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Mechanics Lecture 2, Slide 1 Classical Mechanics Lecture 2 Today's Concepts: a) Vectors b) Projec@le mo@on c) Reference frames Monday, September 26, 2011

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Page 1: Classical Mechanics Lecture 2 · Mechanics))Lecture)2,)Slide)18 Monkey Troubles You)are)avettrying)to)shootatranquilizer)dartinto)amonkey) hanging)from)abranch)in)adistanttree.)You)know)thatthe)monkey)is)

Mechanics    Lecture  2,  Slide  1

Classical Mechanics Lecture 2

Today's  Concepts:a)  Vectorsb)  Projec@le  mo@onc)  Reference  frames

Monday, September 26, 2011

Page 2: Classical Mechanics Lecture 2 · Mechanics))Lecture)2,)Slide)18 Monkey Troubles You)are)avettrying)to)shootatranquilizer)dartinto)amonkey) hanging)from)abranch)in)adistanttree.)You)know)thatthe)monkey)is)

Mechanics    Lecture  2,  Slide  2

Not  everyone  is  doing  the  pre-­‐lecture  

This  is  a  bad  strategy  –  you  are  losing  easy  points

Monday, September 26, 2011

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Mechanics    Lecture  2,  Slide  6

Think  of  a  vector  as  an  arrow.  (An  object  having  both  magnitude  and  direc@on)

The  object  is  the  same  no  ma/er  how  we  chose  to  describe  it

Ax

Ay

Vectors

Monday, September 26, 2011

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Mechanics    Lecture  2,  Slide  7

θ

Think  of  a  vector  as  an  arrow.  (An  object  having  both  magnitude  and  direc@on)

The  object  is  the  same  no  ma/er  how  we  chose  to  describe  it

Vectors

Monday, September 26, 2011

Page 5: Classical Mechanics Lecture 2 · Mechanics))Lecture)2,)Slide)18 Monkey Troubles You)are)avettrying)to)shootatranquilizer)dartinto)amonkey) hanging)from)abranch)in)adistanttree.)You)know)thatthe)monkey)is)

Mechanics    Lecture  2,  Slide  8

Vector Addition

Monday, September 26, 2011

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Mechanics    Lecture  2,  Slide  9

A B C D E

Vectors          and          are  shown  to  the  right.  Which  of  the  following  best  describes            +

Clicker Question

Monday, September 26, 2011

Page 7: Classical Mechanics Lecture 2 · Mechanics))Lecture)2,)Slide)18 Monkey Troubles You)are)avettrying)to)shootatranquilizer)dartinto)amonkey) hanging)from)abranch)in)adistanttree.)You)know)thatthe)monkey)is)

Mechanics    Lecture  2,  Slide  10

A B C D E

Vectors          and          are  shown  to  the  right.  Which  of  the  following  best  describes            −

Clicker Question

Monday, September 26, 2011

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Mechanics    Lecture  2,  Slide  11

A B C D E

Vectors          and          are  shown  to  the  right.  Which  of  the  following  best  describes            +

Clicker Question

Monday, September 26, 2011

Page 9: Classical Mechanics Lecture 2 · Mechanics))Lecture)2,)Slide)18 Monkey Troubles You)are)avettrying)to)shootatranquilizer)dartinto)amonkey) hanging)from)abranch)in)adistanttree.)You)know)thatthe)monkey)is)

Mechanics    Lecture  2,  Slide  12

A  vector  can  be  defined  in  2  or  3  (or  even  more)  dimensions:

Vectors in 3D

Monday, September 26, 2011

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Mechanics    Lecture  2,  Slide  13

Kinematics in 3D

Monday, September 26, 2011

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Mechanics    Lecture  2,  Slide  14

A)  The  launched  marble  hits  first.

B)  The  dropped  marble  hits  first.

C)  They  both  hit  at  the  same  @me.

DEMO

Checkpoint 1

A  physics  demo  launches  one  marble  horizontally  while  at  the  same  instant  dropping  a  second  marble  straight  down.  Which  one  hits  the  ground  first?  

Monday, September 26, 2011

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Mechanics    Lecture  2,  Slide  15

Horizontal Vertical Boring

Projectile Motion

Monday, September 26, 2011

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Mechanics    Lecture  2,  Slide  16

A  flatbed  railroad  car  is  moving  along  a  track  at    constant  velocity.    A  passenger  at  the  center  of  the  car  throws  a  ball  straight  up.    Neglec@ng  air  resistance,  where  will  the  ball  land?

