL POTENTIAL ENERGY RELATIVE TO THE WATER WHEN THE MAN
STOPS FALLING?
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EXAMPLEA 70.0 kg stuntman is attached to a bungee cord with an
unstretched length of 15.0 m. He jumps off a bridge spanning a river from a height of 50.0 m. When he finally
stops, the cord has a stretched length of 44.0 m. Treat the stuntman as a point mass, and disregard the weight
of the bungee cord and air resistance. Assuming the spring constant of the bungee cord is 71.8 N/m,
WHAT IS THE TOTAL POTENTIAL ENERGY RELATIVE TO THE WATER WHEN THE MAN
STOPS FALLING?PEtot = PEg + PEelastic
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EXAMPLEA 70.0 kg stuntman is attached to a bungee cord with an
unstretched length of 15.0 m. He jumps off a bridge spanning a river from a height of 50.0 m. When he finally
stops, the cord has a stretched length of 44.0 m. Treat the stuntman as a point mass, and disregard the weight of the bungee cord. Assuming the spring constant of the
bungee cord is 71.8 N/m, What is the total potential energy relative to the water when
the man stops falling?
GIVEN?
UNKNOWN?
FBD?
Choose the water level to be 0 PEg
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EXAMPLEmass = 70.0
kg
k = 71.8 N/m
h = 50.0 – 44.0 = 6.0 m
x = 44.0 – 15.0 = 29.0 m
PE = 0 J (at river level)
PEtot = PEg + PEelastic = ?
h Choose the water level to be 0 PEg
x
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EXAMPLEmass = 70.0
kg
k = 71.8 N/m
h = 50.0 – 44.0 = 6.0 m
x = 44.0 – 15.0 = 29.0 m
PE = 0 J (at river level)
PEtot = PEg + PEelastic = ? PEg = m ∙ g ∙ hPEelastic = ½ kx2
PEtot = 3.43 x 104 J
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WORKSHEET EXAMPLEWhen a 2.00 kg mass is attached to a vertical spring, the spring is stretched 10.0 cm such that the mass is 50.0
cm above the table.a.What is the gravitational
potential energy associated with this mass relative to the table?
b.What is the spring’s elastic potential energy if the spring
constant is 400.0 N/m?
c.What is the total potential energy of this system?
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WORKSHEET EXAMPLEWhen a 2.00 kg mass is attached to a vertical spring, the
spring is stretched 10.0 cm such that the mass is 50.0 cm above the table.
a. What is the gravitational potential energy associated with this mass relative to the table?
b. What is the spring’s elastic potential energy if the spring constant is 400.0 N/m?
c. What is the total potential energy of this system?
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HOMEWORKWorksheet:Problems: Practice D
43
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MECHANICAL ENERGY
Chemical, nuclear,
electrical…
ME = KE + PE
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MECHANICAL ENERGY
PENDULUM
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MECHANICAL ENERGY
Describe each picture in terms of potential and kinetic
energy
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MECHANICAL ENERGY
PEg present (at max)
No KE present
PEg presentKE present
No PEg present
KE present (at max)
PEg present (at max)
No KE present
PEg present KE present
No PEg present
KE present (at max)
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MECHANICAL ENERGY
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MECHANICAL ENERGY
ME = KE + ∑PE
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CONSERVATION OF ENERGY
Who can describe what is
happening in the next
demonstration?
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ME is often conserved E remains
constant
KEi + ∑ PEi = KEf + ∑ PEf
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CONSERVATION OF ENERGY
KEi + ∑ PEi = KEf + ∑ PEf
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CONSERVATION OF ENERGY
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EXAMPLEStarting from rest, a child zooms down
a frictionless slide from an initial height of 3.00 m. WHAT IS HER SPEED
AT THE BOTTOM OF THE SLIDE? Assume she has a mass of 25.0 kg.
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EXAMPLEStarting from rest, a child zooms down
a frictionless slide from an initial height of 3.00 m. WHAT IS HER SPEED
AT THE BOTTOM OF THE SLIDE? Assume she has a mass of 25.0 kg. GIVEN
?UNKNOWN
?FBD?
vi = 0.0
m/sh = hi = 3.00 mhf = 0.00
m
vf = ? m/s
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EXAMPLEStarting from rest, a child zooms down
a frictionless slide from an initial height of 3.00 m. WHAT IS HER SPEED
AT THE BOTTOM OF THE SLIDE? Assume she has a mass of 25.0 kg.
FBD?PEg,i = m ∙ g ∙ hi
PEg,f = 0 J
KEi = 0 J
KEf = ½ mvf
2
KEi + ∑PEi = KEf + ∑PEf
vf = 7.67 m/s
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WORKSHEET EXAMPLEA small 10.0 g ball is held to a
slingshot that is stretched 6.0 cm. The spring constant is 2.0 × 102 N/m.
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WORKSHEET EXAMPLEA small 10.0 g ball is held to a
slingshot that is stretched 6.0 cm. The spring constant is 2.0 × 102 N/m.a. What is the elastic potential energy of the slingshot before
it is released?b. What is the kinetic energy
of the ball just after the slingshot is released?
c. What is the ball’s speed at that instant?
d. How high does the ball rise if it is shot directly upward?
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WORKSHEET EXAMPLEA small 10.0 g ball is
held to a slingshot that is stretched 6.0
cm. The spring constant is 2.0 × 102
N/m.a. What is the elastic
potential energy of the slingshot before it is
released?b. What is the kinetic energy of the ball just after the slingshot is
released?c. What is the ball’s
speed at that instant?d. How high does the ball rise if it is shot
directly upward?
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HOMEWORKProblems: Practice E
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QUIZDate: Tuesday, Dec 17
What?: Chapter 5.2 Mechanical Energy
61
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ANSWERS TO
WORKSHEET EXAMPLES
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WORKSHEET EXAMPLEA 6.0 kg cat runs after a mouse at
10m/s. What is the cat’s kinetic
energy?KE = 300 J
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WORKSHEET EXAMPLEHow much net work is needed to
accelerate a 1000.0 kg car from 20.0 m/s to 30.0 m/s
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Can You Have a Negative PE?
You could bring a textbook from a table height to a zero – level (ground) –
performing a negative work
If yes, give an example
If not, explain why.
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Can you have an object with a positive PE relative to one point and negative PE to another point at the same time?
A textbook which is 1.0 m below a table (negative PE relative to the
table)
If yes, give an example
If not, explain why.
A textbook which is 1.0 m above the ground (positive PE relative to
the table)
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WHAT IS THE UNIT OF k?
N/m
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WORKSHEET EXAMPLEWhen a 2.00 kg mass is attached to a vertical spring, the
spring is stretched 10.0 cm such that the mass is 50.0 cm above the table.
a. What is the gravitational potential energy associated with this mass relative to the table?
b. What is the spring’s elastic potential energy if the spring constant is 400.0 N/m?
c. What is the total potential energy of this system?