Nobel Prize in Physics 2008 Yoichiro Nambu Makoto Kobayashi Toshihide Maskawa "for the discovery of the mechanism of spontaneous broken symmetry in subatomic physics" "for the discovery of the origin of the broken symmetry which predicts the existence of at least three families of quarks in nature" Broken Symmetries

Particles and Forces2 The origin of mass Higgs Mechanism: A field fills all of space because of a mechanism called spontaneous symmetry breaking. It ‘sticks’ to particles, making it ‘harder for them to move’. This is what gives quarks and leptons their mass. Spontaneous symmetry breaking As a consequence, there should also be a spin-0 boson, the Higgs boson. It has not been found yet. Similar to the celebrity effect in a crowd. Credit: CERN Physics H Particle

The Standard Model (SM) describes all these particles and 3 of 4 forces. We have confirmed the existence of those in the laboratory experiments. The Standard Model + Higgs boson Higgs has not yet been discovered The mass is constrained from LEP and Tevatron data: 114 GeV<M H <154 GeV Precision Cosmology at the LHC 3 proton

SPUTNIK: spaceflight era begins October 4, pound basketball- size satellite Lasted 3 months

R-7 launcher: world’s first intercontinental ballistic missile Total mass: 367 tons Payload: about 1 ton Thrust: 3.9x10 6 N November 3, 1957: Sputnik 2, 1120 pounds Laika May 15, 1958: Sputnik 3, 1.5 tons January 15, 1958: Explorer 1 launched (US)

April 12, 1961 Yuri Gagarin February 20, 1962 John Glenn

Early timeline April 12, 1961: the first human in space (Yuri Gagarin) February 20, 1962: the first American on orbit (John Glenn) 1963: the first woman in space (Tereshkova ) 1965: the first spacewalk (Leonov) 1969: first men on the moon (Collins, Armstrong, Aldrin) 1971: first space station (Salyut) 1981: first space shuttle flight (Columbia) Robotic missions to all planets

Sergei Korolyov Fathers of space programs Werner von Braun

All forces are CONSERVATIVE or NON-CONSERVATIVE Chapter 8

A force is conservative if: The work done by the force in going from to is independent of the path the particle follows The work done by the force when the particle goes from around a closed path, back to, is zero. or

Non-conservative: doesn’t satisfy the above conditions

Theorem: if a force can be written as the gradient (slope) of some scalar function, that force is conservative. U(x) is called the potential energy function for the force If such a function exists, then the force is conservative 1D case:

does NOT depend on path! If F x (x) is known, you can find the potential energy function as

Work-energy theorem: Energy conservation law!

Then use or A strategy: write down the total energy E = K + U at the initial and final positions of a particle;

Examples Force of gravity Spring force y x x0x0

A block of mass m is attached to a vertical spring, spring constant k. A If the spring is compressed an amount A and the block released from rest, how high will it go from its initial position?

A particle is moving in one direction x and its potential energy is given by U(x) = ax 2 – bx 4. Determine the force acting on a particle. Find the equilibrium points where a particle can be at rest. Determine whether these points correspond to a stable or unstable equilibrium.

Potential Energy Diagrams For Conservative forces can draw energy diagrams Equilibrium points –If placed in the equilibrium point with no velocity, will just stay (no force) F x >0 a) Spring initially compressed (or stretched) by A and released; b) A block is placed at equilibrium and given initial velocity V 0

Stable vs. Unstable Equilibrium Points The force is zero at both maxima and minima but… –If I put a ball with no velocity there would it stay? –What if it had a little bit of velocity?

Block of mass m has a massless spring connected to the bottom. You release it from a given height H and want to know how close the block will get to the floor. The spring has spring constant k and natural length L. H y=0 L

Several dimensions: U(x,y,z) Compact notation using vector del, or nabla: Another notation: Partial derivative is taken assuming all other arguments fixed

Geometric meaning of the gradient Direction of the steepest ascent; Magnitude : the slope in that direction Direction of the steepest descent Magnitude : the slope in that direction

If or then

H

Water Slide Who hits the bottom with a faster speed?

Roller Coaster You are in a roller coaster car of mass M that starts at the top, height H, with an initial speed V 0 =0. Assume no friction. a)What is the speed at the bottom? b)How high will it go again? c)Would it go as high if there were friction? H

Roller Coaster with Friction A roller coaster of mass m starts at rest at height y 1 and falls down the path with friction, then back up until it hits height y 2 (y 1 > y 2 ). Assuming we don’t know anything about the friction or the path, how much work is done by friction on this path?

A gun shoots a bullet at angle θ with the x axis with a velocity of magnitude V m. What is magnitude of the velocity when the bullet returns to the ground? How high it will go?

Power Power is a rate at which a force does work If work does not depend on time: Otherwise: Even if instantaneous power depends on time, one can talk about the average power

How many joules of energy does 100 watt light bulb use per hour? How fast would a 70-kg person have to run to have that amount of energy? Power could also define the rate at which any form of energy is spent, not only mechanical