Physics Final Exam Study Guide
Physics Final Exam Study Guide PHYS2001
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This 12 page Study Guide was uploaded by Grace Lillie on Friday April 22, 2016. The Study Guide belongs to PHYS2001 at University of Cincinnati taught by Alexandru Maries in Fall 2016. Since its upload, it has received 57 views. For similar materials see College Physics 1 (Calculus-based) in Physics 2 at University of Cincinnati.
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Date Created: 04/22/16
Chapter 1 – Physics and Measurement 1.1 – Standards of Length, Mass, and Time 1.3 – Dimensional analysis 1.4 – Conversion of Units Chapter 1 is very basic material. Just be sure you are able to convert units, since you’ll need to a lot. Be extra careful with units for area and volume; a lot of errors happen when you don’t take into account the square or cube of the conversions for length. Chapter 2 – Motion in One Dimension 2.1 – Position, Velocity, and Speed 2.2 – Instantaneous Velocity and Speed 2.3 – Analysis Model: Particle Under Constant Velocity 2.4 – Acceleration 2.5 – Motion Diagrams 2.6 – Analysis Model: Particle Under Constant Acceleration 2.7 – Freely Falling Objects - This Chapter is mostly about motion-related equations and understanding how to use them (see the box to the right). **These will all be on the equation sheet for the exam** - One additional thing is to be able to read motion diagrams (2.5). These can be position vs. time, velocity vs. time, or acceleration vs. time plots or pictograms using images, arrows, or dots. position vs. time – the slope is the velocity, so a horizontal line is no motion, straight line is constant velocity, and curved line is changing velocity. velocity vs. time – the slope is acceleration, so a horizontal line is constant velocity (a=0), straight line is constant acceleration, and curved line is changing acceleration. - from A to B, slope is positive so acceleration is positive (to the right). But since velocity is negative, the object is moving to the left, so it’s actually slowing down. - from B to C, slope is positive and velocity is positive so the object is speeding up towards the right - from C to D slop is 0 and velocity is positive so the object moves at constant velocity to the right **Signs are important. Take these two equations: They are the same equation applied to horizontal motion and vertical free fall. For horizontal motion, you add 2 ½at and choose positive or negative acceleration depending on the problem. For free fall, g is always negative (down). This negative is already included in the second equation, so you use 9.81 m/s for g and not -9.81 m/s. Chapter 3 – Vectors 3.1 – Coordinate Systems 3.2 – Vector and Scalar Quantities 3.3 – Some Properties of Vectors 3.4 – Components of a Vector and Unit Vectors Again, pretty basic stuff. Know the difference between scalar (just magnitude) and vector (magnitude and direction) quantities and how to add/subtract/etc. them. Also be able to find components of vectors because you’ll do that a lot when computing force and torque later on. It’s all just trig, mostly sin and cos, but be sure you know the difference. Chapter 4 – Motion in Two Dimensions 4.1 – The Position, Velocity, and Acceleration Vectors 4.2 – Two-Dimensional Motion with Constant Acceleration 4.3 – Projectile Motion The first half just continues applying the equations from Chapter 2 using your new knowledge of vectors. With motion in two dimensions, you need to take into account the x- and y-components of position, velocity, and acceleration. 4.4 – Analysis Model: Particle in Uniform Circular Motion 4.5 – Tangential and Radial Acceleration We didn’t cover these sections in class until after we learned chapter 5 because they have more to do with Chapter 6 and circular motion. The equations are on the equation sheet: Some things worthy of note: - Centripetal force is not a force. It’s just a name given to the net force acting on an object moving in a circle with constant speed Chapter 5 – The Laws of Motion 5.1 – The Concept of Force Forces are the result of interactions between objects Tension force is always directed away from the object of interest and through the string/cord/cable/etc. 5.2 – Newton’s First Law and Inertial Frames Newton’s first law is inertia 5.3 – Mass 5.4 – Newton’s Second Law Newton’s second Law: the effect of a net force acting on an object of mass m is to impart an acceleration a=F netm 5.5 – The Gravitational Force and Weight 5.6 – Newton’s Third Law Interactions always cause action-reaction force pairs that act on different objects The example to the right shows up a lot. Even though the big truck is pushing the little car, the force that it exerts on the car and the force that the car exerts on it are equal. The net force that causes their