Lecture 3. Equations of motion for constant acceleration
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1 Lecure 3 Equaions of moion for consan acceleraion Course websie: hp://faculy.uml.edu/andriy_danylo/teaching/physicsi Lecure Capure: hp://echo360.uml.edu/danylo2013/physics1fall.hml , Fall 2013, Lecure 3 Deparmen of Physics and Applied Physics
2 Ouline Chaper 2: Secions 5-7 Consan acceleraion Equaions of moion Free fall (graiy) Problem soling , Fall 2013, Lecure 3 Deparmen of Physics and Applied Physics
3 95.141, Fall 2013, Lecure 3 Deparmen of Physics and Applied Physics Mah es resuls
4 Moion a CONSTANT acceleraion Consider a special, imporan ype of moion: Objecs are poin masses; hae mass, no size In a sraigh line (one dimension) Acceleraion is consan (a=cons) , Fall 2013, Lecure 3 Deparmen of Physics and Applied Physics
5 Moion a Consan Acceleraion , Fall 2013, Lecure 3 Deparmen of Physics and Applied Physics
6 Moion a Consan Acceleraion (equaion 1) by definiion ( ) o, accelerai on a and a ( ) o he elociy is increasing a a consan rae , Fall 2013, Lecure 3 Deparmen of Physics and Applied Physics
7 Moion a Consan Acceleraion (equaion 4) aerage elociy ( o ) 2 0 When acceleraion is consan, he aerage elociy is midway beween he iniial and final elociies , Fall 2013, Lecure 3 Deparmen of Physics and Applied Physics
8 Moion a Consan Acceleraion (equaion 2) The aerage elociy of an objec during a ime ineral is x x( ) x 0 ( ) o 2 = 0 +a o x( ) x o Combining hese wo equaions , Fall 2013, Lecure 3 Deparmen of Physics and Applied Physics
9 95.141, Fall 2013, Lecure 3 Deparmen of Physics and Applied Physics Equaion 2. Deriaion
10 0 We need an equaion wihou ime , Fall 2013, Lecure 3 Deparmen of Physics and Applied Physics
11 Deparmen of Physics and Applied Physics , Fall 2013, Lecure 3 We can also combine hese equaions so as o eliminae : Moion a Consan Acceleraion (equaion 3) a x x o o o ) ( 2 ) ( ) ( 0
12 Moion a Consan Acceleraion (equaion 3) , Fall 2013, Lecure 3 Deparmen of Physics and Applied Physics
13 Moion a Consan Acceleraion (all equaions) We now hae all he equaions we need o sole consanacceleraion problems , Fall 2013, Lecure 3 Deparmen of Physics and Applied Physics
14 Problem Soling How o sole: Diide problem ino knowns and unknowns Deermine bes equaion o sole he problem Inpu numbers Example 2-9 A plane aking off from res a runway needs o achiee a speed of 28 m/s in order o ake off. If he acceleraion of he plane is consan a 2 m/s 2, wha is he minimum lengh of he runway which can be used? , Fall 2013, Lecure 3 Deparmen of Physics and Applied Physics
15 Example , Fall 2013, Lecure 3 Deparmen of Physics and Applied Physics
16 Velociy/Acceleraion/Posiion 1 a a 1 >0 2 x V=0 a 2 >0 a 3 =0 a 4 < U-urn x a 5 < ,5 negaie acceleraion, bu from 0< < 4 or 5 decceleraion bu for > 4 or 5 acceleraion , Fall 2013, Lecure 3 Deparmen of Physics and Applied Physics
17 Freely Falling Objecs Near he surface of he Earh, all objecs experience approximaely he same acceleraion due o graiy. This is one of he mos common examples of moion wih consan acceleraion , Fall 2013, Lecure 3 Deparmen of Physics and Applied Physics
18 Freely Falling Objecs The acceleraion due o graiy a he Earh s surface is approximaely 9.80 m/s 2. A a gien locaion on he Earh and in he absence of air resisance, all objecs fall wih he same consan acceleraion , Fall 2013, Lecure 3 Deparmen of Physics and Applied Physics
19 Clicker quesion 1 A C B D You drop a rubber ball. Righ afer i leaes your hand and before i his he floor, which of he aboe plos represens he s. graph for his moion? (Assume your y-axis is poining up). y
20 Clicker quesion 1 y A C B D You drop a rubber ball. Righ afer i leaes your hand and before i his he floor, which of he aboe plos represens he s. graph for his moion? (Assume your y-axis is poining up). The ball is dropped from res, so is iniial elociy is zero. Because he y-axis is poining upward and he ball is falling downward, is elociy is negaie and becomes more and more negaie as i acceleraes downward.
21 Clicker quesion 2 A C B D You oss a ball sraigh up in he air and cach i again. y Righ afer i leaes your hand and before you cach i, which of he aboe plos represens he s. graph for his moion? (Assume your y-axis is poining up).
22 Clicker quesion 2 A C B D You oss a ball sraigh up in he air and cach i again. Righ afer i leaes your hand and before you cach i, which of he aboe plos represens he s. graph for his moion? (Assume your y-axis is poining up). The ball has an iniial elociy ha is posiie bu diminishing as i slows. I sops a he op ( = 0), and hen is elociy becomes negaie and becomes more and more negaie as i acceleraes downward.
23 Freely Falling Objecs 0 if y g hen a = -g if y g hen a = g , Fall 2013, Lecure 3 Deparmen of Physics and Applied Physics
24 Quesion 3 You hrow a ball upward wih an iniial speed of 10 m/s. Assuming ha here is no air resisance, wha is is speed when i reurns o you? Up in he Air I 1) more han 10 m/s 2) 10 m/s 3) less han 10 m/s 4) zero 5) need more informaion
25 ConcepTes 2.10a Up in he Air I You hrow a ball upward wih an iniial speed of 10 m/s. Assuming ha here is no air resisance, wha is is speed when i reurns o you? 1) more han 10 m/s 2) 10 m/s 3) less han 10 m/s 4) zero 5) need more informaion The ball is slowing down on he way up due o graiy. Eenually i sops. Then i acceleraes downward due o graiy (again). Because a = g on he way up and on he way down, he ball reaches he same speed when i ges back o you as i had when i lef.
26 95.141, Fall 2013, Lecure 3 Deparmen of Physics and Applied Physics Example 2-16
27 Freely Falling Objecs Example 2-16: Ball hrown upward. A person hrows a ball upward ino he air wih an iniial elociy of 10.0 m/s. Calculae (a) how high i goes, and (b) how long he ball is in he air before i comes back o he hand. Ignore air resisance , Fall 2013, Lecure 3 Deparmen of Physics and Applied Physics
28 Example 2-16(a) , Fall 2013, Lecure 3 Deparmen of Physics and Applied Physics
29 Example 2-16 (b) , Fall 2013, Lecure 3 Deparmen of Physics and Applied Physics
30 Example 2-16 (b) Y (m) (m/s) (s) (s) , Fall 2013, Lecure 3 Deparmen of Physics and Applied Physics
31 The End See you on Monday. HW2 is due o on Sunday (6pm) , Fall 2013, Lecure 3 Deparmen of Physics and Applied Physics
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