Review Exam 1

Formulas

Time Dilation:

Length Contraction:

Relativistic Momentum:

ptt

pLL

2

21c

u

mup

Formulas

Relativistic Energy:

Rest Energy:

Total Energy:

20 mcE

2

2

2

0

1c

u

mcEKE

Useful Formulas for Speed, Energy, and Momentum:

hc

hfE c

f E

pc

c

u

22222 )(mccpE

2, mcEforpcE

Photoelectric Effect:

Compton’s equation:

Plank’s Law:

hfmv

eV

max

2

0 2

)cos1(12 cm

h

e

1

8)(

52

kT

hc

e

hcu

Stefan-Boltzman Radiation Law:

Stefan-Boltzman constant:

Wien’s displacement law:

Rayleigh-Jeans Law:

4

4

TAP

TR

42810672.5

Km

W

KmtconsT 3max 10898.2tan

48)()( kTkTnu

JeVnmeVmJhc

kgmprotontheofMass

CeelectronofeCh

cMeVkgmelectronofMass

seVsJhs

mc

p

e

1925

27

19

231

15348

106022.118.1239109864.1

1067.1:

106.1:arg

511.0101094.9:

10135.410626.6103

• Specific Heat:Specific Heat:

• Latent Heat:Latent Heat:

• Work done by engine: Work done by engine:

• Thermal Efficiency: Thermal Efficiency:

TmcQTm

Qc

LmQm

QL

chnetengine QQQW

eng 1h c c

h h h

W Q Q Qe

Q Q Q

Typical Problems

Two identical twins Speedo and Goslo join a Two identical twins Speedo and Goslo join a migration from the Earth to Planet X. It is migration from the Earth to Planet X. It is 20.0 LY20.0 LY away in a reference frame in which both planets away in a reference frame in which both planets are in the rest. The twins, of the same age, departs are in the rest. The twins, of the same age, departs at the same time on different spacecrafts. at the same time on different spacecrafts. Speedo’s craft travels steadily at Speedo’s craft travels steadily at 0.950c0.950c, and , and Goslo’s at Goslo’s at 0.750c0.750c. Calculate the age difference . Calculate the age difference between the twins after Goslo’s spacecraft lands between the twins after Goslo’s spacecraft lands on Planet X. Which twin is the older?on Planet X. Which twin is the older?

A proton in high-energy accelerator moves A proton in high-energy accelerator moves with a speed with a speed c/2c/2. Use the work kinetic energy . Use the work kinetic energy theorem to find the work required to increase the theorem to find the work required to increase the speed to (a) speed to (a) 0.750c0.750c and (b) and (b) 0.995c0.995c. .

In the constellation Orion we can observe two In the constellation Orion we can observe two bright stars: bright stars: BetelgeuseBetelgeuse appears to glow red, while appears to glow red, while Rigel Rigel looks blue in color. Which star has a higher looks blue in color. Which star has a higher surface temperature? (surface temperature? (λλredred=700nm=700nm; ; λλblueblue=430nm=430nm))

Electrons are ejected from a metallic surface Electrons are ejected from a metallic surface with speed ranging up to with speed ranging up to 4.60x104.60x1055 m/s m/s when light when light with a wavelength of with a wavelength of 625 nm625 nm is used. What is the is used. What is the work functionwork function of the metal? What is the of the metal? What is the cutoff cutoff frequencyfrequency of this surface? of this surface?

A A 0.110-nm0.110-nm photon collides with a stationary photon collides with a stationary electron. After the collision, the electron moves electron. After the collision, the electron moves forward and the photon recoils backward. Find the forward and the photon recoils backward. Find the momentummomentum and the and the kinetic energykinetic energy of the electron. of the electron.

((Compton effect problem)Compton effect problem)

Find the power per unit area radiated from Find the power per unit area radiated from the surface of the sun in the wavelength range the surface of the sun in the wavelength range 600.0600.0 to to 605.0 nm605.0 nm

The power output of the Sun is The power output of the Sun is 3.773.77×10×1026 26 WW..

How much mass is converted to energy in How much mass is converted to energy in the Sun each second?the Sun each second?