Review before final exam . Guide how to identify type of the - PowerPoint PPT Presentation

Review before final exam . Guide how to identify type of the problem

Guide how to identify type of the problem conditions The question is about? acceleration force for system at rest (linear or angular) a x =0 Only if the problem explicitly says “average acceleration” a y =0 or if the acceleration is constant a =0 a= D v/ D t may be used The problem is for application of Newton’s 2 nd Law: Does/can center-of-mass Does/can any of any object move? object rotate? I a = S i t i Circular motion? m a x = S i F i x a x =v 2 /R Also often needed: m a y = S i F i y (0=) a =a/R for the x-axis Usually a y is zero t =  r F sin q pointing towards for proper choice the circle center or  r ┴ F of coordinates Rolling combines both for the same object

Only if the problem explicitly The question is about? velocity says “average velocity” or if the velocity is constant Wave velocity? (linear or v= D x/ D t may be used v = w /k =f l angular) Some free fall problems are easier to A free fall problem? Collision? solve using energy conservation (the only force is weight) (two objects, there is Use conservation of y “before” and “after” v fx = v ix mechanical energy the “interaction”) v fy = v iy - g D t E tot i =E tot f x D x = v ix D t Any rotation involved? K i +U i =K f +U f D y = v iy D t - 1 / 2 g ( D t) 2 Rotating object: K= 1 / 2 I w 2 yes no Linear motion: K= 1 / 2 mv 2 Use conservation of Use conservation of U=mgh angular momentum linear momentum Gravitational: L tot i =L tot f P tot i =P tot f Elastic (spring) : U= 1 / 2 kx 2 Extended object: L=I w p=mv Does the text say “perfectly” inelastic Point-like object: Does the text L=  r mv sin q or the objects stick say “elastic” ? to each other ? or  r ┴ mv no yes In addition, yes v 1f =v 2f use K i =K f

The question is about? position (linear or angular) A free fall problem? Some free fall problems are easier to solve using energy conservation (the only force is weight) D x = v ix D t Use conservation of D y = v iy D t - 1 / 2 g ( D t) 2 y mechanical energy v fx = v ix v fy = v iy - g D t E tot i =E tot f x K i +U i =K f +U f Rotating object: K= 1 / 2 I w 2 Is velocity constant? Linear motion: K= 1 / 2 mv 2 D x = v D t U=mgh Gravitational: Is acceleration constant? Elastic (spring) : U= 1 / 2 kx 2 D x = v i D t + 1 / 2 a ( D t) 2 v f = v i + a D t linear a angular x q v a w a a

Modification of the slide on “velocity” and “position” problems … Use conservation of Is mechanical energy conserved? mechanical energy (Is work by external or non-conservative forces zero?) yes no Use energy-work Use conservation of theorem mechanical energy D E tot =W ext. or non-cons. E tot i =E tot f E tot f - E tot i =W ext. or non-cons.

Only if the problem explicitly The question is about? The question is about? position velocity says “average velocity” or if the velocity is constant Wave velocity? (linear or (linear or v= D x/ D t may be used angular) v= w /k =f l angular) A free fall problem? Some free fall problems are easier to Some free fall problems are easier to A free fall problem? solve using energy conservation Collision? (the only force is weight) solve using energy conservation (the only force is weight) D x = v ix D t (two objects, there is Use conservation of Use conservation of y “before” and “after” D y = v iy D t - 1 / 2 g ( D t) 2 v fx = v ix mechanical energy y mechanical energy the “interaction”) v fx = v ix v fy = v iy - g D t E tot i =E tot f x v fy = v iy - g D t E tot i =E tot f D x = v ix D t x Any rotation involved? K i +U i =K f +U f K i +U i =K f +U f D y = v iy D t - 1 / 2 g ( D t) 2 yes no Extended object: K= 1 / 2 I w 2 Extended object: K= 1 / 2 I w 2 Point-like object: K= 1 / 2 mv 2 Is velocity constant? Use conservation of Use conservation of Point-like object: K= 1 / 2 mv 2 U=mgh angular momentum linear momentum Gravitational: D x = v D t U=mgh Gravitational: L tot i =L tot f P tot i =P tot f Elastic (spring) : U= 1 / 2 kx 2 Is acceleration constant? Elastic (spring) : U= 1 / 2 kx 2 Extended object: L=I w p=mv Does the text say D x = v i D t + 1 / 2 a ( D t) 2 “perfectly” inelastic Point-like object: v f = v i + a D t L=  r mv sin q Does the text or the objects stick linear a angular x q say “elastic” ? to each other ? or  r ? mv no v a w In addition, yes yes a a v 1f =v 2f use K i =K f Physics 211 Sound Waves 29 Physics 211 Sound Waves 28

