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# Exam 1 Study Guide PHYS 1100

RPI

GPA 3.7

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This 10 page Study Guide was uploaded by Tiffany Mae Paskiewicz on Saturday October 3, 2015. The Study Guide belongs to PHYS 1100 at Rensselaer Polytechnic Institute taught by a professor in Fall 2015. Since its upload, it has received 11 views. For similar materials see Physics I in Physics 2 at Rensselaer Polytechnic Institute.

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Date Created: 10/03/15

Physics 01 Class 01 Measurements What is physics Physicists study the fundamental objects and interactions of nature and their manybody manifestations Quantitative Measurement determine the relevant physical variables Predictive If we can predict the behavior of the physical system then we understand the system and its interactions Mathematical the parts we understand are framed in appropriate mathematical language to facilitate predictions This is called a theory Units of Measurements Standardized units allow measured quantities to be compared and predicted results to be compared with experimental results SI units are most used in physics Measurement Uncertainties since measurement re key to developing a physical theory we also need to understand the limitations of a measurement We quantify the accuracy of a measurement using the same units as the measured quantity We will ften make very sloppy estimates of measurement uncertainties but crude estimates are better than none at all Always state experiment uncertainties Random uncertainties the results of a measurement are randomly distributed about the average value Caused by unpredictable fluctuation in the measuring technique these fluctuations may be due to interference of the environment or due to human limitations Statistical Analysis to report random uncertainties assume they have been produced by a large number of uncontrolled variables in the measurement In this limit all random uncertainties take a specific form called a Gaussian distribution Gaussian Distribution The error of a series of measurements can be quantified by calculating the quotstandard deviation a Z x a cf SD Ngl SD can also be seen as o I Significant Figures The term significant figures refers to the number of important single digits in the coefficient of and expression in scientific notation The number of significant figures in an expression indicated the confidence or precision of a measurement When multiplying or dividing number the number of significant figures in the final answer is the number of significant figures in the factor having the least number of significant figures When adding or subtracting numbers the number of decimal places in the result is the smallest number of decimal places in any term 1 Dimensional Motion Variables Displacement Final position initial position Distance Total traveled length Position x and displacement Ax Time t and interval At Instantaneous or average Velocity arrow over v arrow over v sub avg Acceleration arrow over a arrow over a sub avg Constant acceleration Arrow over a Velocity speed and direction It is a vector with speed as its magnitude Average velocity is AxAt Instantaneous velocity velocity at a moment It is the limit as t approaches 0 AxAt dxdt Integration of velocity equals displacement Vectors Position and displacement vectors Vector Addition and subtraction Velocity and acceleration vectors Multiplying vectors Vector and Scalar 0 Vector a quantity that has both magnitude and direction 0 Scalar a quantity that has only magnitude How to express a Vector o Graphical An arrow with a magnitude and directions 0 Components a component of a vector is the projection of the vector on an axis the x component and the ycomponent o Magnitude is the square root of x2 y2 0 Unit vectors a vector that has a magnitude of 1 and points in a particular directions it specifies only a direction Position Vector The Location of a particle relative to the origin is given by a position vector Displacement Vector Displacement is the shortest distance from the initial to the final position Average velocity in 3 dimensions Time t scalar Position rgt vector Displacement Argtrgtrgt0 Time interval At tto Definitions 0 Acceleration velocity is speeding up slowing down or changing direction 0 Speed magnitude of the velocity vector 0 Speeding up velocity vector s magnitude is increasing 0 Slowing down velocity vector s magnitude is decreasing Scalar Product dot product Starts with two vectors and gives a scalar that is independent of coordinate system Vector Product cross product Cartesian components of cross product Vector describes motion in a way that is independent of the choice of coordinate system 2 Dimensional Motion Problem solving strategy 0 Motion in the X direction is independent of motion in the X direction 0 Break the problem into two parts on for the X motion and one form the Y motion 0 Handle each part like a 1D problem 0 Express y as a function of x and t for each of the two objects 0 Combine the equations to eliminate unknowns Force and Motion 1 Newton s Laws of Motion Newton s Laws of Motion How to describe objects in motion A theory of Gravity Newton s First Law o If the body is at rest it will remain at rest static equilibrium o If the body is in motion then its velocity remains constant dynamic equilibrium 0 The key condition is Zero net force Newton s Second