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Physics 1D03
Work and Kinetic Energy
•
Work by a variable force
•
Kinetic Energy and the Work-Energy Theorem
Serway 7.4, 7.5
Suggested Problems
:
Chapter 7, problems 15, 17, 21, 31, 35
Physics 1D03
Work is the area under a graph of force vs.
distance:
dx
F
W
x
x
f
i
∫
=
i
x
f
x
Split displacement into short
steps
Δ
x
over which F is nearly
constant.
..
F(x)
x
i
x
f
x
F(x)
x
Take the limit as
x
→
0
and the
number of steps
→ ∞
x
F
W
Δ
⋅
≈
∑
We get the total work by adding up the work done in all the small steps.
As we let
x
become small, this becomes the area under the curve, and
the sum becomes an integral.

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Physics 1D03
In 1D (motion along the x-axis):
dx
F
W
x
x
f
i
∫
=
Another way to look at it: Suppose W(x) is the total work done in
moving a particle to position x. The
extra
work to move it an
additional
small distance
Δ
x is, approximately,
W
≈
F(x)
x.
Rearrange to get
x
W
x
F
Δ
Δ
≈
)
(
In the limit as
x goes to zero,
dx
dW
x
F
=
)
(
Physics 1D03
Example: an ideal spring.
Hooke’s Law: The tension in a spring is
proportional to the distance stretched.
or,

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