PHYS 172: Modern Mechanics Summer 2012 Lecture 10 – The Energy Principle Read 6.1 – 6.7

TODAY The Energy Principle Energy is Conserved Rest Energy and Kinetic Energy Work =

What Is Energy? Why Introduce Energy? Energy is just some number you can compute that obeys a conservation law. It’s helpful book-keeping. (See Feynman Lectures on Physics, Vol. 1, Sec. 4-1) Why Introduce Energy? Without following the details of a complicated process, we can: Basically, for some problems, using energy is much simpler than using the momentum principle. Often, however, we’ll use both principles in combination. say something about initial and final states of a system predict whether some process CAN occur

Compare With Momentum Principle: The Energy Principle “cause” (due to interactions) “effect” * We mean the Work done ON a System by a Force in the Surroundings* Compare With Momentum Principle: W is work done on system by surroundings. Q is energy flow between systems. “effect” “cause” (due to interactions) NOTE: Momentum is a vector. Energy is a scalar (no direction).

Energy is A Conserved Quantity Energy is a useful thing to consider because energy can’t be destroyed: it can only change forms. Compare with Conservation of Momentum: Reminder: Momentum is a vector. Energy is a scalar (no direction).

Energy of a Single Particle System Note that even at zero speed, E > 0. Rest mass energy.

Rest Energy A particle at rest has some energy just because it exists! Rest energy = mc2.

Kinetic Energy mc2 Excess energy above rest energy (mc2) is due to motion (ignoring internal degrees of freedom):

Kinetic Energy What?? What happened to ? At low velocities, Use a Taylor expansion (power series):

Energy And Momentum ALWAYS TRUE. EVERY REFERENCE FRAME.

Energy and Force It takes twice as much energy to raise a heavy box a distance 2h, compared to lifting it only h. Thus, it is distance that seems to matter, not time.

Force at an angle y x 12

Force at an angle y Only x-component of force “works”! x Force component along the path of motion y 13

Work as a dot product Dot product: y x 14 14

Sign of Work Circular orbit Sun does work on comet, speeding it up. Earth does no work on the Moon. Sun does work on comet, speeding it up.

What’s the Sign of the Work? * We mean the Work done ON a System by a Force in the Surroundings*

What Causes The Energy of A System to Change? Energy can be transferred from the surroundings to a system in two ways: Energy transfer by heat (next chapter) Energy transfer by work set = 0 for now

Example You hold a ball of mass 0.5 kg at rest in your hand and throw it forward so that it leaves your hand at speed 20 m/s. How much work did you do on the ball? vf = 20 m/s vi = 0 m/s Rest energy did not change 18

Change of identity – change of rest energy How much kinetic energy do the products have? =0 (At rest) Neutron decay >0 An electron-volt (eV) unit: 1 eV = 1.610-19 J 1 MeV = 106 eV Mass of products is smaller than mass of reactant! Mass is converted into kinetic energy 1 Volt 19

WHAT WE DID TODAY The Energy Principle Energy is Conserved Rest Energy and Kinetic Energy Work =