A)  Forward  of  the  center  of  the  car

B)  At  the  center  of  the  car

C)  Backward  of  the  center  of  the  car

correct

Demo  -­‐  train

Ball  and  car  start  with  same  x  posi@on  and  x  velocity,  Since  a = 0  they  always  have  same  x  posi@on.

Train Demo Clicker Question

vtrain car

Monday, September 26, 2011

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Mechanics    Lecture  2,  Slide  17

Time  spend  in  the  air  depends  on  the  maximum  height

Maximum  height  depends  on  the  ini@al  ver@cal  velocity

vtrain car

Monday, September 26, 2011

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Mechanics    Lecture  2,  Slide  18

Monkey Troubles

You  are  a  vet  trying  to  shoot  a  tranquilizer  dart  into  a  monkey  hanging  from  a  branch  in  a  distant  tree.  You  know  that  the  monkey  is  very  nervous,  and  will  let  go  of  the  branch  and  start  to  fall  as  soon  as  your  gun  goes  off.  In  order  to  hit  the  monkey  with  the  dart,  where  should  you  point  the  gun  before  shoo@ng?

A)    Right  at  the  monkeyB)    Below  the  monkey

C)    Above  the  monkey

Monday, September 26, 2011

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Mechanics    Lecture  2,  Slide  19

Monkey x = xo

Dart

x = vo t

Shooting the Monkey…

Monday, September 26, 2011

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Mechanics    Lecture  2,  Slide  20

Shooting the Monkey…

y = voy t − 1/2 g t 2

S@ll  works  even  if  you  shoot  upwards! y = yo − 1/2 g t 2

Dart  hits  themonkey  

Monday, September 26, 2011

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Mechanics    Lecture  2,  Slide  21

Projectile Motion & Frames of Reference

Monday, September 26, 2011

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Mechanics    Lecture  2,  Slide  22

Enemy  1Destroyer Enemy  2

A)  Enemy  1

B)  Enemy  2

C)  They  are  both  hit  at  the  same  @me

55%  of  you  got  this  one  right…lets  try  again

Checkpoint 2A  destroyer  simultaneously  fires  two  shells  with  the  same  ini@al  speed  at  

two  different  enemy  ships.  The  shells  follow  the  trajectories  shown.  Which  ship  gets  hit  first.

Monday, September 26, 2011

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Mechanics    Lecture  2,  Slide  24

Enemy  1Destroyer

Checkpoint 3A  destroyer  fires  two  shells  with  different  ini@al  speeds  at  two  different  

enemy  ships.  The  shells  follow  the  trajectories  shown.  Which  enemy  ship  gets  hit  first?

Enemy  2

A) Enemy 1B) Enemy 2C) They are both hit at the same time

62%  of  you  got  this  one  right…lets  try  again

Monday, September 26, 2011

Page 21: Classical Mechanics Lecture 2 · Mechanics))Lecture)2,)Slide)18 Monkey Troubles You)are)avettrying)to)shootatranquilizer)dartinto)amonkey) hanging)from)abranch)in)adistanttree.)You)know)thatthe)monkey)is)

Mechanics    Lecture  2,  Slide  26

Field Goal ExampleA  field  goal  kicker  can  kick  the  ball  30  m/s  at  an  angle  of  30  degrees  w.r.t.  the  ground.    If  the  crossbar  of  the  goal  post  is  3m  off  the  ground,  from  how  far  away  can  he  kick  a  field  goal?

y-direction

voy = vo sin(30o) = 15 m/s

y = yo + voyt + ½ at 2

3 m = 0 m + (15 m/s) t – ½ (9.8 m/s2) t 2

t = 2.8 s or t = 0.22 s.

x-direction

vox = vo cos(30o) = 26 m/s

D = xo + vox t + ½ at 2

= 0 m + (26 m/s)(2.8 s) + 0 m/s2 (2.8 s )2

= 72.8 m

D

3 m

y

x

Video of 70 yard Field Goal

Monday, September 26, 2011

http://www.youtube.com/watch?v=VvT9wvWHFM8
http://www.youtube.com/watch?v=VvT9wvWHFM8

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