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Physics 1301A/B
Martin Zinke- Allmang

Chapter 3 – ForCES Force  Interaction between of two distinguishable objects  Throw a ball towards the wall (in air) o No interaction = non force  Throw a ball up o Interaction due to force of gravity Properties of a Force  Push or pull  Acts on material object 1 N = kg∙m/s2 1 m = 1 000 000 cm 3  Applied by a material object  Contact or contact-free force  Vector  Paired – e.g. interaction forces: forces of the pair are simultaneously exerting a force on each other  Additive Fundamental Forces (contact free)  Gravity 𝑭 = 𝑮 × 𝑴𝟏 × 𝑴𝟐 Universal Gravitational Constant: 𝒓𝟐 G = 6.674 * 10-1N∙m /kg 2  Electromagnetic o 2 charged objects/particles interact o Muscle force on tendon 𝒒𝟏 × 𝒒𝟐 9 2 2 𝑭 = 𝒌 𝒓𝟐 k = 8.99 * 10 N∙m /c o Wind force  Strong nuclear forces (strongest) o Holds protons and neutrons together in nucleus o Overcomes repulsive electric force o Short-range force  Weak nuclear force o Disintegration of certain radioactive nuclei o Shorter-range force Convenience Forces (Contact Forces)  Normal force o Perpendicular to contact surface  Force of Friction o Parallel to contact surface o Independent to contact area and proportional to normal force  Tension  Spring Force  Drag Translational Equilibrium  Static Equilibrium o Net force is 0 o Does not move  Dynamic equilibrium o Net force is 0 o Constant velocity 1 Chapter 4 – Newton’s Laws Newton’s First Law  An object at rest or in motion with constant velocity remains in its state unless acted upon by a net force  Inertia o Heavier objects have fewer tendencies to change velocity  Inertial Frame of Reference o Valid in first law o Noninertial frame of reference for accelerated frames  Problem solving o Tension and string at equilibrium Newton’s Second Law  If a Fnet is applied to an object of mass m, it accelerates in the direction of the Fnet  Problem solving 𝑭𝒏𝒆𝒕= 𝒎 × 𝒂 o Block on slope  Free body diagram for hanging block: draw gravity horizontally  Break force of gravity into x and y components (x parallel to slope) o Applied force o Human arm and dumbbell  Diagram for arm: Tension in arm = weight of arm – force pulled by dumbbell  Diagram for dumbbell: force pulled by dumbbell – weight of dumbbell Newton’s Third Law  If an object exerts a force on another, they will exert a force equal in magnitude and opposite in direction  Action – reaction pair o Act on two different objects 𝑭 𝑨 𝒐𝒏 𝑩 − 𝑭 𝑩 𝒐𝒏 𝑨  Sprinters (pg. 89)  Problem Solving o Push two blocks side by side  Only block that is being contacted has applied force  Overall system ignores action reaction forces o Tension in muscles  Fnet = F tendon on bone – F tendon on muscle o Pulley  Draw diagram so vertical (one of Fg is going up)  Tension on both sides of pulley are the same  Held by 2 strings = 2 tensions going up  Tension of string attached to ceiling = force of gravity since at rest Weight and Apparent Weight  Apparent weight o Weight measured by a contact force o at rest acc = 0 gravity (down direction) + a = accelerating up + a = decelerate down - a = accelerate down - a = decelerate up 𝑵 = 𝒎 ∙ 𝒈 𝑵 = 𝒎(𝒂 + 𝒈) 2 Chapter 3 and 4 Example Questions How many normal forces act on a polar bear?  4 (one per leg) Which of the following forces has always the same orientation relative to the vertical direction?  Weight Are you heavier or lighter on the moon?  Lighter on the moon because the mass of the moon is less If you are moving at a constant speed, which law do you use to describe your motion?  Newton’s First Law Due to Newton's third law we can make the following statement:  The arm exerts on the trunk a force which equals – T An object of mass m accelerates with acceleration magnitude a. How does the magnitude of the acceleration change if we double the mass of the object but keep the accelerating force unchanged?  Acceleration is halved Pulley one string attached to ceiling and another string attached to pulley with another mass.  mass attached to string that is attached to ceiling is heavier When is the tension equal in magnitude to the weight for an object suspended from a single massless string?  only when the string is vertical A spider hangs from its spider silk string, half way down from a leaf. Is the following statement correct? "The silk string pulls the spider up, and this represents the reaction force to the spider's weight acting downward"  never Consider the weight of the arm as 7% of the weight of the person, and include the force due to the bar. Express the result in the unit [N].  