Physics of AstronomyTuesday, winter week 7 (21 Feb.06)

Math-A: Giancoli Ch.7&8 – Work and Energy

Discuss rotational dynamics lab

Math-B: Giancoli 11, Raff Ch.11.2.1-3: Intro to QM

HW setup

Dr. Neal Hurlburt visits Wednesday – lunch discussion 1:00 here

Looking ahead: quiz this Thus.

Relationship between force and work/energy

Examples of energy …

Work done = force . displacement in the same direction

Dot product: product of PARALLEL components of vectors

Do Ch.7 (p.171) Forces & Work #4, 6, 7, Dot products # 21, 25

xx x x

dv dxW m dx m dv mv dv

dt dt F dx

7-3: Work done by a varying force

Example: Spring obeys Hooke’s law: F = -kx

Do Ch.7 (p.172) F(x) #31-34, 39

( )W kx dx F dx

7-4: Work & Energy

Loss of potential energy→work done→increase in Kinetic energy

- U → W → + K

Ex: falling mass in last week’s experiment

Ch.7 (p.173) # 41, 46, 49, 52, (p.175) #65,

Energies vs time

-1.00E-020.00E+001.00E-022.00E-023.00E-024.00E-025.00E-026.00E-027.00E-028.00E-02

0 5 10 15 20 25 30 35

Time (s)

En

erg

y(J)

U=mgh

Kt=1/2 mv̂ 2

Kdisk

Ktop

Kpulley

Ktot

Etot

Ch.8: Energy conservation

Conservative force:

• Work done doesn’t depend on path taken (curl x F = 0)

• Net work done around a closed path = 0

• potential energy U depends only on x, and Fx= -dU/dx

• Etot = K + U = constant (conservation of mechanical energy)

• Gravity and Felec are conservative; Friction and Fmag are not

Ch.8 (p.200) #7,9, 10, 16, 17, (p.202) 32, 36(a), 41, 42-47, 73, 82, 89, 93

Gravitational potential energy and force

Near earth far from Earth

Force F

Potential energy U

Ch.8-8,9: Energy diagrams and Power

Power = rate of change of Energy

P = dE/dt

Minimum energy = stable state (F=0)

Ch.8 (Power, 203) #57, 59, 62, 65, 67, (Diag) 68-71, 94-97

Phys.B: Raff 11.2.1-3: Introduction to Quantum Mechanics – Blackbody radiation

• Blackbodies were carefully studied in labs in late 1800s• Rayleigh-Jeans theory explained long-wavelength tail:

~ 1/T (Wien’s law)• Ultraviolet catastrophe at short !

Planck’s quantization of photon energy

• Planck’s phenomenological relation fit, but why?

• Three weeks later, Planck’s revolutionary explanation

Probs. 11.7 and 11.8: Long and short- limits of blackbody radiation.

Blackbody radiation: notation

Q = energy (joules) energy density u = Q/volume

Q = dQ/d (J/m) energy density /wavelength

u(T, ) = Q /volume

Power = dQ/dt (J/s) emissive power = dP/d / area

Luminosity = Power/area

Prob. 11.9: Find energy maximum where du/d = 0

Photons as particles: Photoelectric effect

Photons can knock electrons out of metal, if they can overcome the binding energy to the metal, or work function W.

Ephoton = KEelectron + binding energy: h = KEmax + W

Brighter light yields more electrons.Shorter wavelength light yields more energetic electrons.Even “weak” light beam of single photons can release e.

Atomic models