Why does the earth “have more gravity,” i.e. g is larger on earth, than does the moon?

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Physics 1710Physics 1710—Warm-up Quiz—Warm-up QuizWhy does the earth “have more gravity,” Why does the earth “have more gravity,” i.e. g is larger on earth, than does the i.e. g is larger on earth, than does the moon?moon?

A B C D E

A.A. The earth as an atmosphere.The earth as an atmosphere.B.B. The earth has a larger diameter.The earth has a larger diameter.C.C. The earth has more mass.The earth has more mass.D.D. The earth rotates faster.The earth rotates faster.E.E. None of the above.None of the above.

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Analysis:Analysis:

• The earth has an atmosphere because of The earth has an atmosphere because of its larger g, not vis versa.its larger g, not vis versa.

• The larger diameter means smaller The larger diameter means smaller g~1/Rg~1/R22

• The larger mass of the earth m = 4/3The larger mass of the earth m = 4/3πρRπρR33 makes a larger g=GM/makes a larger g=GM/RR22

•Gravity has nothing to do with the rate of Gravity has nothing to do with the rate of rotation.rotation.

Physics 1710Physics 1710—C—Chapter 14 Fluid hapter 14 Fluid DynamicsDynamics

Summary: Summary: •Pressure Pressure is the force per unit area. P =F/A is the force per unit area. P =F/A

• Unit of pressue [Pacal] = [N]/[mUnit of pressue [Pacal] = [N]/[m22]]

•The The hydrostatic pressurehydrostatic pressure is P = P is P = Poo + + ρρghgh

• Archimedes’ PrincipleArchimedes’ Principle: F: Fbouyant bouyant = = ρρfluid fluid g Vg V

• Equation of ContinuityEquation of Continuity: A: A11vv11 = A = A22vv22

• Bernoulli’s Equation:Bernoulli’s Equation: P + ½ ρvP + ½ ρv22 + ρgy = + ρgy = constant.constant.

80/20Pressure = Force per unit Area

P = F /A

80/2080/20The unit of pressure in SI units is The unit of pressure in SI units is the the

Pascal [Pa] = 1 Newton/ mPascal [Pa] = 1 Newton/ m22

1 Newton 1 Newton forceforce

1 square meter 1 square meter areaarea

1 Pascal 1 Pascal pressure:pressure:

80/2080/20Standard atmosphere = 1.0 Standard atmosphere = 1.0 atm atm

=101 kPa=101 kPa

=14.7 psi=14.7 psi

Tire Tire pressurepressure

A few 100 A few 100 kPakPa

Which applies Which applies

the greatest the greatest

pressure on pressure on

their foot?their foot?

Which applies the greatest Which applies the greatest pressure on their foot?pressure on their foot?

A.A. Man. Man.

B.B. Elephant. Elephant.

C.C. Woman.Woman.

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Force = 200 lb = Force = 200 lb = 891 N891 N

Force = 4,000 lb = Force = 4,000 lb = 17,800 17,800 NN

Force = 100 lb = Force = 100 lb = 445 N445 N

Foot Area = 36.2 inFoot Area = 36.2 in22 = = 0.023 m0.023 m22

Foot Area = 43.5 inFoot Area = 43.5 in22 = = 0.028 m0.028 m22

Foot Area = 12.7 inFoot Area = 12.7 in22 = = .0082 m.0082 m22

p = F/A =200/(2 x 36.2) = 2.8 psip = F/A =200/(2 x 36.2) = 2.8 psip = 891/(2 x 0.023) = p = 891/(2 x 0.023) = 19 kPa19 kPa

p = F/A =4000/(4 x 43.5) = 23. psip = F/A =4000/(4 x 43.5) = 23. psip = 17800/(4 x 0.028) = p = 17800/(4 x 0.028) = 159 kPa159 kPa

p = F/A =100/(2 x 12.7) = 3.9 psip = F/A =100/(2 x 12.7) = 3.9 psip = 445/(2 x 0.0082) = p = 445/(2 x 0.0082) = 27 kPa27 kPa