acceleration is the force of the engine of the truck working on the truck. The two forces are an action-reaction pair because they act on different objects. Also, the normal and gravitational forces cancel out in this case because there is no acceleration vertically (n=g). **Just because two forces are equal and opposite doesn’t mean they’re an action- reaction pair. They have to act on different objects** 5.7 – Analysis Models Using Newton’s Second Law 5.8 – Forces of Friction - Kinetic friction opposes motion and has a magnitude of μ N,kwhere N is the normal force - Static friction is opposite ‘possible’ motion of a stationary object and s ≤ μsN - If you are trying to push a block to the left, static friction acts towards the right until you push hard enough to get the block moving Chapter 6 – Circular Motion and Other Applications of Newton’s Laws 6.1 – Extending the Particle in Uniform Circular Motion Model - A particle in uniform circular motion experiences centripetal acceleration that is always perpendicular to the velocity (if it’s moving in a circle, c always points towards the center of the circle) - The force causing the centripetal acceleration acts toward the center of the circle. If the force stops, the object would move in a straight line tangent to the circle. 6.2 – Nonuniform Circular Motion Chapter 7 – Energy of a System 7.1 – Systems and Environments 7.2 – Work Done by a Constant Force - Work is only done by the component of the force parallel to the direction of motion: - It’s always helpful to DRAW A PICTURE of the situation to understand the direction of the forces involved and the trig functions you need to use to find the right components. If you pull a block to the right by a string parallel to the ground, cosθ=1 so you just need force times distance - the SI unit is joule (J) which is a newton-meter - Work is a vector so it can be negative (opposing motion) or positive (in the direction of motion) 7.3 – The Scalar Product of Two Vectors This is just about some calculus you should already know: A · B = ABcosθ 7.4 – Work Done by a Varying Force If a force varies with position, work is the area under a curve of force vs. position: Hooke’s Law describes spring force. That and work done by a spring depend on the distance stretched from equilibrium and the spring constant: 7.5 – Kinetic Energy and the Work-Kinetic Energy Theorem Again, all of these equations will be provided for you, but you still need to understand them. The Work-Kinetic Energy Theorem says that the net work is equal to the change in kinetic energy 7.6 – Potential energy of a System Potential energy can be gravitational or elastic (spring): 7.7 – Conservative and Nonconservative forces - A force is conservative if the work done by it only depends on initial and final position (not the path taken) and if the work done on a particle moving around a closed path equals zero. - Nonconservative forces, like friction, depend on the path taken. - Mechanical Energy is the sum of kinetic and potential energy in a system 7.8 – Relationship Between Conservative Forces and Potential Energy Conservation of Mechanical energy is true if only conservative forces act on a system. 7.9 – Energy Diagrams and Equilibrium of a System You should always DRAW AN ENERGY BAR CHART to solve conservation of energy problems: This one is just one example. There’s initial kinetic and gravitational potential energy, some energy is lost to a nonconservative force like friction, and the rest of the final energy is kinetic Chapter 8 – Conservation of energy 8.1 – Analysis Model: Nonisolated System (Energy) Nonisolated is when the system interacts with the environment; isolated is when it does not. 8.2 – Analysis Model: Isolated system (Energy) In an isolated system, change in mechanical energy is always 0 8.3 – Situations Involving Kinetic Friction Like the example energy bar chart. Mechanical energy is not conserved because energy leaves the system due to the work done by friction. 8.4 – Changes in Mechanical Energy for Nonconservative Forces 8.5 – Power Power is the change in energy divided by the change in time, or W/t Chapter 9 – Linear Momentum and Collisions 9.1 – Linear Momentum 9.2 – Analysis Model: Isolated System (Momentum) *The momentum of an isolated system is conserved, but the momentum of one particle in the system is not necessarily conserved. 