Answer:

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Physics 1710 Chapter 7Work
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• Answer
• a v 2 /r (15 m/s)2/(0.2 m) 1125 m/s2
• a113 g!!!
• F m a (1.00 x 10 4kg)/(1.1 x10 3 m/s2)
  0.11 kg m/s2 0.11 N

Which way will the ant fly off?
m
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Physics 1710 Chapter 7Work
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• Query
• What was the most significant international
  development to occur in the 19th century?

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Physics 1710 Chapter 7Work
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• Most significant international development of in
  the 19th century (1800 s)?

Peer Instruction Time
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Physics 1710 Chapter 7Work
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• What was the Industrial Revolution?

Our concept of work changed forever.
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Physics 1710 Chapter 7Work
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• 1' Lecture
• Work is defined to be the distance traveled
  multiplied by the distance over which the force
  acts.
• ?W ?ab Fd r

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Physics 1710 Chapter 7Work
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• Work
• Work is the product of the distance moved in the
  direction of the force and the magnitude of the
  force.
• OR
• Work is the distance moved multiplied by the
  component of the force in the direction moved.

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Physics 1710 Chapter 7Work
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• Work
• dW Fd r Force times distance
• Note Scalar Product, inner product,
• dot product
• dW Fd r Fx dx Fy dy Fz dz
• OR
• dW Fd r F cos ?dr

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Physics 1710 Chapter 7Work
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• Scalar Product
• AB Ax Bx AyBy Az Bz

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Physics 1710 Chapter 7Work
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• Scalar Product
• AB Ax Bx AyBy Az Bz

AB AB cos ?
?
ß
a
ABcos ? ABcos(ß-a) ABcos(ß)cos(a)
sin(ß)sin(a) Acos(a)Bcos(ß) Asin(a)Bsin(ß)
Ax BxAyBy
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Physics 1710 Chapter 7Work
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• Scalar Product (properties)
• AA Ax2 Ay2 Az2 ?A?2
• AB BA
• A(B C) AB AC

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Physics 1710 Chapter 7Work
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• Work
• W ?Fd r
• Scalar Product
• W ?Fd r ? Fx dx ? Fy dy ? Fz dz
• OR
• W ? Fd r ?F cos ?dr

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Physics 1710 Chapter 7Work
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• Unit of Work
• F ? d N?m Joule J

Joule
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Physics 1710 Chapter 7Work
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• Scalar Product
• AB a scalar
• AB Ax Bx Ay By Az Bz
• AB AB cos ?
• Unit vectors i?i j?j k?k 1
• Orthogonal i?j i?k j?k 0

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Physics 1710 Chapter 7Work
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• Work done by varying Force
• W ? Fd r
• For Example Spring
• Fspring - k x
• W ? Fspring d x ? -x 0(-k x) dx ½ k x 2

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Physics 1710 Chapter 7Work
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• Work Done
• W ? F ?d x
• ?0.5 x3 dx
• ¼ (0.5) x 41 ¼ (0.5) (0.2) 4
• 0.2 mJ

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Physics 1710 Chapter 7Work
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• Work Done to accelerate body
• The work done to accelerate a body from a speed
  vi to a speed vf is
• F m a
• W ? m a ?d x
• m ?dv/dt vdt
• m ?if vdv
• ½ m v f 2 - ½ m v i 2

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Physics 1710 Chapter 7Work
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• Summary
• Work is defined to be the distance traveled
  multiplied by the distance over which the force
  acts.
• W ? Fd r
• Joules N m