Force = 100 lb = Force = 100 lb = 445 N445 NHeel Area = 0.16 inHeel Area = 0.16 in22 = = .0001 m.0001 m22p = F/A =100/(2 x 0.16) = 313. psip = F/A =100/(2 x 0.16) = 313. psip = 445/(2 x 0.0001) = p = 445/(2 x 0.0001) = 2200. kPa2200. kPa

p = p = 19 kPa19 kPa

p = p = 159 kPa159 kPa

p = p = 27 kPa27 kPa

The Mysterious Swami Seat

80/20Pressure = Force per unit Area

p = F /A

Same ForceSame Force

Different AreaDifferent Area

∴∴Different Different PressurePressure

Pressure is the hydraulic stress:Pressure is the hydraulic stress:

Hydraulic Stress: Hydraulic Stress: Bulk Modulus BBulk Modulus B

Stress = modulus x strainStress = modulus x strainσ = σ = F/A = p = B F/A = p = B ε = B ε = B ΔV/VΔV/V

ΔVΔV

Pressure is isotropic:Pressure is isotropic:

PP PPPP PP

F1= A1P; F2 = A2P

Hydrostatic Pressure is due to weight Hydrostatic Pressure is due to weight of fluid above:of fluid above:

F = m g = (Ah)ρfluid g

P = F/A = ρfluid g h

Archimedes PressureArchimedes Pressure

F = AΔP - mg= A ρfluid g Δh – mg

F = Fbouyant - mg

Fbouyant = ρfluid g V

Archimedes PressureArchimedes Pressure

Fbouyant = ρfluid g V

PP- ρfluid V g

ContinuityContinuity

V constant if fluid is incompressible.

A1v1 = A2v2

Work done on fluid Work done on fluid

ΔW = ½ m v2 + mg y

dW/dV = ½ ρ v2 +ρg y = d (Fy)/dV = dF/dA =ΔP

½ ρ v2 +ρg y =ΔP

Summary: Summary: •Pressure Pressure is the force per unit area. P =F/A is the force per unit area. P =F/A

• Unit of pressue [Pacal] = [N]/[mUnit of pressue [Pacal] = [N]/[m22]]

•The The hydrostatic pressurehydrostatic pressure is P = P is P = Poo + gh + gh

• Archimedes’ PrincipleArchimedes’ Principle: F: Fbouyant bouyant = = ρρfluid fluid g Vg V

• Equation of ContinuityEquation of Continuity: A: A11vv11 = A = A22vv22

• Bernoulli’s Equation:Bernoulli’s Equation: P + ½ ρvP + ½ ρv22 + ρgy = + ρgy = constant.constant.

No Talking!No Talking!Think!Think!

Confer!Confer!

Peer Instruction Peer Instruction TimeTime

Why does the platform spin faster Why does the platform spin faster when he brings his arms in?when he brings his arms in?

Physics 1710Physics 1710—C—Chapter 11 App: E & Ehapter 11 App: E & E

Why does the platform spin faster when he Why does the platform spin faster when he brings his arms in?brings his arms in?

A B C D E

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A.A. He increases his angular He increases his angular momentum.momentum.

B.B. He increase his moment of He increase his moment of inertia.inertia.

C.C. He decrease his moment of He decrease his moment of inertia.inertia.

D.D. He pushes against the He pushes against the inertia of the weights.inertia of the weights.

E.E. None of the aboveNone of the above

Answer Answer Now !Now !

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Physics 1710Physics 1710—C—Chapter 11 App: E & Ehapter 11 App: E & E

Where should the fulcrum be place to balance the teeter-totter?

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Which way will the torque ladder move?1010

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A.A. Clockwise Clockwise B.B. CounterclockwiseCounterclockwiseC.C. Will stay balancedWill stay balanced

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Why does the earth “have more gravity,” i.e. g is larger on earth, than does the moon?

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