Lecure 3 Chaper 2 Physics I 01.29.2014 Equaions of moion for consan acceleraion Course websie: hp://faculy.uml.edu/andriy_danylo/teaching/physicsi Lecure Capure: hp://echo360.uml.edu/danylo2013/physics1spring.hml
Ouline Chaper 2: Secions 5-7 Consan acceleraion Equaions of moion Free fall (graiy)
Simplificaions 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)
Wha do we wan?
Velociy equaion. Equaion 1. (consan acceleraion) by definiion ( ) o, acceleraion a and 0 0 0 a ( ) o he elociy is increasing a a consan rae 0
Aerage elociy. Equaion 4 (consan acceleraion) aerage elociy ( o ) 2 0 When acceleraion is consan, he aerage elociy is midway beween he iniial and final elociies.
Posiion equaion. Equaion 2 (consan acceleraion) The aerage elociy of an objec during a ime ineral is: x x( ) x 0 ( ) o 2 o x( ) x o Combining hese wo equaions = 0 +a
Le s derie Equaion 2
No ime equaion. Equaion 3 (consan acceleraion) We can also combine hese equaions so as o eliminae : x( ) xo ( ) o 2 ( ) a o I s useful when ime informaion is no gien.
No ime equaion deriaion.
Moion a Consan Acceleraion (all equaions) We now hae all he equaions we need o sole consanacceleraion problems.
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?
Example 2-9
Velociy/Acceleraion/Posiion a a 1 >0 a 2 >0 a 3 =0 a 4 <0 a 5 <0 1 x 2 0 4 5 5 4 3 U urn x 0 5 1 2 4 4 3 5 V=0 4,5 negaie acceleraion, bu from 0< < 4 or 5 decceleraion bu for > 4 or 5 acceleraion
Freely Falling Objecs One of he mos common examples of moion wih consan acceleraion is freely falling objecs. Near he surface of he Earh, all objecs experience approximaely he same acceleraion due o graiy. All free-falling objecs (on Earh) accelerae downwards a a rae of 9.8 m/s 2 Air resisance is negleced
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
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.
Freely Falling Objecs 0 if y g hen a = g if y g hen a = g + + +
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.
Example 2-16(a)
Example 2-16(b)
Example 2-16 (b) Y (m) 5 3 1 (m/s) 0.4 0.8 1.2 1.6 2 (s) (s)
Graphical Analysis - cure displacemen
Example
There is a difference beween negaie acceleraion and deceleraion: Negaie acceleraion is acceleraion in he negaie direcion as defined by he coordinae sysem. Deceleraion occurs when he acceleraion is opposie in direcion o he elociy.
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