Chapter 7
Kinetic Energy and Work
¾
Kinetic energy
¾
Work done by a force
¾
WorkKinetic Energy Theorem
¾
Power
m
m
Kinetic Energy
Kinetic energy
K
is defined as:
2
1
2
Km
v
=
Work:
(symbol W)
If a force
F
is applied to an object of mass
m
it can accelerate it and increase
its speed
v
and kinetic energy
K
.
Similarly
F
can decelerate
m
and decrease
its kinetic energy.
We account for these changes in
K
by saying that
F
has transferred energy
W
to or from the object.
If energy it transferred
to
m
(its
K
increases) we say that work was done by
F
on
the object (
W
> 0).
If on the other hand energy its transferred
from
the object (its
K
decreases)
we say that work was done
by
m
(
W
< 0)
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m
Consider a bead of mass
that can move without friction
along a straight wire along the
Finding an expr
xaxis. A cons
ession for Work done by a constant f
tant force
applied at an angle
or
to t
c:
h
e
m
φ
F
G
e wire is acting on the bead.
22
Apply Newton's second law:
Assume that the bead has an initial velocity
and after it has travelled a distance
its velocity is .
Apply the constant acceleration equation:
2
xx
o
ox
Fm
a
vv a
=
−=
v
dv
G
G
G
Multiply both sides by
2
2
2
cos
222
2
and
cos
Thus the work
done
the force
the bead is give
by
n by:
cos
on
x
x
io
f
f
i
x
d
m
F
mmm
m
vv
a
d
d
F
d
Fd
m
mm
KvK
v
K
K
F
d
WW
F
d
F
d
→
=
=
=
==
→
−
=
cos
WF
d
=
W
=⋅
GG
m
m
Note 1:
Note 2:
The unit of
is the same as that of
i.e.
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 Spring '10
 Cohen
 Physics, Energy, Force, Kinetic Energy, Mass, Potential Energy, Work, Joule

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