9.3 – Analysis Model: Nonisolated System (Momentum) f ∆ p=p −p = ∫∑ F dt=I⃗ f i t -the impulse of the net force acting on a particle over i the time interval Δt=t -t is a vector with a magnitude equal to the area under a f i force-time curve. It’s direction is the same as the direction of the change in momentum - impulse-momentum theorem—the change in the momentum of a particle equals the impulse of the net force acting on the particle: I = Δp/Δt = FΔt 9.4 – Collisions in One Dimension - momentum is conserved in any collision - elastic collision—the total kinetic energy is conserved. Objects bounce apart - inelastic collision—total kinetic energy of the system is not conserved. Objects stick **change in direction means greater change in momentum which over the same amount of time applies a larger force **Momentum and KE of a system are conserved, not of the individual objects 9.5 – Collisions in Two Dimensions Break up the velocity vectors into x- and y-components using sine and cosine 9.6 – The Center of Mass center of mass—a single point in a system used when describing the overall motion of a system. 9.7 – Systems of Many Particles Chapter 10 – Rotation of a Rigid Object About a Fixed Axis 10.1 – Angular Position, Velocity, and Acceleration *right-hand rule: when you wrap your four fingers around the axis of rotation and extend your thumb, it points in the direction of angular velocity. If ω is increasing, angular velocity points in the same direction; if ω is decreasing, angular velocity points in the opposite direction. *Kinematics are pretty much the same (and on the formula sheet!) 10.2 – Analysis Model: Rigid Object Under Constant Angular Acceleration Two things to keep in mind: 1) you have to specify a rotation axis 2) the object keeps returning to its original orientation (can make multiple revolutions) 10.3 – Angular And Translational Quantities - The formula sheet includes the equations to convert between translation and angular motion: 10.4 – Torque - torque τ is the tendency of a force to rotate an object around an axis Fsinφ -Only the perpendicular component causes torque ( in the example) *Torque depends on your choice of axis! You can eliminate unknown variables when solving problems 10.5 – Analysis Model: Rigid Object Under a Net Torque - I is the moment of inertia - the moment of inertia is the resistance to changes in rotational motion. It depends on the mass of the object and how the mass is distributed around the rotation axis 10.6 – Calculation of Moments of Inertia - parallel-axis theorem – simplifies the calculation of the moments of inertia of an object (fourth equation in the box to the right) 10.7 – Rotational Kinetic Energy 10.8 – Energy Considerations in Rotational Motion The work-kinetic energy theorem holds for rotational motion too! - Net work done by external forces is the change in total kinetic energy (the sum of translational and rotational kinetic energy). - Conservation of energy can also be applied to rotational situations. Just remember to include both translational and rotational kinetic energy 10.9 – Rolling Motion of a Rigid Object - Total Kinetic Energy of a rolling object is the sum of rotational energy about its center of mass and the translational kinetic energy of its center of mass. - For an object to undergo accelerating rolling motion without slipping, there must be friction present to produce a net torque. **Even though there’s friction, mechanical energy is still conserved because the contact point is at rest relative to the surface Chapter 11 – Angular Momentum 11.1 – The Vector Product and Torque you can find torque using the vector product: (also on formula sheet) 11.2 – Analysis Model: Nonisolated System (Angular Momentum) - torque plays the same role in rotational motion that force plays in translational motion - more equations that will be giving to you *the same axis must be used to measure both angular momentum and torque 2 *the SI unit for angular momentum is kg·m /s *using right hand rule, angular momentum is perpendicular to linear momentum and position vectors 11.3 – Angular Momentum of a Rotating Rigid Object Angular momentum is in the same direction as angular velocity ∑ ⃗ ext Rotational form of Newton’s second law 11.4 – Analysis Model: Isolated System (Angular Momentum) In an isolated system, angular momentum is conserved Chapter 12 – Static Equilibrium and Elasticity 12.1 – Analysis Model: Rigid Object in Equilibrium rigid object in equilibrium: both net external force and net external torque must be zero - translational equilibrium (translational acceleration of center of mass is zero) - rotational equilibrium (angular acceleration about any axis must be zero) static equilibrium: the object is at rest relative to the observer (no translational or angular speed) 12.2 – More on the Center of Gravity 12.3 – Examples of Rigid Objects in Static Equilibrium Net external torque is zero when the center of gravity is directly over the support point Chapter 14 – Fluid Mechanics 14.1 – Pressure - The force exerted by a static fluid on an object is always perpendicular to the surfaces of the object - pressure—a scalar quantity, P=F/A, measured in pascals, where 1 Pa = 1 N/m 2 14.2 – Variation of Pressure with Depth - water pressure increases with depth; atmospheric pressure