PHYSICS 231 PH 2 1 Review 1 PHY 231 1 For Mid Term Exam PHY 231 2 For Mid Term Exam One double sided help p sheet is allowed PHY 231 3 Syst me Internationale SI 7 Base B s Units We W will ill us use th them m Quantity Name unit l th length meter t m mass kilogram kg time second electrical Current Ampere A temperature Kelvin amount of substance mole s K Examples mp of f Derived units Speed S d m s Acceleration m s2 Force kg m s kg m s2 N mol Luminous intensity candela cd NIST http physics nist gov cuu index html PHY 231 4 Review of Velocity PHY 231 5 Review of Acceleration PHY 231 6 x v a example 0 time Draw v vs t and a vs t PHY 231 7 v m s t 1 v 2 2 0 0 T s Q 1 2 1 What is the distance covered in 1 second 2 What is the area indicated by a b c The area under the v t curve is equal to d th displacement the dis l m t of f th the object bj t PHY 231 1 1 2 2 1 2 1 2 8 a m s2 2 0 1 1 2 3 T s If the initial velocity at T 0 is 4 m s 1 What is the velocity at T 2 second 2 What is the area indicated by Q 1 2 a b c The area under the a t curve is equal to d th change the h in i the th velocity l it vf vi PHY 231 5 7 1 3 1 3 1 3 9 Motion in One Dimension with constant acceleration 1 x x0 v0 t a t 2 v v0 a t 3 x x0 v t 4 v v v0 5 v v 2a x x0 1 2 2 1 2 2 2 0 PHY 231 10 100 m dash After long training Ben Lewis can accelerate with a 3 00 m s2 over a distance of 20 0 m A After how many seconds Ben reaches his top speed B What is his speed p at that time A 20 0 m 1 2 3 00 t2 v t 3 65 s B v t 3 65 3 00 t 10 95 m s PHY 231 t 11 Vector operations in equations X X X X Xb a b a b a Ya b Ya Yb Ya Yb y xb yb B X a b X a X b X a X b Y Y Y Y Y b a b a b a a b ya b x A B A xa ya x Example X a b 5 3 2 Ya b 2 2 4 PHY 231 12 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 13 2 y quiz for extra credit Three planes are traveling with equal motor power to the south as indicated by the blue arrow south arrow At t 0 t 0 a wind starts to blow in different ways but with equal strength as indicated by the red arrows The pilots do not correct speed or steering Which plane has the largest displacement after 1 hour of flying and 2nd and 3rd a C largest displacement then A then B b A largest displacement then C then B c C largest displacement displacement then B then A d A largest displacement then B then C 14 PHY 231 answer A L A B A B 2 A2 B2 2AB B L A B L A B C L A2 B2 largest displacement 3 d 3rd 2nd So right answer A C B A C B answer b PHY 231 15 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 16 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 17 Parabolic motion a catapult vx v0cos vy v0sin 2g 0 V v0 vx v0cos vy v0sin vx v0cos vy v0sin 1g Vt v0 at vx v0cos vy v0sin 3g vx v0cos vy v0sin 4g vx v0cos vy v0sin 5g 5 t 0 t 1 t 1 t 2 t 2 PHY 231 t 3 t 3 t 4 t 4 t 5 18 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 if t 30sin 0 5gt 0 0 5gt 0 t 0 or t 30sin 0 5g X t 30sin 0 5g 900cos sin 0 5g 900sin 2 900 i 2 g if 30o X 79 5 m PHY 231 19 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 20 General strategy 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 2nd law for forces in the parallel direction and perpendicular direction Solve …
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