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Lecture 6 Non Inertial Frames Energy-Waves-Radiation. ASTR 340 Fall 2006 Dennis Papadopoulos. FRAMES OF REFERENCE.
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Lecture 6 Non Inertial Frames Energy-Waves-Radiation ASTR 340 Fall 2006 Dennis Papadopoulos
FRAMES OF REFERENCE We have already come across idea of frames of reference that move with constant velocity. In such frames, Newton’s law’s (esp. N1) hold. These are called inertial frames of reference. Suppose you are in an accelerating car looking at a freely moving object (I.e., one with no forces acting on it). You will see its velocity changing because you are accelerating! In accelerating frames of reference, N1 doesn’t hold – this is a non-inertial frame of reference.
Real and fictitious forces In non-inertial frames you might be fooled into thinking that there were forces acting on free bodies. Such forces are call “fictitious forces”. Examples – • G-forces in an accelerating vehicle. • Centrifugal forces in fairground rides. • The Coriolis force on the Earth. Fictitious forces are always proportional to the inertial mass of the body just like gravity.
Non – Inertial Frames • Monkey and hunter g • Accelerometer f a T ma mg Two real forces mg downwards and T. When car accelerates they must add to ma by Newton’s 2nd law An observer in the car feels a force that pushes everything backwards. To explain his result
He adds a “fictitious force” equal to Fin=-ma This is known as inertial force. T Sum of forces equal to zero ma mg vt Centrifugal vs. Centripetal vt a vr The only real force is the Centripetal force pulling towards the center so the ball must be accelerating o An observer sitting on the ball feels a fictitious force Centrifugal that pushes him outwards balanced by the string held at O.
Look atthe rotor in amusement park. People on the outside See only a Centripetal force from the wall pushing riders inwards into circular motion. People inside the rotor feel the fictitious Centrifugal force pushing them outward with the force from the wall balancing it. Centrifugal force Fc= mvt2/R An observer in a non-inertial system with acceleration a should add to the real forces a fictitous inertial force Fin= -ma in order to describe the dynamics of the system correctly, i.e. to provide a description equivalent to an observer observing from an inertial frame. Weight-less-ness. Weight in an elevator or the shuttle.
Gravitational and inertial masses and forces are equivalent. Gravity is indistinguishable from any other form of acceleration Weak or Newtonian equivalence principle Maybe gravity is a fictitious force… … and we live in an accelerating frame of reference?
NEWTON’S WORRIES • Newton knew that his theory has problems • Gravity is “action at a distance” – he didn’t like that! • A static universe would be gravitationally unstable. Reading this week Chapter 4
Given in Joules • WHAT IS WORK ? • WHAT IS ENERGY ? -> CAPACITY TO DO WORK in Joules KE vs PE Forms of Energy -> Heat, Chemical, nuclear Conservation of Energy and Conservation of matter (Classical) What is Temperature ? Energy of random motion in a unit volume • Thermodynamics KEHEAT • Conservation of Energy • Easy to transform KE to heat (rub your hands) but • difficult to transform heat to KE • Heat in = KE+ heat out (Car, refrigerator) No perpetual motion • Entropy Measure of Disorder • 3. Difficult to cool at very low temperatures • Absolute zero (0 K) cannot be attained (-273.15 C)
ENERGY TRANSFORMATIONS Lift a classmate where is the energy coming from ? Muscular Energy, ie. released chemical energy caused by food oxidizing the body What is chemical energy? Form of PE stored due to the locations of electrons in electric field of molecules. It comes from the food, eg. plant you eat. Plant converts radiant energy from Sun into chemical energy by photosynthesis Sunlight came from fusion of hydrogen in the Sun Sun’s hydrogen nuclei were created from energy of the event that created the universe ALL ENERGY CAME FROM THE BIG BANG
Energy : The measure of a system’s capacity to do work • Units of Energy: Joule = Nt x m, eV= 1.6 x 10-19 J, Cal = 4.2 x 103 J • Examples : It takes 100 Joules to lift 10 kg by 1 meter against the • Earth’s gravity (g= 10 m/sec2); It takes .4 MJ to accelerate a 1000 kg • car to 30 m/sec (105 km/hr); It takes about 1010J to accelerate a • missile to 5 km/sec. [E=1/2 M(kg) v2 (m/sec) J] • Chemical Energy Storage : Chemical energy is stored in the • chemical bonds of molecules. As an order of magnititude a few eV • per bond. A 1 kg steak store approximately 1000 Cal or approximately 4 MJ. This is the amount (4-10 MJ/kg)stored in one kg of chemical explosives (TNT). Also a typical battery has few MJ of stored energy. • Energy Transformations: Energy has many forms, e.g. potential, • kinetic, chemical,acoustic, radiation, light etc. Each can be transformed • to the other, but overall energy is conserved.