decreases with height - density—mass per unit volume *Pressure at a given depth is the same, regardless of the shape of the container Pascal’s Law—a change in the pressure applied to a fluid is transmitted undiminished to every point of the fluid and to the walls of the container 14.3 – Pressure Measurements absolute pressure is the pressure P and gauge pressure is the difference P- P 0 14.4 – Buoyant Forces and Archimedes’s Principle buoyant force—the upward force exerted by a fluid on any immersed object Archimedes’s Principle—the magnitude of the buoyant force on an object always equals the weight of the fluid displaced by the object B=ρ fluiddisp the density of the fluid and the amount of fluid displaced 14.5 – Fluid Dynamics A1v1=A 2 2constant equation of continuity for fluids 14.6 – Bernoulli’s Equation 1 P+ ρv +ρgy=constant Bernoulli’s equation – the pressure of a fluid 2 decreases as the speed and/or elevation increase Chapter 19 – Temperature 19.1 – Temperature and the Zeroth Law of Thermodynamics - zeroth law of thermodynamics—If objects A and B are separately in thermal equilibrium with a third object, C, then A and B are in thermal equilibrium with each other. - temperature—the property that determines whether an object is in thermal equilibrium with other objects. Two objects in thermal equilibrium have the same temperature 19.2 – Thermometers and the Celsius Temperature Scale - Celsius temperature scale—based on the ice point and steam point (0° and 100°C) 19.3 – The Constant-Volume Gas Thermometer and the Absolute Temperature Scale - absolute temperature scale—zero point at -273.15°C, or absolute zero - Kelvin scale, with SI unit of absolute temperature, kelvin ***ALWAYS CONVERT TEMPERATURES TO KELVINS unless it’s a difference in temperature*** You’re even provided the conversion equations: 19.4 – Thermal Expansion of Solids and Liquids Thermal expansion in one dimension is linear, and you get the equation for it: The constant α will depend on the material 19.5 – Macroscopic Description of an Ideal Gas - mole—on mole of a substance is 6.022e23 particles. Number of moles, n=m/M, where M is molar mass - the equation sheet for ch.20-22 gives you the constants you need to know and the ideal gas law which you should know anyway by now: PV=nRT Chapter 20 – The First Law of Thermodynamics 20.1 – Heat and Internal Energy - heat is a process of transferring energy across the boundary of a system because of a temperature difference between the system and its surroundings; the amount of energy Q transferred by this process * Heat is not energy in a hot substance that’s internal energy * Heat is not warmth of an environment that would be temperature - calorie (cal)—the amount of energy transfer necessary to raise the temperature of 1 g of water from 14.5°C to 15.5°C. 1 cal = 4.186 J 20.2 – Specific Heat and Calorimetry Q=mc∆T - specific heat (c)—the heat capacity per unit mass: - greater specific heat means more energy needs to be added to change the temperature 20.3 – Latent Heat - latent heat—this added or removed energy doesn’t result in temperature change Q=L∆m energy transferred to a substance during a phase change. You’ll have problems where you need to include: - latent heat of fusion—solid to liquid (f ) - latent heat of vaporization—liquid to gas (Lv) For example, when water freezes, you have the energy from the temperature change to reach the freezing point and then use latent heat of fusion and add the two steps together. 20.4 – Work and Heat in Thermodynamic Processes Work done on a gas is negative the area under the curve of a PV diagram 20.5 – The First Law of Thermodynamics ∫ ¿=Q+W - first law of thermodynamics: ∆ E¿ This is included in the table for the formula sheet and is particularly helpful for the processes in section 20.6 20.6 – Some Applications of the First Law of Thermodynamics - adiabatic process—no energy enters or leaves by heat, P,V,T change - isobaric process—pressure is constant: V and T change - isovolumetric—volume is constant: P and T change - isothermal process—temperature is constant: P and V change **Look at the table on the formula sheet. You don’t have to memorize it, but understand how to apply it. One potential problem is the difference between work done by the gas and work done on the gas. The formula sheet does on, so make it negative to find by. Chapter 21 – The Kinetic Theory of Gases 21.1 – Molecular Model of an Ideal Gas There’s a whole section on the kinetic theory of ideal gases on the formula sheet. All the equations you need are there, but make sure you use the right ones (pay attention if the gas in the problem is monatomic or diatomic, for instance) - theorem of equipartition of energy—Each degree of freedom contributes 3 kBT to the energy of a system, where possible degrees of freedom are 2 associate with translation, rotation, and vibration 21.2 – Molar Specific Heat of an Ideal Gas ∫ ¿=K = 3 N k T= nRT tot tr2ns B 2 Internal energy of an ideal monatomic gas E ¿ ∫ ¿=nC ∆V ∆E ¿ applies to all ideal gases C −C =R C = R3 P V for all ideal gases; V 2 for all monatomic ideal gases CP 5 R/2 5 γ= = = =1.67 ratio of molar specific heats for a monatomic ideal gas CV 3 R/2 3 Again, these equations are provided. 