energy and work energy - the ability of a body or system of bodies to perform work. a body is given...
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Energy and Work
Energy - the ability of a body or system of bodies to perform work.
A body is given energy when a force does work on it.
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But What is Work?
A force does work on a body (and changes its energy) when it causes a displacement.
If a force causes no displacement, it does no work.
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Riddle Me This
If a man holds a 50 kg box at arms length for 2 hours as he stands still, how
much work does he do on the box?
Nada Zip
Zilch
NONEZERO
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Counterintuitive Results There is no work done by a force
if it causes no displacement. Forces perpendicular to
displacement, such as the normal force, can do no work.
Likewise, centripetal forces never do work.
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Calculating WorkWork is the dot product of
force and displacement.
Work is a scalar resulting from the interaction of two vectors.
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Vector Multiplication
There are three ways to multiply vectors:
•Scalar Multiplication
•Dot Product
•Cross Product
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Scalar Multiplication
•Magnitude of vector changes.•Direction of vector does not change.
amF
a = 10 m·s-1
F = 50 N
If m = 5 kg
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Dot Product
BAW
Note that the dot
product of two vectors gives a scalar .
. and between angle theis BA
cosABBA
θ
A
B
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Dot Product
Geometrically, the dot product is the projection of one vector on a second
vector multiplied by the magnitude of the second vector.
θ
A
B
cosA
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Calculating WorkcosFssFW
dxxFW )(
θ
F
s
cosF
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Which does more work?
θ
F1
F2
Two forces are acting on the box shown causing it to move across the floor. Which force does more work?
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Vectors and Work
F
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Vectors and Work
Fs
W = F • sW = F s cos 0o
W = F sMaximum positive work
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Vectors and Work
F
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Vectors and Work
s
W = F • sW = F s cos Only the component of force aligned with displacement does work. Work is less.
F
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Vectors and Work
F
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Vectors and Work
F s
W = F • sW = F s cos 180o
W = - F sMaximum negative work.
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Gravity often does negative work.
mg
F
When the load goes up, gravity does negative work and the crane does positive work.
When the load goes down, gravity does positive work and the crane does negative work.
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Positive, zero, or negative work?
A box is being moved with a velocity v by a force P (parallel to v) along a level floor. The normal force is FN, the frictional force is fk, and the weight of the box is mg.
Decide which forces do positive, zero, or negative work.
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Positive, zero, or negative work?
v
mg
P
FN
fk
s
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Units of Work
cosFssFW
J = N·m
J = kg·m2·s-2
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Work and variable force
The area under the curve of a graph of force vs displacement gives the work done by the force.
F(x)
xxa xb
W = F(x) dxxa
xb