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# PHYS 220 Exam II Study Guide Phys 220

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This 9 page Study Guide was uploaded by Kathryn Chaffee on Thursday February 4, 2016. The Study Guide belongs to Phys 220 at Purdue University taught by Dr. Elliot in Fall 2015. Since its upload, it has received 256 views. For similar materials see Physics 220 in Physics 2 at Purdue University.

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Date Created: 02/04/16

PHYSICS 220 Exam II Chapter 6: Work and Energy An important pattern in work experiments is that an external force is exerted on an object in the system, causing a displacement of the object in the same direction as the external force. An object in the environment (ie; you) did positive work on the system. In the experiments, the system changed because of the positive work done on it by the external forces. Four types of energy: 1) Gravitational potential energy (U )g– the energy of the object- Earth system associated with the elevation of the object above Earth The higher above Earth, the greater the gravitational potential energy 2) Kinetic energy (K) – energy due to an object’s motion The faster the object is moving, the greater its kinetic energy 3) Elastic potential energy (U s – energy associated with an elastic object’s degree of stretch The greater the stretch (or compression), the greater is the object’s elastic potential energy 4) Internal energy (U int energy associated with both temperature and structure When the external force is in the direction of the object’s displacement, the external force does positive work, causing the system to gain energy. If the external force points opposite a system object’s displacement, the external force does negative work, causing the system’s energy to decrease. If the external force points perpendicular to a system object’s displacement, the external force does zero work on the system, causing no change to its energy. The work done by a constant external force exerted on a system object while that system object undergoes a displacement d is W=Fdcosθ where F is the magnitude of the force in newtons (always positive), and θ is the angle between the direction of F and the direction of d. The sign of cosθ determines the sign of the work. Work is a scalar physical quantity. The unit of work is the joule. In the experiments, when the force and direction were in the same direction: θ= 0°, and cos0°= +1.0. Positive work was done. When the force and displacement were in opposite directions: θ=180°, and cos180° = -1.0. Negative work was done. When the force and displacement were perpendicular to each other: θ=90°, and cos90°=0. Zero work was done. If no work is done on the system, the energy of the system should not change; it should be constant. Energy is a conserved quantity – it is constant in an isolated system and changes as a result of work done on a non-isolated system. Work-energy principle: the sum of the initial energies of a system plus the work done on the system by external forces equals the sum of the final energies of the system. Gravitational potential energy = U gmgy m = mass g = 9.8 m/s 2 h = position of the object K= mv 2 Kinetic energy = 2 The magnitude of the force exerted by the scale on each spring is proportional to the distance that each spring stretches. FScaleonspring The coefficient of proportionality k (the slope of the F versus x graph) is called the spring constant. Hooke’s law: If any object causes a spring to stretch or compress, the spring exerts an elastic force on that object. If the object stretches the spring along the x-direction, the x-component of the force the spring exerts on the object is F =−kx SonO x The elastic force exerted by the spring on the object points in a direction opposite to the direction it was stretched (or compressed) – hence the negative sign in front of kx. The object in turn exerts a force on the spring: FOonS xkx Elastic potential energy: The elastic potential energy of a spring-like object with a spring constant k that has been stretched or compressed a distance x from its undisturbed position is 1 2 Us= k x 2 When a car skids to a stop, there is negative work done by the friction force and the internal energy of the system increases. Increase in the system’s internal energy due to friction: ∫ ¿=+ fkd ∆U ¿ In the work done by friction approach, the negative work done by friction W =− f d is included if one of the surfaces is not in the friction k system. A collision is a process that occurs when two (or more) objects are in direct contact with each other for a short time interval. Types of collisions: 1) Elastics collisions Both the momentum and kinetic energy of the system are constant The internal energy of the system does not change Colliding objects never stick together 2) Inelastic collisions The momentum of the system is constant but the kinetic energy is not Colliding objects do not stick together Internal energy increases during collisions 3) Totally inelastic collisions Inelastic collisions in which the colliding objects It is harder for the same person to run up a flight of stairs than to walk even when the change in gravitational potential energy of the system person-Earth is the same. The amount of internal energy converted into gravitational energy is the same in both cases, but the rate of that conversion is not. The rate at which the conversion occurs is called the power. The power of a process is the amount of some type of energy converted into a different type divided by the time interval∆ t in which the process occurred: ∆U Power=P= | ∆t If the process involves external forces doing work, then power can also be defined as the magnitude of the work W done on or by the system divided by the time interval ∆t needed for that work to be done: Power=P= W |∆t Gravitational potential energy of a system consisting of Earth and any object: m m U g−G E O rE−O Chapter 7: Extended Bodies at Rest When an object moves as a whole from one location to another, without turning, it is called translational motion. A rigid body is a model of a real extended object. When we model an extended object as a rigid body, we assume that the object has a nonzero size but the distances between all parts of the object remain the same (the size and shape of the object do not change). The center of mass of an object is a point where a