P3 Fluids and Elasiticity of Solids

7/30/2019 P3 Fluids and Elasiticity of Solids

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Physics Day 3-Fluids and Elasticity of SolidsHydrostatics

Density:V

m Specific Gravity

OH2

31000

2 m

kgOH

Pressure

A

F

P

1atm=760torr = 760mmHg ~ 100,000Pa

Hydrostatic Pressure (Gauge Pressure)Every 10m depth in H2O is ~1 atm pressuregDP fluid where D=depth

Manometers

Buoyancy Force (Archimedes Principle)

gVWF submergedfluiddisplacedfluidB _

objectB WF (if the object is floating)

% submerged 100fluid

object

Hydraulic Jack

2

2

1

1

A

F

A

F 2211 dAdA

Hydrodynamics

Flow Rate: A = cross-sectional areaAvf velocityv

2211 vAvA

Bernoullis Equation

2

2

221

2

112

1

2

1gyvPgyvP


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Springs

kxF k=spring constant x=displacement from equilibrium position

2

2

1.. kxEP

Conservation of Mechanical Energy

Elasticity of Solids

Stress = Modulus x Strain Stress Modulus Strain

Youngs ModulusStretching/Compression Stretching/Compression A

F=

Y

0L

L

Shear Modulus0L

LY

A

F S

A

F=

0L

X

Shear Deformation

Bulk Modulus

Volume DeformationP = B

0V

V

Shear Deformation

0L

XS

A

F

Volume Deformation

0V

VBP


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In-Class ProblemsFluids

1. The applied force is tripled and the area over which it is applied is cut in half. What is the affect on thepressure?

2. A snorkeler dives to a depth of 25m in a freshwater lake. What is the total pressure at this depth? Whatis the hydrostatic pressure?

3. A large piece of Styrofoam with a mass of 2kg and a specific gravity of 0.05 is floating in a pool of water.

What volume of the piece of Styrofoam is submerged below the surface?

4. If an object normally weighs 500N and while submerged in water it has an apparent weight of 300N,

what is the density of the object?

5. A block of wood having a specific gravity of 0.6 is floating in a pool of water. What percentage of the

block of wood is above the surface?

6. For the following hydraulic jack, how much force must be applied to the small side of the jack in order tolift a 250kg engine on the large side?


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7. If the radius of the larger portion of the pipe is 3 times larger than the radius of the smaller end of the

pipe, in which portion of the pipe is the velocity of an ideal fluid undergoing steady flow higher and how

much higher? Where is the pressure higher?

8. For an ideal fluid undergoing steady flow, in which region of the pipe is the pressure higher? Region 1?

Region 2? Not enough information given to determine?

2

1

Springs

9. If a 50N force displaces a spring 2cm from its equilibrium position, what displacement would a 10N forceresult in?

10. A spring with a spring constant of 800N/m and a 2kg mass on the end is stretched 10cm from itsequilibrium position. What is the velocity of the mass on the end of the spring as it passes through the

equilibrium position?

Elasticity of Solids11. A stretching force of 100N is applied to a 100cm length of wire of radius 1mm resulting in an elongation

of 5mm. What is the Youngs modulus of the wire?

12. A solid piece of metal with a bulk modulus of 1.0x1011 is dropped to a depth of 1000m. What is the

fractional change in the volume of this piece of metal?

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P3 Fluids and Elasiticity of Solids