Chap. 5: Energy and Work
Today:
Work, Kinetic Energy, Work-Energy Theorem for 1D motion
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Motivation: Why do we learn about work and energy???
Energy : Central concept in science and engineering
… and in our daily lives…
Energy transforms from one type to other, but conserved.
In Physics 102, we learn about “Mechanical Energy”.
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Kinetic energy
Kinetic energy (K.E.): An energy associated with motion
Kinetic energy of an object of mass m and speed v
1 2
K .E.  K  mv
2
v
m
 Energy is a scalar quantity (No direction!)
SI Unit for energy: J (Joule)
2
m
m
J  kg  2  kg  2  m  N  m
s
s
3
1 2
K .E.  K  mv
2
The heavier and the faster,
the kinetic energy gets greater.
(KE of a fast baseball) vs (KE of a slow baseball) ?
(KE of a car at 60 mi/h) vs (KE of a trailer at 60 mi/h) ?
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iClicker
When the velocity of the object doubles,
its kinetic energy __________ .
(a)
(b)
(c)
(d)
doubles
quadruples
becomes half
unchanged
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What makes kinetic energy change?
(1 D motion)
Fnet  ma
Fnet x
defined as “Net Work”, Wnet , in 1D
Change in kinetic energy is equal to the “net work”!
Work-Energy Theorem
K f  Ki  K  Wnet
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Definition of work by a single force, F, in 1D:
WF  F x
m
(Work) = (Force) x (Displacement)
F
Work done by a force F on an object,
the displacement of which is
.
x
If F and
x are in the same direction,
If F and
x are in the opposite direction,
work done by F is positive.
work done by F is negative.
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iClicker Quiz 1
Work done by a gravity on a falling elephant
W  F x
is _________.
a) Positive
b) Negative
c) zero
If force and displacement point
the same direction, the work is _______.
Example: In this case, suppose m=1000 kg and
distance = 10 m, calculate work done by gravity.
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iClicker Quiz2: Work done by a gravity on a ball that is going up
Gravity
Displacement
W  F x
Is work positive, negative, zero?
a) Positive
b) Negative
c) zero
Gravity
If force and displacement point
the opposite directions, the work is ______.
Example: In this case, suppose m=10 kg and distance = 10 m,
calculate work done by gravity.
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Net Work when multiple forces are exerted on a single object
Wnet  Fnet x
 ( F1  F2  F3  ...)x
 F1x  F2 x  F3 x  ...
 W1  W2  W3  ...
Work-Energy Theorem
K f  Ki  K  Wnet
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Work-Energy Theorem
As shown for 1D motion,
K f  Ki  K  Wnet
 Work-Energy Theorem
Positive net work: KE increases (iClicker Quiz 1)
Negative net work: KE decreases (iClicker Quiz 2)
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iClicker Quiz
1. As a sled is pulled by dogs across a flat, snow-covered
field at a constant velocity, work done by the air
resistance and friction is _______,
2. …and the work done by dogs is ________,
3. … and net work done on the sled is _______.
a) Positive
b) Zero
c) Negative
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Example
A 5-kg object is moving at 7 m/s. A 2-N force is applied in the
opposite direction of motion and then removed after the object
has traveled an additional 20 m.
A) What is the initial kinetic energy?
B) What is the work done by 2N force?
C) What is the final kinetic energy?
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Example
A horizontal force of 200 N is applied to a 55-kg cart across a 10-m
rough level surface. If the cart accelerates at 2.0 m/s2, then what
is the work done by the force of friction as it acts to retard the
motion of the cart?
What is the work done by the 200 N force?
What is the net force?
Suppose the initial kinetic energy is 300 J. What is the final kinetic
energy?
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iClicker
A horizontal force of +100 N is applied in the x direction to a 20-kg
cart initially moving at -10 m/s in the x-direction. The cart finally
reaches a velocity of zero, reverses direction, and reaches +10 m/s
finally.
What is the work done by 100 N force between initial and the time
when the velocity reaches zero?
What is the work done by the 100 N force between initial and final?
a)
b)
c)
d)
e)
-1000 J
+1000 J
+2000 J
-2000 J
zero
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