force exerted on the object pointing directly toward or away from that point, will not cause the object to turn. The location of this point depends on the mass distribution of the object. When objects turn around an axis, physicists say that they undergo rotational motion. Three factors affect the turning ability of a force: 1) The place where the force is exerted 2) The magnitude of the force 3) The direction in which the force is exerted An object is said to be in static equilibrium when it remains at rest (does not undergo either translational or rotational motion) with respect to a particular observer in an inertial reference frame. Counterclockwise turning about an axis of rotation is positive and clockwise turning negative. The torque produced by a force exerted on a rigid body about a chosen axis of rotation is τ=±Flsinθ For an object in static equilibrium, if a vertical line passing through the object’s center of mass is within the object’s area of support, the object does not tip. If the line is not within the area of support, the object tips. The equilibrium of a system is stable against rotation is the center of mass of the rotating object is below the axis of rotation. Chapter 8: Rotational Motion The rotational position θ of a point on a rotating object (sometimes called the angular position) is defined as an angle in the counterclockwise direction between a reference line (usually the positive x-axis) and a line drawn from the axis of rotation to that point. The units of rotational position can be either degrees or radians. 360°=2 πrad The average rotational velocity (sometimes called the angular velocity) of a turning rigid body is the ratio of its change in rotational position ∆ θ and the time interval ∆ t needed for that change: ω= ∆θ ∆t Rotational (angular) speed is the magnitude of the rotational velocity. The most common units for rotational velocity and speed are radians per second and revolutions per minute (rpm). The linear velocity of a point on a rotating object is sometimes called tangential velocity. The average rotational acceleration of a rotating rigid body (sometimes called the angular acceleration) is its change in rotational velocity ∆ ω during a time interval ∆ t divided by that time interval: ∆ω α= ∆ t 2 The unit of rotational acceleration is (rad/s)/s = rad/s Translational Motion Rotational Motion v =v +a t ω=ω +αt x 0 x x 0 1 2 1 2 x=x 0v tOx axt θ=θ +0 t+ O αt 2 2 2 2 2 2 2a x(x =v0)v x 0 x 2α θ(θ =ω0)ω 0 Rotational acceleration depends on net torque. The greater the net torque, the greater the rotational acceleration. Another important factor that affects the rotational acceleration of a rigid body is the distribution of mass of the rotation object. The closer the mass of the object to the axis of rotation, the easier it is to change its rotational motion. This physical quantity characterizing the location of the mass relative to the axis of rotation is called the rotational inertia (also known as the moment of inertia). Rotational inertia depends on both the total mass of the object and the distribution of that mass about its axis of rotation. For objects of the same mass, the more mass that is located near the axis of rotation, the smaller the object’s rotational inertia will be. For objects of different mass but the same distribution, the more massive object has more rotational inertia. The higher the rotational inertia of an object, the harder it is to change its rotational motion. Two factors that affect the rotational acceleration of an object: Rotational inertia of the object Net torque produced by forces exerted on the object Rotational momentum is defined as L=Iω Rotational momentum and rotational impulse: We now have a quantitative relation between rotational momentum L=Iω and rotational impulse. L =Στ∆ t=L i f The initial rotational momentum of a turning object plus the product of the net external torque exerted on the object and the time interval during which it is exerted equals the final rotational momentum of the object. If the net torque that external objects exert on the turning object is zero, or if the torques add to zero, then the rotational momentum L of the turning object remains constant: Lf=L iI ωf=Ifω i i Linear speed and rotational speed are related: v=rω Thus, the kinetic energy of a particle moving in a circle can be written as: rω ¿ K = mv = m¿1 rotation2l 2 2 I=mr Chapter 9: Gases The ideal gas model is a model of a system in which gas particles are considered point-like and only interact with each other and the walls of their container through collisions. This model also assumes that the particles and their interactions are accurately described using Newton’s laws. Pressure is a physical quantity equal to the magnitude of the perpendicular component of the force F that a gas, liquid, or solid exerts on a surface divided by the contact area A over which that force is exerted: F P= A Unit for pressure is the pascal (Pa); 1 Pa = 1 N/m 2 5 5 2 Atmospheric pressure: 1.0 atm = 1.0 x 10 Pa = 1.0 x 10 N/m Gauge pressure is the difference between the pressure in some container and the atmospheric pressure outside the container: Pgauge−P atm The density of a substance or of an object equals the ratio of the mass of a volume of the substance divided by that volume: m ρ= V 3 The unit of density is kg/m . Avogadro’s number N =6.02x10 23 particles is called a mole. The A number of particles in a mole is the same for all substances and is the number of particles whose total mass equals the atomic mass of that substance. For an ideal gas, the quantities pressure P, volume V, number of particles N, temperature T (in kelvins), and Boltzmann’s constant -23 k=1.38x10 J/K are related in the following way: PV=NkT The law can also be written in terms of the number of moles of particles n, and the universal gas constant R= 8.3 J/K-mole: PV=nRT Processes in which T, V, or P are constant are called isoprocesses. Isothermal – T=constant P1V 1P V2 2 Isochoric – V=constant P P = 2 T1 T 2 Isobaric – P=constant V V = 2 T 1 T 2 P 1 1 P2V 2 T = T 1 2 The average molecular kinetic energy of gas particles depends on the temperature of the gas: 1 2 3 K= 2v = kT2 The root-mean-square speed of a gas atom or molecule (the rms spped) is: 2 3kT vrms√ = √ m Thermal energy is the random kinetic energy of all atoms and molecules in a system: 3 U thermal 2T)

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