Work and Fluid Pressure

1
Work and Fluid Pressure

• Lesson 7.7

2
Work

• DefinitionThe product of
• The force exerted on an object
• The distance the object is moved by the force
• When a force of 50 lbs is exerted to move an
  object 12 ft.
• 600 ft. lbs. of work is done

12 ft
3
Hooke's Law

• Consider the work done to stretch a spring
• Force required is proportional to distance
• When k is constant of proportionality
• Force to move dist x k x F(x)
• Force required to move through i thinterval, ?x
• ?W F(xi) ?x

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Hooke's Law

• We sum those values using the definite integral
• The work done by a continuous force F(x)
• Directed along the x-axis
• From x a to x b

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Hooke's Law

• A spring is stretched 15 cm by a force of 4.5 N
• How much work is needed to stretch the spring 50
  cm?
• What is F(x) the force function?
• Work done?

6
Winding Cable

• Consider a cable being wound up by a winch
• Cable is 50 ft long
• 2 lb/ft
• How much work to wind in 20 ft?
• Think about winding in ?y amt
• y units from the top ? 50 y ft hanging
• dist ?y
• force required (weight) 2(50 y)

7
Pumping Liquids

• Consider the work needed to pump a liquid into or
  out of a tank
• Basic concept Work weight x dist moved
• For each ?V of liquid
• Determine weight
• Determine dist moved
• Take summation (integral)

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Pumping Liquids Guidelines

• Draw a picture with thecoordinate system
• Determine mass of thinhorizontal slab of liquid
• Find expression for work needed to lift this slab
  to its destination
• Integrate expression from bottom of liquid to the
  top

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Pumping Liquids
4

• Suppose tank has
• r 4
• height 8
• filled with petroleum (54.8 lb/ft3)
• What is work done to pump oil over top
• Disk weight?
• Distance moved?
• Integral?

8
(8 y)
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Fluid Pressure

• Consider the pressure of fluidagainst the side
  surface of the container
• Pressure at a point
• Density x g x depth
• Pressure for a horizontal slice
• Density x g x depth x Area
• Total force

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Fluid Pressure

• The tank has cross sectionof a trapazoid
• Filled to 2.5 ft with water
• Water is 62.4 lbs/ft3
• Function of edge
• Length of strip
• Depth of strip
• Integral

(-4,2.5)
(4,2.5)
(-2,0)
(2,0)
y 1.25x 2.5x 0.8y 2
2 (0.8y 2)
2.5 - y
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Assignment

• Lesson 7.7a
• Page 307
• Exercises 1 13 odd, 21
• Lesson 7.7b
• Page 307
• Exercises 23 35 odd