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Physics 141: Weekly Topics - Kepler's Laws, Fluid Dynamics, Oscillations, and Pressure - P, Study notes of Physics

University of MarylandPhysics
Prof. Wolfgang Losert

The weekly topics and concepts covered in physics 141, including kepler's laws, fluid dynamics, oscillations, and fluid pressure. Topics include elliptical orbits, angular momentum conservation, force balance, pascal's law, archimedes' principle, buoyancy in partially submerged bodies, and bernoulli's equation. Students are encouraged to review chapters 9-15 for midterm 2, focusing on conservation of energy and newton's laws.

Typology: Study notes

Pre 2010

Uploaded on 02/13/2009

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Phys141 – Mon 10/30
Applications of Force, Momentum & Energy Laws
- Kepler’s laws (Chapter 13)
- Fluid Dynamics (Chapter 14.1,14.4-6 )
•Wed 11/1: Oscillations: Chapter 15.1-3.
•Fri 11/3 Oscillations: Chapter 15.4-7
•Mon 11/6: Review
•Wed 11/8 Midterm 2:
–Same format as Midterm 1
–All chapters including chapter 15, problems from chapters 9-15, but
don’t forget conservation of energy or Newton’s Law s…
–see Webassign for a list of skipped chapter sections and for example
problems
Keplers Laws: Motion due to the
gravitational force (13.4)
• Kepler’s First Law
– All planets move in elliptical orbits with the Sun at
one focus point of the ellipse
Notes About
Ellipses
•F1and F2are each a focus of
the ellipse
– They are located a distance cfrom
the center
• The longest distance through
the center is the major axis
–ais the semimajor axis
• The shortest distance through
the center is the minor axis
–bis the semiminor axis
• The eccentricity of the ellipse is
defined as e= c/a
– For a circle, e= 0
– The range of values of the
eccentricity for ellipses is 0 < e < 1
pf3
pf4
pf5

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Download Physics 141: Weekly Topics - Kepler's Laws, Fluid Dynamics, Oscillations, and Pressure - P and more Study notes Physics in PDF only on Docsity!

Phys141 – Mon 10/

Applications of Force, Momentum & Energy Laws

  • Kepler’s laws (Chapter 13)
  • Fluid Dynamics (Chapter 14.1,14.4-6 )
  • Wed 11/1: Oscillations: Chapter 15.1-3.
  • Fri 11/3 Oscillations: Chapter 15.4-
  • Mon 11/6: Review
  • Wed 11/8 Midterm 2:
    • Same format as Midterm 1
    • All chapters including chapter 15, problems from chapters 9-15, but don’t forget conservation of energy or Newton’s Laws…
    • see Webassign for a list of skipped chapter sections and for example problems

Keplers Laws: Motion due to the

gravitational force (13.4)

• Kepler’s First Law

  • All planets move in elliptical orbits with the Sun at one focus point of the ellipse

Notes About

Ellipses

  • F 1 and F 2 are each a focus of the ellipse - They are located a distance c from the center
  • The longest distance through the center is the major axis - a is the semimajor axis
  • The shortest distance through the center is the minor axis - b is the semiminor axis
  • The eccentricity of the ellipse is defined as e = c / a - For a circle, e = 0 - The range of values of the eccentricity for ellipses is 0 < e < 1

Angular momentum conservation: Kepler 2nd

The force produces no torque, so angular momentum is conserved L = r x p = MP r x v = const

In a time dt , the radius vector r sweeps out the area dA , which is half the area of | r x d r |

Magnitude of L constant:

-> Area swept by radius vector per unit time is constant

P P

dA

L M M const

dt dt

×

r dr

Force balance: Kepler 3

rd

(Assume a circular orbit of radius r and period T )

Gravitational force = centripetal force

Note: Ks is a constant -> T 2 proportional to r 3

2 Sun Planet Planet 2

2 π

GM M M v

r r

r

v

T

2 2 3 Sun 2 3

= S

T r

GM

T K r

Chapter 14: Forces in Fluid - Pressure

Pressure P: Force per unit area

Unit of pressure is pascal (Pa)

F P A

≡

2

1 Pa =1 N/m

Buoyancy in partially submerged bodies

V ice is the total volume of the ice

V water is the volume of the water displaced

  • Equal to the volume of the submerged fraction of the iceberg (89% of the ice is below water) V water=0.89* V ice

Buoyancy force: ρwater V (^) water g = Weight of iceberg: ρiceV (^) ice g ρwaterV (^) water g = ρiceV (^) ice g ρwater0.89 V ice = ρiceVice ρwater0.89 = ρice

Energy conservation in a fluid

Bernoulli’s equation: P + ½ ρ v^2 + ρ gy = constant

Multiply by volume V = Adx

PV + ½ ρ Vv^2 + ρ Vgy = constant

PAdx + ½ ρ Vv^2 + ρ Vgy = constant

Fdx + ½ m v^2 + m gy = constant

Work + Kinetic Energy + Gravitational energy= constant

Equation of Continuity

• fluid moving through a

pipe of nonuniform

diameter

• The mass that crosses

A 1 in some time interval

is the same as the mass

that crosses A 2 in that

same time interval

Equation of Continuity, cont

• m 1 = m 2 →ρ A 1 v 1 = ρ A 2 v 2

• Since the fluid is incompressible, ρ is a

constant

• A 1 v 1 = A 2 v 2

– Equation of continuity for fluids

• The product, Av , is called the volume

flux or the flow rate