Physics 231 Final Review Alex Brown PHY 231 Spring 2015 Nov 17MSU 2014 1 Review for Final Final Exam is on Wednesday May 6 8 10 pm Room 1410 BPS It covers chapters 1 14 It s a 2 hours long closed exam with 35 bubbles Chapters 13 and 14 occupy 7 bubbles with 22 of the total points You can should bring written equation sheets four sides total on a 8 5x11 sheet of paper MSU PHY 231 Spring 2015 2 How to prepare for it Listen carefully to this review Lecture notes and homework sets Previous Review 1 2 3 notes MSU PHY 231 Spring 2015 3 Review of Acceleration MSU PHY 231 Spring 2015 4 4 Ball Toss Problem Dave throws a ball straight up with a velocity of 5 0 m s 1 How high does it go relative to the height at which it was released 2 After how much time does it reach that height x t x0 v0t at2 v t v0 at x t 0 5t 9 8 t2 v ttop 0 5 9 8ttop it decelerates at it highest point the velocity is zero ttop 5 9 8 0 51 s time to reach highest point xtop x t 0 51s 5 0 51 9 8 0 51 2 1 3 m MSU PHY 231 Spring 2015 5 Vector length and its components Y xa ya l x Length of vector use pythagorean theorem x a l cos l xa2 y a2 y a l sin tan y a x a MSU PHY 231 Spring 2015 6 Review Trajectory of Projectile Horizontal motion constant velocity 1 x x0 vx 0t 2 vx vx 0 Vertical motion free fall Use notation convention 3 y y0 v y 0t 12 gt 2 4 v y v y 0 gt 5 y y0 v y t 6 v y 12 v y v y 0 7 v y2 v y20 2 g y y0 vx0 vx t 0 vy0 vy t 0 MSU PHY 231 Spring 2015 7 Newton s Laws First Law If the net force exerted on an object is zero the object continues in its original state of motion if it was at rest it remains at rest If it was moving with a certain velocity it will keep on moving with the same velocity Second Law The acceleration of an object is proportional to the net force acting on it and inversely proportional to its mass a F m or F ma Third Law If two objects interact the force exerted by the first object on the second is equal but opposite in direction to the force exerted by the second object on the first F12 F21 8 MSU PHY 231 Spring 2015 8 PHY 231 Identifying the forces in a system MSU PHY 231 Spring 2015 PHY 231 9 9 Force Mass and Weight Forces are quantified in units of Newton N 1 N 1 kg m s2 Fnet m a A force is a vector it has direction The net force causes acceleration in the same direction as the net force MSU PHY 231 Spring 2015 PHY 231 10 Two forces that act upon us nearly all the time n Gravitational Force Fg Fg mg referred to as weight g 9 81 m s2 1 Fnet Fg n 0 2 Fg mg n magnitudes 3 Fg n Normal Force elastic force acting perpendicular to the surface the object is resting on Name n Fg MSU PHY 231 Spring 2015 PHY 231 11 11 inclinded plane angles to remember 90 Choose your coordinate system in a clever way Define one axis along the direction where you expect an object to start moving the other axis perpendicular to it these are not necessarily the horizontal and vertical direction MSU PHY 231 Spring 2015 12 A first example n Fgy mg cos 1 Draw all Forces acting on the red object 2 If 40o and the mass of the red object equals 1 kg what is the resulting acceleration in the direction of motion assume no friction Fgx mg sin Balance forces in directions where you expect no acceleration whatever is left causes the object to accelerate Fg mg n Fgy magnitudes ma Fnet Fgx mg sin a g sin a 6 3 m s2 MSU PHY 231 Spring 2015 13 MSU PHY 231 Spring 2015 PHY 231 14 14 n mg Ffr n mg T M Fg mg a No acceleration no net force Ffr T maximal Ffr sn so T sn TRUE b k s and acceleration will start if T sn so FALSE MSU PHY 231 SpringFALSE 2015 c At rest so no net force F 0 1515 Tension Fg w MSU PHY 231 Spring 2015 16 Friction n 20 kg fs pull A person wants to drag a crate of 20 kg over the floor If he pulls the crate with a force of 98 N the crate starts to move What is s Fg Answer fsmax sn sMg 20 9 8 s 196 s Just start to move Fpull fsmax 0 fsmax Fpull 98 196 s so s 0 5 After the crate starts moving the person continues to pull with the same force Given k 0 4 what is the acceleration of the crate F ma F 98 0 4Mg 98 0 4 20 9 8 98 78 4 19 6 N 19 6 20a a 0 98 m s2 MSU PHY 231 Spring 2015 17 Example A 1000 kg car is pulling a 300 kg trailer Their acceleration is 2 15 m s2 Ignoring friction find a the net force on car c b the net force on the trailer t c the net force exerted by the trailer on the car c 1000 Ftc Fct Fengine Fe t 300 Ftc Fct Force provided by engine Fe mc mt a 2795 N Fct mt a 645 N so Ftc 645 N a Fc Fe Ftc 2795 645 N 2150 N b Ft Fct 645 N c Ftc 645 N MSU PHY 231 Spring 2015 18 Energy note its units Potential energy PE Energy associated with position Gravitational PE mgh Energy associated with position in grav field Kinetic energy KE mv2 Energy associated with motion Elastic PE kx2 energy stored in stretched compressed spring Fs kx Hooke s law k spring constant in units of N m Mechanical energy ME ME KE PE Conservative forces MEi MEf 0 Non conservative forces MEi MEf Enc MSU PHY 231 Spring 2015 19 Work the amount of energy transfer W Fcos x To measure how fast we transfer the energy we define Power The rate of energy transfer Power P Work time W t J s Watt P Fcos x t Fcos vaverage MSU PHY 231 Spring 2015 20 Overview Equations of kinematics x t Xo Vo t at2 v t Vo at Newton s second Law F ma Conservation of mechanical energy MEi MEf Enc 0 Closed system Work energy Theorem Enc MEi MEf Work W Fcos x MSU PHY 231 Spring 2015 21 Question A ball rolls down a slope as shown in the figure The …
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