weight would be only 7% of the weight of the person or standard man Lift force of birds  lift force = force of gravity Angles on slant  angle to horizontal – angle of ramp Angle between horizontal and normal on a slant  90 – angle of ramp 3 Chapter 7 – Energy and Its Conservation Basic Concepts  Work o Energy that is transferred in or out of a system o Theta is the angle between force and displacement  If the angle is 90, work = 0 o Positive work  Work is done on the system (block) by the environment (piston) o Negative work  System does work on the environment  E.g. work done by a person lowering an object 2 2 𝑾 = 𝑭 ∙ 𝒅 ∙ 𝒄𝒐𝒔𝜽 1 J = N∙m = kg∙m /c  System/environment interface o Isolated system: no transfer of energy or matter, environment ignored o Closed system: transfer of energy only o Open system: transfer of energy and matter  Power 𝑾 o Rate at which work is done 𝑷 = ∆𝒕 Kinetic Energy  𝟏 𝑬 𝒌𝒊𝒏= ∙ 𝒎 ∙ 𝒗 𝑾 = 𝑬 𝒌𝒊𝒏 𝒇 𝑬 𝒌𝒊𝒏 𝒊 𝟐 Potential Energy  Height can be relative to anywhere 𝑬 = 𝒎 ∙ 𝒈 ∙ ∆𝒉 𝑾 = 𝑬 − 𝑬 𝒈 𝒈 𝒇 𝒈 𝒊 Is Mechanical Energy Conserved?  𝑬 + 𝑬 = 𝑬 + 𝑬 𝑬 + 𝑬 = 𝒄𝒐𝒏𝒔𝒕𝒂𝒏𝒕 𝒊𝒏𝒕𝒆𝒓𝒏𝒂𝒍 𝒆𝒏𝒆𝒓𝒈𝒚 𝒌𝒊 𝒈𝒊 𝒌𝒇 𝒈𝒇 𝒌𝒊 𝒈𝒊 Sample Questions How does the kinetic energy of an object change when its speed is reduced to 50% of its initial value?  The kinetic energy becomes 25% of the initial value An isolated object, onlkinand Epotf object change. If object accelerates from 5 m/s to 10 m/s, its Eg has:  decreased by a factor we cannot determine from the problem as stated kinetic energy graph is a parabola internal energy graph is constant (0 slope) The person is too weak and object drops to ground under its own weight W.  The object has done work on the person; this work is calculated as Work = F Δs Which object has at the end of the process the higher kinetic energy?  The mass has to be given in order to know Represent an isolated system: In midair Same total energy: Depends on mass of the object Hot Air Balloon: Pressure in balloon = pressure outside 4 Chapter 8 – Gases The Basic Parameters of the Respiratory System at Rest  Gas Parameter I: Volume (Pg. 188) o Spirometer: clinical instrument that allows us to measure gas volume in lungs o Tidal volume: inhales and exhales about 0.5 L o Inspiratory and expiratory reserve volume: short term additional air exchange o Residual volume: remaining gas volume  Gas Parameter II: Pressure o 𝑭 = 𝑨𝒓𝒆𝒂 ∙ 𝒑𝒓𝒆𝒔𝒔𝒖𝒓𝒆 (𝑷𝒂) 𝟏 𝑳 = 𝟎.𝟎𝟎𝟏 𝒎 (𝑺𝑰 unit) 1 atm = 101300 Pa 1 torr = 1 mmHg = 133.33 Pa  Gas Parameter III: Temperature o Zeroth law of thermodynamics  In a thermal equilibrium, every part of the system has the same temperature Pressure-Volume Relations of the Air in the Lungs (Pg. 193)  Respiration Curve at rest o Transmural pressure = P alveoli – P pleura always positive o Gauge pressure = P alveoli positive or negative  Negative = lung volumes are smaller than 3L = pressure in lungs is less than atm pressure o Respiratory equilibrium V = 3L  Gauge pressure = 0 lung capacity pressure in lungs = atmospheric pressure o V = 4.5 L, alveoli and pleura are positive Empirical Gas Laws  Boyle’s Law o PV = const o Isotheral process (constant temperature) o Graph: left side of parabola final  intial  Charles’s Law o V/T = const o Isobaric conditions (constant pressure)  Gas Law o 𝝆 𝑷 ∙ 𝑽 = 𝒏𝑹𝑻 𝑴 = 𝑷 ∙ 𝑹 ∙ 𝑻 𝝆 = 𝒅𝒆𝒏𝒔𝒊𝒕𝒚 Kinetic Gas Theory  The individual volumes of the particles are negligible  The gas consists of a very large number of identical particles so size smaller than inter-particle distane  The particles are in continuous random motion  The only form of interaction between particles or between particles and the container walls are elastic collisions  Treat particles as point-like objects (only translational motion – straight lines)𝟏 𝑷 ∙ 𝑽 = 𝟑 ∙ 𝑵 ∙ 𝒎 ∙ 𝒗 𝒆𝒏𝒔𝒊𝒕𝒚 Internal Energy (U)  Independent of pressure and volume of the gas 𝑬 = 𝑼 𝑼 = 𝟑∙ 𝒏 ∙ 𝑹 ∙ 𝑻 𝒌𝒊𝒏 𝟐 𝒆𝒏𝒔𝒊𝒕𝒚 Root Mean Square 𝑽𝒓𝒎𝒔 = 𝟑∙𝑹∙𝑻mm = kg/mol 𝒎𝒎 Air is a Gas Mixture  Humid air is lighter than dry air o Water lighter than nitrogen and oxygen molecules 5 Sample Questions Assume that no external force is applied to the piston. Can you predict in which direction the piston accelerates?  Not enough information  If in mechanical equilibrium, p = p air  Accelerate left if p > air Horses and cross sectional area 2  F = (pressure)*πr We consider 1 mol of an ideal gas under isothermal conditions. If the pressure is doubled ...  The volume is halved Charles' law can be written as V/T = const if ... 