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# unit 1 notes CHM 111

UM

GPA 3.6

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This 7 page Class Notes was uploaded by Gabriel Iriza on Monday February 9, 2015. The Class Notes belongs to CHM 111 at University of Miami taught by Nita Lewis in Spring2015. Since its upload, it has received 39 views.

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Date Created: 02/09/15

Chapter 4 2D Motion Constant Velocity Acceleration a is equal to 0 Kinematics formulas x xovot amp y yovot 39 V Vo Constant Acceleration Acceleration a remains the same and velocity v constantly rises y xovoxt 12 axtquot2 amp y yoVoyt 12 aytquot2 vx vOX axt amp vyv0y ayt vxquot2 vex 2 ZaxAx amp vyquot2 VoyA2 2ayAy Projectile Motion n projectile motion ax is equal to zero neglecting air resistance and ayis equal to g which is 981 msquot2 The symbol g will always be a positive 981 msquot2 think of it as the magnitude of gravity while it s actual vector acceleration is 981 msquot2 x xovoxt amp yyo Voyt 1 2gtquot2 vxvox v of x will stay constant amp VyVoy39gt vyquot2 voyAZZgAy If the launch angle is zero Voy will be 0 since sin 0 0 and vx will always be equal to Vox Rules of thumb for general launch angles xoyo0 voxvocose voyvosin6 The range of a projectile is the horizontal distance traveled before landing Range is defined as voAZg sin26 The time of flight for a projectile is defined as Zvogsin6 Chapter 5 Newton s Law of Motion Force and Mass Net force is the sum of all forces acting on an object or ZF Mass measures how difficult it is to change the velocity of an object to stop it move it or change its direction Newton s First Law Force is required only to change an object s motion Newton s First Law An object at rest remains at rest as long as there is no net force acting on it ZF ma O AKA Law of Inertia An object moving with constant velocity continues to move with the same speed as long as no net force acts on it Inertial frame of reference is a frame of reference in which the law of inertia holds A net force of zero means that the velocity is constant Newton s Second Law Unbalanced forces cause acceleration Acceleration a is proportional to force F F ma Newton s Second Law An object s force is equal to its mass times its acceleration F ma The force is measured in Newtons N Freebody diagrams are often used to portray nonrotational motion In free body diagrams an object is treated as a point particle with forces acting on it Newton s Third Law Newton s Third Law For every force that acts on an object there is a reaction force acting on a different object that is equal in magnitude and opposite in direction If object 1 exerts a force 1339 on object 2 object 2 exerts a force I339 on object 1 F When objects are touching each other the actionreaction forces are often called contact forces internal forces Weight of an object on Earth s surface is the gravitational force exerted on it by the Earth W mg SI unit N Weight is a force with vector quantities Apparent Weight Wa W ma Normal Force Normal force N is always perpendicular to the surface It is exerted on objects by the surface opposes weight N can be found by setting all y components equal to 0 Normal force is a measure of weight you keep your weight Wmg but with no surface or normal force you feel weightless Chapter 6 Applications of Newton s Laws Frictional Forces Two most commonly used types of friction are kinetic and static friction Kinetic Friction Fk 0 Friction encountered when surfaces slide against one another with a finite relative speed 0 In general the magnitude of Fk is proportional to the magnitude of the normal force N o Fk ukN where u is equal to the constant of proportionality also known as the coefficient of kinetic friction Rules of thumb for kinetic friction o Proportional to the magnitude of the normal force Fk ukN 0 Independent of the relative speed of the surfaces 0 Independent of the area of contact between surfaces Fk stays constant after movement begins Static Friction F5 0 F5 gt Fk 0 After Fsmax Fk takes over 0 Fsmax SN 0 The coefficient of static friction can reach values greater than 1 Rules of thumb for static friction o It takes any value between zero and the maximum possible force of static friction 0 Independent of the area of contact o It is parallel to the surface of contact in the direction that oppose relative motion Strings and Springs Ropes and pulleys are assumed massless unless told otherwise Springs and Hooke s Law 0 F being the magnitude of the spring force Fkx o k is the force constantspring constant Units are in Nm 0 The larger the value of k the stiffer the spring 0 Hooke s law Fxkx Translational Equilibrium An object being at transitional equilibrium means that its net force is zero Connected Obiects F m1m2a Only include external forces in free body diagram don t include internal forces such as contact forces Circular Motion To make an object move in a circle with constant speed a force must be acting on it that is directed towards the center of the circle This is called centripetal acceleration At ZrGv acp vquot2r with radius r and constant speed v Fcp macp mvquot2r Fcp must be equal to static friction F5 for the object not to skid Chapter 7 Work and Kinetic Energy Work Done by a Constant Force Work is force done in the direction of the displacement W Fd measured in Nm or Joules Work is a vector quantity and has direction W FcosGd chosG Kinetic Energy and the WorkEnergy Theorem When work W is positing speed is increasing there is an acceleration Kinetic energy K is defined through work in the workenergy theorem K 12 mvquot2 W AK 12 meAZ 12 mviquot2 Work Done by a Variable Force Work done can be found through the area of a force vs position graph Work to stretch or compress a string W 12 kxquot2 Work done by a variable force WFavgd Power Power P is a measure of how quickly work is done P Wt measured in Jsec Formula Sheet Formulas for Kinematic Motion Given constant velocity 0 x xovot amp y yovot Given constant acceleration o y xovoxt 12 axtquot2 amp y yo39l39Voyt39l39 12 aytquot2 o vx vOX axt amp VyVoy ayt o vxquot2 voxquot2 ZaxAx amp VyA2 VoyA2 2ayAy Projectile Motion 0 x xovoxt amp yyo Voyt 1 2gtquot2 o VxVox v of x will stay constant amp vyvoygt o vyquot2 voyAZZgAy Regarding Newton s Second Law ZFma Wzmg Frictional Forces Fk MN 39 Fsmax HsN Hooke s Law Fxkx Connected Obiects F m1m2a Circular Motion At ZrGv 39 acp VAZr 39 Fcp macp mvquot2r Work W Fd FcosGd chosG Kinetic Energv WorkEnergy Theorem K 12 mvquot2 W AK 12 meAZ 12 mviAZ Variable Forces W 12 kxquot2 spring 39 wFavgd Power PWt

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