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# Phys 172: Modern Mechanics - Study Guide Phys 172

Purdue

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## Popular in Physics 2

This 6 page Study Guide was uploaded by India Bergeland on Thursday October 16, 2014. The Study Guide belongs to Phys 172 at Purdue University taught by Hochan Lee in Fall. Since its upload, it has received 598 views. For similar materials see Modern Mechanics in Physics 2 at Purdue University.

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Date Created: 10/16/14

Chapter 1 Interactions and Motion 1 Recall the huge range of sizes for material objects from atoms to galaxies that are subject to the laws of Physics 2 Provide arguments for whether interactions are present for a given situation Generate motion diagrams that illustrate all possible types of motion 0 change of direction of motion 0 change in speed 0 change in velocity speed or direction 3 Recite Newton39s first law of motion 0 An object moves in a straight line and at constant speed unless its being acted on by another force Apply Newton39s first law to a wide variety of physical situations 4 List additional beyond changes in motion indicators of interactions 0 change in identity 0 change in shape 0 change in temp 5 Generate our standard quotright handedquot 3D coordinate system Articulate the difference between a vector and a scalar 0 vectora quantity with magnitudespeed and direction 0 scalara single quantity without direction speed is a scalar Use vector notation for appropriate quantities such as position and velocity 0 velocity vector v position vector r Articulate the difference between a quantity and a change in that quantity Calculate the change in a vector quantity graphically and algebraically 0 adding tip to tail 0 subtracting tail to tail Calculate a unit vector from the angles a vector makes with the coordinate axes and vice versa 0 use cosine sine and tangent 6 Conduct quotdimensional analysisquot to convert between different sets of measurement units including SI 7 Calculate the average speed of an object 0 distancetimespeed NO DIRECTION Scale a vector to fit on a graph 0 scale down in same direction Use the position update formula to relate changes in the position of an object to its average velocity during a time interval 0 Predicting new position r2 r1Vavgt2t1 Distinguish between speed average velocity and instantaneous velocity 0 SPEED distancetime no direction 0 AVG VELOCITY positionr2r1timet2t1 0 INST VELOCITYspeed at a particular instant most aprx derivative of slope 0 direction of inst velocity of an object is tangent to the path of the objects motion 0 smaller time intervals give more accurate results Relate the two parts of acceleration to an object39s change in speed and direction 0 Vavgchange in speed 0 rquotdirection 8 Write the definition of momentum 0 momentummass velocity Calculate the momentum of a particle at any speed articulating when it is appropriate to use the nonrelativistic approximation 0 pmv Use an object39s momentum to calculate its change in position over a given time interval 0 DIRECTION OF MOMENTUM IS SAME AS VELOCITY Chapter 2 The Momentum Principle 1 Explain what is meant by the system and the surroundings 0 one or more objects can be considered a system 0 everything not in the system is in the surroundings 0 momentum principle relates the change in momentum of a system to the amount of interaction with its surroundings For every problem clearly specify the system and the surroundings 2 Write down the momentum principle including subscripts 0 change of momentum of a system is equal to the net force acting on the system times the time 0 time interval must be small enough so net force is nearly constant Explain what is meant by quotnetquot force 0 quantifies the interactions between two objects 0 sum of all forces acting on a system Recite the definition of impulse 0 amount of interaction affecting an object 0 time interval must be small enough so force is nearly constant 0 the change of momentum of a system is equal to the net impulse applied to it Calculate the approximate average velocity of an object and describe when it is exactly correct 0 VavgViVf2 WHEN velocity is CONSTANT 0 Vavg x2 x1t2t1 Apply appropriate assumptions to use the position or momentum update formula in the presence of changing momentum or force 0 If force is not constant direction and magnitude of forces change 5 Use the momentum and position update formulas to iteratively predict the motion of an object with and without the aid of a computer 0 calculate the vector forces acting on the system update the momentum of the system update the position repeat Vavg Recite the approximation of gravitational force near the Earth39s surface 0 Fgravmg Interpretdraw the position vs time and velocity vs time and force vs time graphs for an object like a block interacting with a spring 0 the initial position of block the initial momentum of block find the net force of the block update the momentum of the block momentum principle update position of block repeat 8 Explain what is meant by and defend the use of physical models 0 they have the important details without extraneous details Chapter 3 The Fundamental Interactions 1 List the four fundamental types of interactions 0 gravitational responsible for attraction between objects that have mass earth exerts gravitational force on moon and moon does to earth 0 electromagnetic responsible for attraction or repulsion between objects that have electric charge electric forces bind protons and electrons together in atoms and are responsible for chemical bonds between atoms in molecules 0 Strongnuclear occurs between objects made up of protons and neutrons hold together the nucleus of an atom 0 Weak affects all kinds of particles but is responsible for decay 2 Calculate the vector gravitational force exerted by one object on another 0 r hat is negative because the force on object 2 due to object 1 is in the direction opposite to r hat 0 when distance between objects increases magnitude of force decreases 3 Utilize the approximation for the gravitational force near the surface of the earth 0 y distance of object above the earth s surface Reradius of the earth Memass of the earth 4 Apply the property of reciprocity to forces between two objects carefully keeping track of the appropriate objects