Law 0 The acceleration of a body is proportional to the net force acting on it 0 Only forces that act on an object contribute to the net force on it o The net force and acceleration are always in the same direction because m is a positive number Newton s Second Law Complex Systems 0 A couple system contains two different forces and objects that the masses are working on Normal Force N the force from an objects contact surface to resist other forces It works in the opposite direction of the object exerting the other force It is at a 90 degree angle from the surface Static Friction f5 the contact force that keeps and object quotstuckquot on a surface and prevents relative motion Static friction is tangent to the surface towards the opposite direction of gravitational pull fs usN uS is the coefficient of static friction Kinetic Friction when an object slides along a surface the surface exerts a contact force in the opposite direction it is always against the motion fk MN pk is the coefficient of kinetic friction Contact force The contact force is the components of the friction force and normal force Inclined force a force pulling or pushing on an object at an angle How to solve problems using the second law 1 Identify all forces acting on the object 2 Choose a coordinate system 3 Draw a quotFree body Diagram 4 Find the components of the forces acting on the object 5 Use Newton s Second Law to write on equation for each considered force 6 Solve the equation Newton s Third Law 0 quotFor every action there is an equal and opposite reactions 0 Forces always occur as interactions between objects Uniform Circular Motion Uniform Circular Motion Circular path at constant speed where Newton s 2quot l law still applies and acceleration is centripetal Rotation 0 There are two types of physical systems that are not easy to analyze using x y and z coordinates 0 Ex rotation of matter around the center of mass of an object or a fixed point 0 The force and the acceleration are towards the center of the rotation 0 Velocity is perpendicular to force and acceleration o Centripetal acceleration is the acceleration of an object directed toward the center of rotation in uniform circular motion 0 There must be a net force on the object that causes this to happen o Centripetal force is the net force on an object directed toward the center of rotation in uniform circular motion 0 Centrifugal force is a fictitious inertial force that arises when one uses accelerating coordinate systems 0 Centrifugal force does not exist Work and Kinetic Energy Newton s second law defines the Workenergy Theorem 0 Work is force over distance o If there is no distance there is no work done despite the force applied on the object o If the velocity is perpendicular to the force there is no work done because cos 90 is 0 Relationships between Work and other variables1 o If work is in the same direction of velocity then W gt 0 and the object speeds up o If work is in the opposite direction of velocity then W lt 0 and the object slows down o If force is perpendicular to velocity then W 0 and the object continues at its original speed What is Work 0 Work is the transfer of energy 0 Work is equal to the change in kinetic energy 0 Work measure the energy that a force puts into or takes away from an object as it moves What is Energy 0 Energy is the ability to do work 0 Different energies include kinetic energy potential energy gravitational elastic electromagnetics chemical radiant thermal etc Potential Energy and Conservation of Energy Work Review 0 Work is positive if it is in the same direction of the velocity 0 Work is negative if it is in the opposite direction of the velocity 0 Work is a scalar quantity Conservative Forces 0 All fundamental forces of nature have work integrals that don not depend on the path they are conservative forces 0 Work along any closed path is equal to zero 0 Ex Gravity F mg 0 Hooke s Law Fx kx o Electrostatic force 1 These relationships are based upon an object on a frictionless surface Nonconservative forces 0 Nonconservative forces are all forces that change depending on the path 0 Ex Muscle contractions 0 Friction 0 Mechanical Engines 0 Nonconservative forces are dissipative forces 0 Because nonconservative forces don no conserve energy there is no potential energy Work Energy Theorem 0 The change in kinetic energy is equal to the work done by both conservative and non conservative forces Potential Energy 0 The change of potential energy is equal to the negative value of conservative work 0 Potential energy is easier to handle as a force 0 Potential energy has an arbitrarychosen point of energy zero as reference 0 At zero potential energy is zero 0 Since the zero is arbitrary potential energy changes as the point of reference changes Conservation of Energy 0 When work is done by only conservative forces nonconservative forces are negligible then the sum of the change of kinetic energy and the change of potential energy equals zero FINE FD F Va 11 1 g 3 L V E 4 f a zullt1BHBB Wi g EFF mebgbkb gl BQILb maxio ENE I HAD M h WiuwPln Ba VlKI IuVmgB u 3 9 KIN IBEMNWV w l HunQDD PEEHNL tm u amuIRKV u n 5 W a f V er and King c 611 deanton dM E39d V l ganjaI 39 W Iquot V Cmsmf he V 5 0x Fa w Pd 4 w lFJaorw warmid I CIJ m doosdquot mgdco 9047 M O Zw de Wort 14mm Enem Wimp u Z w ZaaL P b ifp lot3 dd J2 I39Mp7 WLZ Fnddg 114 145 Jinn139quot W int quot K ki

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