Of the four fundamental forces choose the weakest one?

a) Strong force b) Gravitational force c) Electromagnetic force d) Weak force

Consider a Foucault pendulum is located at different latitudes,  . The time needed for rotation through 360 ° is the period and labeled T. Which one of the following statements is correct. a. At the equator  b. At the North Pole = 0 °  and T= 1 day. = 90 ° and T=O.5 day c. In College Station  d. In Doha  = 25 ° = 30 ° and T= 2 days and T= 1.5 days

Can you think of a way you can make yourself older than those born on your same birthday?

This airplane has remote sensing equipment based on microwave, laser, and sound waves.

Which radar has the highest speed?

Which radar has the highest resolution?

Which radar has the lowest scattering loss?

a) Laser b) Microwave c) Sound wave

Problem 102,ch.2

Relativistic Momentum   Rather than abandon the conservation of linear momentum, let us look for a modification of the definition of linear momentum that preserves both it and Newton ’ s second law.

To do so requires reexamining mass to conclude that: Relativistic momentum (2.48)

Relativistic Momentum  physicists like to refer to the mass in Equation (2.48) as the

rest mass m

0 and call the term

m

=

γm

0 the

relativistic mass

. In this manner the classical form of momentum,

m

, is retained. The mass is then imagined to increase at high speeds.  physicists prefer to keep the concept of mass as an invariant, intrinsic property of an object. We adopt this latter approach and will use the term

mass

exclusively to mean

rest mass

.

Relativistic Mass-energy Equivalence

Relativistic Kinetic Energy Equation (2.58) does not seem to resemble the classical result for kinetic energy,

K

½

mu

2 . However, if it is correct, we expect it to reduce to the classical result for low speeds. Let ’ s see if it does. For speeds

u

<<

c

= , we expand in a binomial series as follows: where we have neglected all terms of power (

u

/

c

) 4 and greater, because

u

gives the following equation for the relativistic kinetic energy at low speeds: <<

c

. This which is the expected classical result.

Relativistic and Classical Kinetic Energies

Total Energy and Rest Energy We rewrite the energy equation in the form (2.63) The term

mc

2 is called the rest energy and is denoted by

E

0 .

(2.64) This leaves the sum of the kinetic energy and rest energy to be interpreted as the total energy of the particle. The total energy is denoted by

E

and is given by (2.65)

The Equivalence of Mass and Energy

  By virtue of the relation for the rest mass of a particle:

T-shirt equation

we see that there is an

equivalence

of mass and energy in the sense that “ mass and energy are interchangeable ”  Thus the terms

mass-energy

and

energy

are sometimes used interchangeably.

Problem 2.71

1.

Converting 0.1 ounce =

E



mc

2     3    3  kg. 8  2   14 . Eating 10 ounces results in a factor of 100 greater mass-energy increase, or  16 J. This is a small increase compared with your original mass-energy, but it will tend to increase your weight

Relationship of Energy and Momentum We square this result, multiply by

c

2 , and rearrange the result.

We use the equation for  to express

β

2 and find

Energy and Momentum

The first term on the right-hand side is just

E

2 , and the second term is E 0 2 . The last equation becomes We rearrange this last equation to find the result we are seeking, a relation between energy and momentum.

(2.70) or (2.71) Equation (2.70) is a useful result to relate the total energy of a particle with its momentum. The quantities (

E

2 –

p

2

c

2 ) and

m

are invariant quantities. Note that when a particle ’ s velocity is zero and it has no momentum, Equation (2.70) correctly gives

E

0 as the particle ’ s total energy.

Massless particles have a speed equal to the speed of light c

  Recall that a photon has “ zero ” rest mass and that equation 2.70, from the last slide, reduces to: E = pc and we may conclude that:

E

= g

mc

2 =

pc

= g

muc

Thus the velocity, u, of a massless particle ¥ follows that: u = c.

2.13: Computations in Modern Physics  We were taught in introductory physics that the international system of units is preferable when doing calculations in science and engineering.  In modern physics a somewhat different, more convenient set of units is often used.

 The smallness of quantities often used in modern physics suggests some practical changes.

Units of Work and Energy   Recall that the work done in accelerating a charge through a potential difference is given by

W = qV

. For a proton, with the charge

e =

10 −19 1.602 × C being accelerated across a potential difference of 1 V, the work done is

W

= (1.602 × 10 −19 )(1 V) = 1.602 × 10 −19 J

The Electron Volt (eV)  The work done to accelerate the proton across a potential difference of 1 V could also be written as

W

= (1

e

)(1 V) = 1 eV  Thus eV, pronounced “ electron volt, ” is also a unit of energy. It is related to the SI (

Système International

) unit joule by the 2 previous equations.

1 eV = 1.602 × 10 −19 J

Other Units 1) Rest energy of a particle: Example:

E

0 (proton)

2) Atomic mass unit

(amu): Example: carbon-12 Mass ( 12 C atom) Mass ( 12 C atom)

Binding Energy  The equivalence of mass and energy becomes apparent when we study the binding energy of systems like atoms and nuclei that are formed from individual particles.

 The potential energy associated with the force keeping the system together is called the binding energy E

B

.

Binding Energy The binding energy is

the difference between the rest energy of the individual particles and the rest energy of the combined bound system

.

In the fission of

235

U, the masses of the final products are less than the mass of

235

U. Does this make sense? What happens to the mass?

Problem 85,Ch2

Electromagnetism and Relativity    Einstein was convinced that magnetic fields appeared as electric fields observed in another inertial frame. That conclusion is the key to electromagnetism and relativity.

Einstein ’ s belief that

Maxwell

’

s equations describe electromagnetism in any inertial frame

was the key that led Einstein to the Lorentz transformations. Maxwell ’ s assertion that all electromagnetic waves travel at the speed of light and Einstein frames seem intimately connected.

’ s postulate that the speed of light is invariant in all inertial

Electromagnetism and Relativity: A Conducting Wire in K In K’ The length contraction of the moving positive charges in the wire accounts for the E-field