and forces 0 equal in magnitude opposite in direction 0 magnetic forces do not have reciprocity applies to gravitational and electric forces 6 Calculate the vector electric force between two charged particles using the electric force law 0 to find the ratio of the magnitude of the electric force one proton exerts on the other to the magnitude of the grav force FelecFgrav 7 Describe where the strong interaction force is found and what it does 0 Found inside the nuclei protons repel eachother electrically but the strong force keeps the protons and neutrons together 0 Gravitational force is weak compared to the electric and strong force when two protons touch each other if protons aren t touching the strong force is zero 9 Explain why numerical computations are usually needed to model the motion of complex systems of objects 0 We need to know the position and velocity of each object at time t so that we can calculate the forces on each object at that time 0 From this we can calculate the position and momentum for each object at a slightly later time tdeltat 0 We need the net force on an object which we get from vector addition calculated from Newton s gravitational force 0 3 BODY PROBLEM use superposition principle to update the momentum of object m2 10 Describe the limitations we face in determining the future state of a complex system 0 our ability to measure a systems initial conditions with sufficient accuracy over time small inaccuracies become very large 0 inability to account for all interactions in our model we use a simplified model where we don t account for every object in the universe 0 computers are not fast enough 0 CHAOS systems with small changes in initial conditions produce large changes in behavior and loss of predictability 0 Newtons laws don t work for all situations small particles use quantum mechanics large use general relativity 0 Heisenberg uncertainty principle states there are limits to our knowledge of the state of physical systems States position and momentum of a particle cant both be simultaneously measured exactly 0 Says uncertainty in position dx and uncertainty in momentum dpx is equal to Planck s constant h Determine the center of mass of a system of objects 0 Position of the center of mass of a system of particles is defined as a weighted average of their positions 0 The center of mass is between the two stars but closer to the more massive star 12 Write down and apply the momentum principle for multiparticle systems 0 States that if we know the external forces acting on a multi object system the forces exerted on objects in the chosen system by objects in the surroundings we can conclude the change of momentum of the system over a time interval without worrying about any of the details of the interactiosn of the objects inside the system with each other 0 Reciprocity eliminates all the internal forces 13 Use the momentum principle to relate the initial and final momentum of a system of two particles that undergo sticking collisions 0 Collision involves an interaction that happens in a short period of time and has a large affect on momentum of objects compared to the effects of other interactions during that time Chapter 4 Contact Interactions 2 Explain how solids can be modeled using balls and springs 0 Each ball in the model represents a massive atomic nucleus surrounded by the inner electrons of the atom 0 The spring in the model represents the chemical bond due to shared electrons 3 Explain how interatomic bonds lead to tension forces in a macroscopic wire 0 When an object is hung from the wire the spring like bonds between atoms stretch significantly because each bond must support the weight of every thing below it 4 Use the ball and spring model to determine the length of an interatomic bond in a solid 0 Calculate the density dmv Calculate atoms denstity1 molemass kgatomsmole Take cubed root of atoms to find how many there are along the edge of a cube Distance meters length of cube on one side m atoms in one side OR 5 Use the ball and spring model to determine the interatomic spring stiffness for a solid 0 End to end a long spring made of two identical springs is half as stiff a the shorter springs 0 Parallel two springs side by side are twice as stiff as a single spring 0 Cross sectional area take area of cross section length is irrelevant 6 Distinguish stress from strain 0 Strain the longer a wire is the more it will stretch Doesn t depend on shape measures stretch and original length of wire 0 Stress the quantity that doesn t depend on thickness of the wire measures tension force and cross sectional area of wire Articulate how the Young s modulus for a solid relates microscopic to macroscopic quantities 0 Young s modulus the ratio of stress to strain for a material It is a property that doesn t depend on size or shape The stiffer the material the larger is young s modulus 0 In atomic quantities 7 Describe the microscopic source of normal forces between objects 0 Gravitational force pushes down whereas normal force pushes back up 8 Calculate the sliding and static friction forces between two surfaces 0 Sliding friction force 0 Static friction force 10 State the derivative form of the momentum principle 0 Use in problems involving objects whose momentum isn t changing at all 0 Acceleration a vector quantity advdt can approximate rate of change of momentum as dpdtma OR Fnetma 0 Correct at any speed involves momentum correct even if mass of an object isn t constant a vector principle reminds us we need to add up all vector forces to give net force 11 Relate the period of oscillation for a block attached to horizontal or vertical spring to the spring constant and the block39s mass 0 Finds the position of a block 0 Angular frequency 0 Period T 0 Frequency Graphically represent the motion of an oscillator position or velocity vs time given properties of its Behavior 0 The position of the mass as a function of time is given by a cosine function 0 The period is independent of the amplitude of the oscillations 12 Relate the speed of sound in a macroscopic solid to microscopic quatities 0 Speed of sound in a solid is faster than in air 0 The lower the mass of the atoms the faster a sound pulse will go through a rod 0 The stiffer the bond the faster the sound will go through the rod 0 Speed of sound in a solid

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