Review of Physics 201 Free Falling Objects The motion of an object tossed up and allowed to fall. Projectile Motion o A projectile moves in a vertical plan that contains the initial velocity vector, v 0. o Its trajectory depends only on v 0 and on the acceleration due to gravity Free body diagrams To help identify relevant forces, draw a free- body diagram. Be careful to include all the forces acting on the object, but be equally careful not to include any forces that the object exerts on any other object. A free-body diagram of a man dragging a crate. The diagram shows all the forces acting on the man, and only forces acting on the man. Contact forces and Friction Newtons Law of Gravitation & Weight Newtons Law of Gravitation Weight Satellite motion Conservation of energy Collisions Collisions can be classified according to energy relationships and final velocities. In an elastic collision between two objects, kinetic energy is conserved and the initial and final relative velocities have the same magnitude. In an inelastic two-object collision, the final kinetic energy is less than the initial kinetic energy; if the two objects have the same final velocity (they stick together), the collision is completely inelastic. Elastic: K conserved Inelastic: Some K lost Impulse and Center of Mass Impulse Center of mass Rotation about a moving axis Torque and Angular Momentum Stress, strain, and elastic deformation Forces that tend to stretch, squeeze, or twist an object constitute stress. The resulting deformation is called strain. For small deformations, Hookes law states that stress and strain may be directly proportional: stress/strain = constant Tensile and compressive stresses stretch and compress an object, respectively. Superposition The principle of superposition states that when two waves overlap, the resulting displacement at any point is obtained by vector addition of the displacements that would be caused by the two individual waves. When a sinusoidal wave is reflected at a stationary or free end, the original and reflected waves combine to make a standing wave. At the nodes of a standing wave, the displacement is always zero; the antinodes are the points of maximum displacement. Density and Archimedes' Principle Density Archimedes principle: buoyancyArchimedes principle states that when an object is immersed in a fluid, the fluid exerts an upward buoyant force on the object equal in magnitude to the weight of the fluid the object displaces. Because the fluid is in equilibrium, the vector sum of the vertical forces on the volume element must be zero: p 2 A-p 1 A-w=0 The forces on the fluid element due to pressure must sum to a buoyancy force equal in magnitude to the elements weight. Thermal Expansion Heat and Phase changes Molar heat capacity Molar mass Specific heat capacity Poly-atomic: more degrees of freedom Heat capacities Work done during volume changes s The work W done is equal to the area under the PV curve Thermodynamic system = exchanges heat with environment Work done in a cyclic process note: For a constant volume process: W=0 For a constant pressure process: W=p.V Thermodynamic processes Fundamental laws of thermodynamics Zeroth LawTwo systems that are each in thermal equilibrium with a third system are in thermal equilibrium with each other. First LawIf Q is added and W is done then the U will change by: U = Q-W Second Law Engine statement It is impossible for any heat engine to undergo a cyclic process in which it absorbs heat from a reservoir at a single temperature and converts the heat completely into mechanical work pV- diagrams of engines Otto or gasoline engine Diesel engine Carnot engine Entropy and Disorder Entropy provides a quantitative measure of disorder Nature Favors Decrease in Order Increase in Entropy The cream spontaneously mixes with the coffee, never the opposite. 2016 Pearson Education, Inc. If you mix cold milk with hot coffee in an insulated Styrofoam cup, which of the following things happen? (There may be more than one correct answer) A.The entropy of the milk increases B.The entropy of the coffee decreases by the same amount that the entropy of the milk increased. C.The net entropy of the coffee-milk mixture does not change, because no heat was added to the system. D.The entropy of the coffee-milk mixture increases. If you mix cold milk with hot coffee in an insulated Styrofoam cup, which of the following things happen? (There may be more than one correct answer) A.The entropy of the milk increases B.The entropy of the coffee decreases by the same amount that the entropy of the milk increased. C.The net entropy of the coffee-milk mixture does not change, because no heat was added to the system. D.The entropy of the coffee-milk mixture increases. Clicker - Questions Entropy and the Coffee Creamer does disperse in coffee, never the opposite. Rooms become dirty. A house of cards naturally will fall. A pressurized gas will spontaneously expand. 2016 Pearson Education, Inc. An insulated box has a barrier that confines a gas to only one side of the box. The barrier springs a leak, allowing the gas to flow and occupy both sides of the box. Which statement best describes the entropy of this system? A.The entropy is greater in the first state, with all the gas on one side of the box. B.The entropy is greater in the second state, with all the gas on both sides of the box. C.The entropy is same in both states, since no heat was added to the gas and its temperature did not change. An insulated box has a barrier that confines a gas to only one side of the box. The barrier springs a leak, allowing the gas to flow and occupy both sides of the box. Which statement best describes the entropy of this system? A.The entropy is greater in the first state, with all the gas on one side of the box. B.The entropy is greater in the second state, with all the gas on both sides of the box. C.The entropy is same in both states, since no heat was added to the gas and its temperature did not change. Clicker - Questions 2016 Pearson Education, Inc. Free expansion=Irreversible process Isothermal expansion=reversible process Example 16.7 Example 16.4: Entropy change in melting ice To access course evaluations: 1.Beginning December 7th at 8:00 A.M., visit the evaluation web site (http://evaluation.tamu.edu/) and sign in with the Central Authentication System (CAS). You will be presented with a list of your PHYS/ASTR courses. Select PHYS 201 and complete your evaluation.http://evaluation.tamu.edu/ 2. You will receive anin your TAMU Mail account on or before December 7th. Thewill include direct links to each enrolled course. Click on a link to complete an evaluation for that course. The links in thedo not require you to sign-in. OR