PHYSICS 231 PH 2 1 Review 4 PHY 231 1 Final Exam for PHY 231 Alternative Exam Monday Dec 14 Monday 14 9 00am 11 00am morning NSCL seminar room You have to sign up in class before this Friday Regular Exam Tuesday Dec 15 5 45pm 7 45pm evening W lls Hall Wells H ll B B 108 108 PHY 231 2 For Final Exam PHY 231 3 Motion in One Dimension 1 x x0 v0 t a t 2 v v0 a t 3 x x0 v t 4 v 12 v v0 5 v v 2a x x0 1 2 2 2 2 0 F ma PHY 231 4 While studying motion in 2D one almost always l makes m k a decomposition d mp iti n into int horizontal and vertical components of the motion which are both described in 1D motion Remember m m that the object j can accelerate in one direction but remain at the same speed in the other direction Remember that after decomposition of 2D motion into horizontal and vertical components you should investigate both components to understand the complete motion of a particle l After decomposition into horizontal and vertical p y directions treat the two directions independently PHY 231 5 The length of a vector and its components Y vx vy x Length of vector use pythagorean theorem v x v cos v v v 2 x v y v sin tan v y v x PHY 231 6 2 y Review Trajectory of Projectile Horizontal H i t l motion ti constant t t velocity l it 1 x x0 vx 0 t 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 vx 0 vx t 0 vy0 vy t 0 PHY 231 7 An example A football player throws a ball with initial velocity of 30 m s at an angle of 30o degrees w r t the ground d H How f far will ill the th ball b ll fly fl b before f hitti hitting the th ground X t 30cos t Y t 30sin t 0 5gt2 0 0 if t 30sin t 30 i 0 5gt 0 0 5 t 0 t 0 or t 30sin 0 5g X t 30sin 0 5g 900cos g sin 0 5g g 900sin 2 g if 30o X 79 5 m PHY 231 8 Newton s Laws First Law If the net force exerted on an object is zero the object continues in its original state of motion ti if it was att rest t it remains i att rest t If it was moving with a certain velocity it will keep on moving g with the same velocity y Second Law The acceleration of an object is proportional to the net force acting on it and i inversely s l proportional ti l tto its mass ss F ma 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 PHY 231 9 General strategy for problems with forces If not given make a drawing of the problem Put all the relevant forces in the drawing object by object object Think about the axis Think about the signs Decompose the forces in direction parallel to the motion and perpendicular to it Write down Newton s Newton s laws for forces in the parallel direction and perpendicular direction Solve for the unknowns Check whether your answer makes sense sense PHY 231 10 fs max sn fk kn Before the object moves the net force equals 0 Thus fs F PHY 231 11 Problem n FgL A If s 1 0 what is the angle g for which the block just starts to slide F mgsin g FgL mgcos B The block starts moving Given that k 0 5 0 5 what is the acceleration of the block Fg mg Fs k A Parallel P ll l direction di ti mgsin i sn 0 0 F ma F Perpendicular direction mgcos n 0 so n mgcos Combine mgsin g smgcos g 0 s sin cos tan 1 so 45o B Parallel direction mgsin 45o kmgcos 45o ma F ma g 2 2 2 a 2 so s a g 2 PHY 231 12 Work and Power Power P W t Fcos x t Fcos v Area A A Fcos x Fcos Fcos W A Work W Fcos x The work done is the same as the area under the graph of f Fcos F versus x PHY 231 13 Work and Energy WORK KINETIC ENERGY mv2 POTENTIAL ENERGY Gravitational PE mgh Spring PE kx2 Mechanical energy ME KE mv2 ME KE PE Conserved if only conservative forces are present KEi PEi KEf PEf Not conserved in the presence of non conservative forces KEf PEf KEi PEi Wnc PHY 231 14 Conservation of mechanical energy only h ld if the holds h system is i closed l d AND all ll forces are conservative When work is done on an object and the only change is its speed p The work done is equal q to the change g in KE W KE final KE initial When work is done on an object and the only change iss its ts height he ght The he work done iss equal to the change in gravitational PE W mgh final mgh initial PHY 231 15 Momentum and Impulse Momentum p mv Newton s 2nd law F p t Impulse the change in momentum p F t PHY 231 16 Types of collisions Inelastic collisions Elastic collisions Momentum Momentum is conserved Momentum Momentum is conserved Some energy is lost in the No energy is lost in the collision KE not conserved collision KE conserved Perfectly inelastic the objects stick together PHY 231 17 Momentum p mv Force F p p t Impulse the change in momentum p F t Types of collisions Inelastic collisions Elastic collisions Momentum is conserved Momentum is conserved Some energy is lost in the No energy is lost in the collision ll KE E not conserved d collision KE conserved Perfectly inelastic the Conservation of momentum objects j stick m1v1i m m2v2i m m1v1f m m2v2f together Conservation of KE Conservation of m1v1i2 m m2v2i2 m m1v1f2 m m2v2f2 momentum 18 v1i v2i v2f v1f m1v1i m2v2i m1 m2 vf PHY 231 Radians Radius Circumference 2 r Part s r r s s r in radians 360o 2 rad 6 28 rad rad 180o deg PHY 231 19 Review f i Average angular t f ti t velocity rad s Instantaneous lim t 0 t Angular velocity f i Average angular t f ti t acceleration rad s2 Instantaneous angular lim t 0 t acceleration PHY 231 2 rad 3600 10 2 360 rad 1 rad 360 2 deg 20 And Angular …
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