21.3 – The Equipartition of Energy 21.4 – Adiabatic Processes for an Ideal Gas Chapter 22 – Heat Engines, Entropy, and the Second Law of Thermodynamics 22.1 – Heat Engines and the Second Law of Thermodynamics - heat engines take in energy by heat and expel part of that energy by work The cyclic process of a heat engine involves: 1. the working substance absorbs energy from a high-temperature energy reservoir 2. work is done by the engine 3. energy is expelled by heat to a lower-temperature reservoir Basically, they convert energy from heat to mechanical work to do something useful. *when doing the math, absolute values make all energy transfers by heat positive. Use signs intentionally to indicate direction* *the equations for heat engines should have absolute values for any Q involved - thermal efficiency—of a heat engine. The ratio of net work done by the heat engine during one cycle to the energy input at the higher temperature during the cycle; what you gain divided by what you give -Kelvin-Planck form of the second law of thermodynamics—you can’t have 100% efficiency 22.2 – Heat Pumps and Refrigerators - Clausius statement—energy can’t transfer by heat from cold to hot without work - coefficient of performance—of a heat pump (COP). Similar to thermal efficiency (gain/lose). It’s a different equation for heater or refrigerator, but both are provided. 22. 3 – Reversible and Irreversible Processes 22.4 – The Carnot Engine - Carnot engine—*theoretical* show that a heat engine in an ideal, reversible cycle (Carnot cycle) is the most efficient engine possible and can establish an upper limit on the efficiency of all other engines. - Carnot’s theorem—No real heat engine can be more efficient than a Carnot engine - the efficiency of a Carnot engine depends only on the temperatures of the reservoirs. The equations for efficiency and COP of Carnot engines are given in the formula sheet. 22.5 – Gasoline and Diesel Engines The important thing is to be able to see a digram like this one and understand which processes are taking place when so you can apply the right equations for the formula sheet. In this case C->D and A->B are adiabatic and B->C and D->A are isovolumetric. Now that you know that, you just look at the handy table on the formula sheet. **Pay attention to signs. Work done on the gas is the negative area under the curve, so for A->B since it goes right to left the negatives cancel out and that work is positive. Work done by the gas is just the area under the curve. 22.6 – Entropy - entropy is a state variable and an ABSTRACT concept - microstate—configuration of the individual constituents of the system - macrostate—description of the system’s conditions from a macroscopic point of view. - uncertainty, choice, and probability: if one is high, the others are high, and vice versa - entropy—(S) represents the level of uncertainty, choice, probability, or missing information in a system 22.7 – Changes in Entropy for Thermodynamic Systems - Thermodynamic systems change continuously between microstates. In equilibrium, there is one macrostate but the system still fluctuates between microstates. - if a system starts in a low-probability macrostate, it will naturally progress to a higher-probability macrostate. Spontaneous increases in entropy are natural. - change in entropy is related to energy spreading - the total change in entropy for a Carnot engine operating in a cycle is ZERO: ∆ S=0 . So in real life it must be higher because there are no perfect heat engines. 22.8 – Entropy and the Second Law Entropy statement of the second law of thermodynamics: The entropy of the Universe increases in all real processes Entropy wasn’t discussed much in class, so I wouldn’t worry too much about it. The formula sheet provides a few equations and the statement relating change in entropy to the second law, so as long as you understand that you’ll be fine. I referenced the formula sheets a lot, and they’re on blackboard so you can go there and print them off and study from them. It’s not enough to just plug numbers into the equation. If you have a better understanding of the equations and concepts, you’ll be able to determine if your answers are reasonable and it will make checking your work make more sense (especially with the thermodynamic processes where positive/negative signs can get tricky if you don’t pay attention) Good luck!
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