3  V is measured in non-standard unit cm A person inhales air at 20 C. By the time the air arrives in the lungs, its temperature has risen to 37 C. Treating air as an ideal gas, the change in internal energy is:  about a 85% increase over the initial value If a gas has an internal energy of U = 0 J, we conclude:  The temperature of the gas is 0 K 3 Rewrite the ideal gas law by combining n and V as ρ/M, in which ρ is the density of the gas (in unit kg/m ) and M is the molar weight (in unit kg/mol). Which parameter in this rewritten ideal gas law MUST decreases from inside to outside across the envelope of a hot air balloon for it to stay airborne?  temperature The ideal gas law is a macroscopic description of a gas, i.e., all parameters can be measured without a model of the microscopic properties and structure of the gas. Still, when Boltzmann, Maxwell and Clausius developed such a model, called the kinetic gas theory, our understanding of the atomic and molecular nature of gases advanced. In their model, which of the following is a result, not an assumption made to develop the model?  The internal energy of an ideal gas depends linearly on the temperature (in unit kelvin). Charles' law can be written as V/T = const if ... 3  V is measured in non-standard unit cm We compare two components of the air in a typical lecture hall: oxygen (O , M = 32 g/mol) and nitrogen (N , M = 28 2 2 g/mol). What is true?  The oxygen molecules are slightly slower than the nitrogen molecules The Maxwell-Boltzmann velocity distribution of an ideal gas in thermal equilibrium allows us not to predict ...  the temperature of the gas  the root-mean-square speed of the gas molecules  the most common speed of gas molecules in the gas  the speed of a single gas particle we let escape from the gas container 6 Chapter 9 – Work and Heat for Non-Mechanical Systems Dynamic Breathing Pg. 218  PV diagram for breathing and not at rest  Pressure in the lungs (alveoli) remains at atmospheric pressure (0)  Transmural pressure does not depend on the breathing itself  Pleura pressure is negative o Decreases lung volume for very slow breathing  Tidal breathing (dynamic breathing) o Exhalation  Pressure larger than atmospheric  Top dotted lines o Inhalation  Bottom dotted lines  Solid lines = slow breathing Work on or by a Gas  positive o Compression of a gas 𝑾 = −𝑷 ∙ ∆𝑽 o Initial > final (final on left side of the PV graph) o Work is done on the system (gas) o Exhale  work is done the gas and active muscles  lungs collapse and pleura expands  Negative o Expansion of a gas o Initial < final (final on right side of PV graph) o System does work on surroundings e.g. gas does work on environment o Inhale  work is done by the active muscles  Lungs expand and pleura collapses Work for Systems with Variable Pressure  Area under the curve of PV graph = work o Sign is determined whether if Vf > Vi or Vi < Vf  Work for a full breathing cycle = 0 Heat and the First Law of Thermodynamics  Heat o Energy flow 𝑸 = 𝒎 ∙ 𝒄 ∙ ∆𝑻 𝑸 = ∆𝑬 𝒕𝒉𝒆𝒓𝒎𝒂𝒍 o heat flowing into the system and work done on the system are positive  increase total energy of the system  first law of thermodynamics o conservation of energy  sum of all energy forms (internal energy) in an isolated system is constant (0)  second law of thermodynamics o ∆𝑼 = 𝑸 + 𝑾 𝒄𝒍𝒐𝒔𝒆𝒅 𝒔𝒚𝒔𝒕𝒆𝒎  Problem solving o Include E thermal into the law of conservation of energy o Staircase pg.228  E chemical  1 cal = 4.19 J 7 Example Questions A gas expands which is sealed in a container by a mobile piston. The following statement is correct:  The gas does work on the piston Which statement about this p-V diagram (Pg.219) is correct?  The work done during inhalation is a negative value. o o A container with an ideal gas is heated from 10 C to 20 C. As a result, its thermal energy ...  increased by less than a factor of 2 The graph shows three steps, labeled I, II, and III, that form a cyclic process in a p-V diagram. Rank the work from smallest to largest for each individual step (Note -5 J < -2 J, but +2 J < +5 J).  I < II < III I compress 1 mol of an ideal gas from 20 L to 10 L in an isothermal process? How does the internal energy of the gas change?  It stays unchanged The Carnot process is a cyclic process in a p-V diagram we focus on the process step labeled III. In this step, the system ...  receives work The figure shows a p-V diagram with the initial and final state of a system indicated. The system undergoes a process that follows the shown line in the diagram. During this process, the system ...  released a net amount of work The figure shows four curves for the pressure of a gas varying with the volume in different ways. The gas expands in each case from the initial volume (labe
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