Dr- Sonia Reda chapter 7 Kinetic energy and Work 7.2 What is energy 7.3Kinetic energy 7.4Work 7.5...
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Transcript of Dr- Sonia Reda chapter 7 Kinetic energy and Work 7.2 What is energy 7.3Kinetic energy 7.4Work 7.5...
Dr- Sonia RedaDr- Sonia Reda
Dr- Sonia RedaDr- Sonia Reda
chapter 7chapter 7Kinetic energy and WorkKinetic energy and Work
7.2 What is energy7.2 What is energy
7.37.3 Kinetic energyKinetic energy
7.47.4 WorkWork
7.57.5 WorkWork andand kinetickinetic EnergyEnergy
7.67.6 Work done by the gravitational forceWork done by the gravitational force
7.77.7 Work done by a Spring forceWork done by a Spring force
7.8 Power7.8 Power
7.2 What is energy7.2 What is energy
7.37.3 Kinetic energyKinetic energy
7.47.4 WorkWork
7.57.5 WorkWork andand kinetickinetic EnergyEnergy
7.67.6 Work done by the gravitational forceWork done by the gravitational force
7.77.7 Work done by a Spring forceWork done by a Spring force
7.8 Power7.8 Power
Outline Chapter 7Outline Chapter 7Work and Kinetic energyWork and Kinetic energy
Work done by a net force results in kinetic energy
Some examples: gravity, spring, friction
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What is Energy? What is Energy? The term energy is so broad that a clear definition is difficult to write.
Technically,
Energy is a scalar quantity associated with the state (or condition) of one or
more objects.
However, this definition is too vague to be of help to us now.
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Kinetic EnergyKinetic Energy
Kinetic energyKinetic energy KK is energy associated is energy associated with the with the state of motionstate of motion of an object. of an object.
For an object of mass For an object of mass mm whose speed whose speed vv is well is well below the speed of light, below the speed of light, Kinetic energyKinetic energy KK is: is:
Unit for Unit for Kinetic energyKinetic energy is: is:
Kinetic energy is a scalar quantity.
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WorkWork
Work Work WW is energy transferred to or from an object by is energy transferred to or from an object by means of a force acting on the object.means of a force acting on the object.
Energy transferred to the object is positive work,Energy transferred to the object is positive work, Energy transferred from the object is negative work.Energy transferred from the object is negative work.
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Properties of WorkProperties of Work
Only the force component along the object’s Only the force component along the object’s displacement will contribute to work. displacement will contribute to work.
The force component perpendicular to the The force component perpendicular to the displacement does zero work. displacement does zero work.
A force does positive work when it has a vector A force does positive work when it has a vector component in the same direction displacement,component in the same direction displacement,
A force does negative work when it has a vector A force does negative work when it has a vector component in the opposite direction. component in the opposite direction.
Work is a scalar quantity.Work is a scalar quantity.
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Finding an Expression for WorkFinding an Expression for Work
we can use Eq. 2-16 to write, for components along the x axis,v2
=vo2 + 2axd
By multiplying the above Eq with ½ m
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Finding an Expression for WorkFinding an Expression for Work
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Kinetic Energy
Work-Kinetic Energy Theorem
Change in KE work done by all forces
K w
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xixf
f
i
f
i
vv
vv vmdvvm ]/[. 221
= 1/2mvf2 – 1/2mvi
2
= Kf - Ki
= KK
Work done by net force
= change in KE
f
i
xx dxFw .
f
i
xx dxma .
f
i
f
i
xx
xx dv
dtdx
mdxdtdv
m ..
Work-Kinetic Energy TheoremF
x
Vec
tor
sum
of
all f
orce
s ac
ting
on
the
body
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Checkpoint 1 Checkpoint 1
A particle moves along an A particle moves along an xx axis. Does the axis. Does the kinetic energy of the particle increase, kinetic energy of the particle increase, decrease, or remain the same if the decrease, or remain the same if the particle’s velocity changesparticle’s velocity changes
(a) from −3 m/s to −2 m/s and (a) from −3 m/s to −2 m/s and
(b) from −2 m/s to 2 m/s? (b) from −2 m/s to 2 m/s?
(c) In each situation, is the work done on the (c) In each situation, is the work done on the particle positive, negative, or zero?particle positive, negative, or zero?
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Example 7-3Example 7-3
During a storm, a crate of crepe is sliding across a During a storm, a crate of crepe is sliding across a slick, oily parking lot through a displacement slick, oily parking lot through a displacement
while a steady wind pushes against while a steady wind pushes against the crate with a force . The the crate with a force . The situation and coordinate axes are shown in Fig. situation and coordinate axes are shown in Fig. 7-57-5. .
(a) How much work does this force do on the crate (a) How much work does this force do on the crate during the displacement? during the displacement?