Only if the problem explicitly The question is about? velocity Guide how to identify type of the problem says “average velocity” or if the velocity is constant Wave velocity? (linear or v= D x/ D t may be used v= w /k =f l angular) conditions The question is about? acceleration force for system at rest Some free fall problems are easier to A free fall problem? (linear or Collision? solve using energy conservation angular) a x =0 Only if the problem explicitly (the only force is weight) (two objects, there is Use conservation of says “average acceleration” a y =0 y “before” and “after” v fx = v ix mechanical energy or if the acceleration is constant the “interaction”) a =0 v fy = v iy - g D t a= D v/ D t may be used E tot i =E tot f x D x = v ix D t Any rotation involved? The problem is for application of Newton’s 2 nd Law: K i +U i =K f +U f D y = v iy D t - 1 / 2 g ( D t) 2 yes no Extended object: K= 1 / 2 I w 2 Use conservation of Use conservation of Point-like object: K= 1 / 2 mv 2 Does/can center-of-mass Does/can any U=mgh angular momentum linear momentum Gravitational: of any object move? object rotate? I a = S i t i Circular motion? L tot i =L tot f P tot i =P tot f Elastic (spring) : U= 1 / 2 kx 2 m a x = S i F i x a x =v 2 /R Also often needed: Extended object: L=I w p=mv m a y = S i F i y Does the text say (0=) a =a/R for the x-axis “perfectly” inelastic Point-like object: Usually a y is zero t =  r F sin q pointing towards L=  r mv sin q Does the text or the objects stick for proper choice the circle center or  r ? F say “elastic” ? to each other ? or  r ? mv of coordinates no Rolling combines both In addition, yes yes for the same object v 1f =v 2f use K i =K f Physics 211 Sound Waves 27 Physics 211 Sound Waves 28

Only if the problem explicitly The question is about? velocity says “average velocity” or if the velocity is constant Wave velocity? (linear or v= D x/ D t may be used v= w /k =f l angular) Some free fall problems are easier to A free fall problem? Collision? solve using energy conservation (the only force is weight) (two objects, there is Use conservation of y “before” and “after” v fx = v ix mechanical energy the “interaction”) v fy = v iy - g D t E tot i =E tot f x D x = v ix D t Any rotation involved? K i +U i =K f +U f D y = v iy D t - 1 / 2 g ( D t) 2 yes no Extended object: K= 1 / 2 I w 2 Use conservation of Use conservation of Point-like object: K= 1 / 2 mv 2 U=mgh angular momentum linear momentum Gravitational: L tot i =L tot f P tot i =P tot f Elastic (spring) : U= 1 / 2 kx 2 Extended object: L=I w p=mv Does the text say “perfectly” inelastic Point-like object: L=  r mv sin q Does the text or the objects stick say “elastic” ? to each other ? or  r ? mv no In addition, yes yes v 1f =v 2f use K i =K f Physics 211 Sound Waves 28

Guide how to identify type of the problem conditions The question is about? acceleration force for system at rest (linear or angular) a x =0 Only if the problem explicitly says “average acceleration” a y =0 or if the acceleration is constant a =0 a= D v/ D t may be used The problem is for application of Newton’s 2 nd Law: Does/can center-of-mass Does/can any of any object move? object rotate? I a = S i t i Circular motion? m a x = S i F i x a x =v 2 /R Also often needed: m a y = S i F i y (0=) a =a/R for the x-axis Usually a y is zero t =  r F sin q pointing towards for proper choice the circle center or  r ? F of coordinates Rolling combines both for the same object Physics 211 Sound Waves 27

Only if the problem explicitly The question is about? velocity says “average velocity” or if the velocity is constant Wave velocity? (linear or v= D x/ D t may be used v= w /k =f l angular) Some free fall problems are easier to A free fall problem? Collision? solve using energy conservation (the only force is weight) (two objects, there is Use conservation of y “before” and “after” v fx = v ix mechanical energy the “interaction”) v fy = v iy - g D t E tot i =E tot f x D x = v ix D t Any rotation involved? K i +U i =K f +U f D y = v iy D t - 1 / 2 g ( D t) 2 yes no Extended object: K= 1 / 2 I w 2 Use conservation of Use conservation of Point-like object: K= 1 / 2 mv 2 U=mgh angular momentum linear momentum Gravitational: L tot i =L tot f P tot i =P tot f Elastic (spring) : U= 1 / 2 kx 2 Extended object: L=I w p=mv Does the text say “perfectly” inelastic Point-like object: L=  r mv sin q Does the text or the objects stick say “elastic” ? to each other ? or  r ? mv no In addition, yes yes v 1f =v 2f use K i =K f Physics 211 Sound Waves 28