.
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(a) How much work does this force from the wind (a) How much work does this force from the wind do on the crate during the displacement?do on the crate during the displacement?
i)m0.3(j)N0.6(i)N0.2(dFW
J0.60)1()J0.6(
ij)m0.3()N0.6(ii)m0.3()N0.2(
Work done by the wind force on crate :
SOLUTION:
The wind force does negative work, i.e. kinetic energy is taken out of the crate.
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(b) If the crate has a kinetic energy of 10 J at the (b) If the crate has a kinetic energy of 10 J at the beginning of displacement , what is its kinetic beginning of displacement , what is its kinetic
energy at the end of ?energy at the end of ?d
d
J0.4)J0.6(J10WKK if
SOLUTION:
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mg
F
h
Lift mass m with constant velocity
Work done by me (take down as +ve)
= F.(-h) = -mg(-h) = mghWork done by gravity
= mg.(-h) = -mgh ________
Total work by ALL forces (W) = 0
What happens if I let go?
=K
Gravitation and work
Work done by ALL forces = change in KE
W = K
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Work Done by a Spring ForceWork Done by a Spring Force
The spring forceThe spring force given by given by Hooke’s Law:Hooke’s Law:
springxF k x
The work done by spring The work done by spring forceforce::
2 22 1
1 1( )2 2
springW kx kx
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Compressing a spring
Compress a spring by an amount x
Work done by me Fdx = kxdx = 1/2kx2
Work done by spring -kxdx =-1/2kx2
Total work done (W) =
0=K
What happens if I let go?
x
F -kx
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Ff
dWork done by me = F.d
Work done by friction = -f.d = -F.d
Total work done = 0What happens if I let go? NOTHING!!
Gravity and spring forces are Conservative
Friction is NOT!!
Moving a block against friction at constant velocity
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Sample Problem 7-8Sample Problem 7-8
In Fig. 7-11, a cumin canister of mass In Fig. 7-11, a cumin canister of mass mm = 0.40 kg = 0.40 kg slides across a horizontal frictionless counter with speed slides across a horizontal frictionless counter with speed vv = 0.50 m/s. It then runs into and compresses a spring = 0.50 m/s. It then runs into and compresses a spring of spring constant of spring constant kk = 750 N/m. When the canister is = 750 N/m. When the canister is momentarily stopped by the spring, by what distance momentarily stopped by the spring, by what distance dd is the spring compressed?is the spring compressed?
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SOLUTION:
We assume the spring is massless. Work done by the spring on the canister is negative. This work is :
221
S kdW
Kinetic energy change of the canister is : 2
21
if mvkk Therefore, 2
212
21 mvkd
cm2.1m10x2.1
m/N750
kg40.0)s/m50.0(
k
mvd
2
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PowerPower The rate at which work is done by a force The rate at which work is done by a force
is called the is called the power.power. The average power due to the work done by a force The average power due to the work done by a force
during that time interval as during that time interval as
We define the We define the instantaneous powerinstantaneous power PP as the as the instantaneous rate of doing work, so thatinstantaneous rate of doing work, so that
W = F . W = F . ΔΔxx
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The units of power The units of power
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Sample Problem 7-10Sample Problem 7-10
Figure 7-14 shows constant forces and Figure 7-14 shows constant forces and acting on a box as the box slides rightward acting on a box as the box slides rightward across a frictionless floor. Force is horizontal, across a frictionless floor. Force is horizontal, with magnitude 2.0 N; force is angled upward with magnitude 2.0 N; force is angled upward by 60° to the floor and has magnitude 4.0 N. by 60° to the floor and has magnitude 4.0 N. The speed The speed vv of the box at a certain instant is 3.0 of the box at a certain instant is 3.0 m/s.m/s.
1F
1F
2F
2F
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(a) What is the power due to each force acting on the box (a) What is the power due to each force acting on the box at that instant, and what is the net power? Is the net power at that instant, and what is the net power? Is the net power
changing at that instant?changing at that instant?
SOLUTION:
0
0.6
60cos)/0.3()0.4(60cos
0.6
180cos)/0.3()0.2(180cos
21
22
11
PPP
W
smNvFP
W
smNvFP
net
The kinetic energy of the box is not changing. The speed of the box remains at 3 m/s. The net power does not change.
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(b) If the magnitude of is, instead, 6.0 N, what (b) If the magnitude of is, instead, 6.0 N, what now is the net power, and is it changing?now is the net power, and is it changing?
2F
SOLUTION:
W0.3
W0.9W0.6PPP
W0.9
60cos)s/m0.3()N0.6(60cosvFP
21net
22
There is a net rate of transfer of energy to the box. The kinetic energy of the box increases. The net power also increases.
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