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© 2005 Pearson Prentice Hall This work is protected by United States copyright laws and is provided solely for the use of instructors in teaching their courses and assessing student learning. Dissemination or sale of any part of this work (including on the World Wide Web) will destroy the integrity of the work and is not permitted. The work and materials from it  should never be made available to students except by instructors using the accompanying text in their classes. All recipients of this work are expected to abide by these restrictions and to honor the intended pedagogical purposes and the needs of other instructors who rely on these materials. ConcepTest   PowerPoints Chapter 6 Physics: Principles with Applications, 6 th  edition Giancoli
ConcepTest 6.1   To Work or Not to Work Is it possible to do work on an object that remains at rest?   1)  yes 2)  no
ConcepTest 6.1   To Work or Not to Work Is it possible to do work on an object that remains at rest?   1)  yes 2)  no Work requires that a  force acts over a distance .  If an object does not move at all, there is  no displacement , and therefore  no work done .
ConcepTest 6.2a   Friction and Work I ,[object Object],1)   friction does no work at all  2)  friction does negative work 3)  friction does positive work
ConcepTest 6.2a   Friction and Work I ,[object Object],Friction acts in the  opposite  direction to the displacement, so the work is  negative .  Or using the definition of work:  W   =  F d cos     since     = 180 o ,  then   W <  0. 1)   friction does no work at all  2)  friction does negative work 3)  friction does positive work f   N   mg   displacement Pull
ConcepTest 6.2b   Friction and Work II Can friction ever do positive work?   1)  yes 2)  no
ConcepTest 6.2b   Friction and Work II Can friction ever do positive work?   1)  yes 2)  no Consider the case of a box on the back of a pickup truck.  If the box  moves along with the truck , then it is actually the  force of friction that is making the box move .
ConcepTest 6.2c   Play Ball! In a baseball game, the catcher stops a 90-mph pitch.  What can you say about the work done by the catcher on the ball?   1)  catcher has done positive work 2)  catcher has done negative work 3)  catcher has done zero work
ConcepTest 6.2c   Play Ball! In a baseball game, the catcher stops a 90-mph pitch.  What can you say about the work done by the catcher on the ball?   1)  catcher has done positive work 2)  catcher has done negative work 3)  catcher has done zero work The force exerted by the catcher is  opposite  in direction to the displacement of the ball, so the work is negative .  Or using the definition of work ( W  =  F d cos    ), since     =  180 o ,  then   W <  0 .  Note that because the work done on the ball is negative, its speed decreases. Follow-up:   What about the work done by the ball on the catcher?
ConcepTest 6.2d   Tension and Work ,[object Object],1)   tension does no work at all  2)  tension does negative work 3)  tension does positive work
ConcepTest 6.2d   Tension and Work ,[object Object],1)   tension does no work at all  2)  tension does negative work 3)  tension does positive work No work is done because the force acts in a  perpendicular  direction to the displacement.  Or using the definition of work:  W  =  F d cos    since     =  90 o ,  then   W =  0. Follow-up:   Is there a force in the direction of the velocity? v  T
ConcepTest 6.3   Force and Work ,[object Object],1)  one force 2)  two forces 3)  three forces 4)  four forces 5)  no forces are doing work
ConcepTest 6.3   Force and Work ,[object Object],Any force not perpendicular to the motion will do work: N  does  no work T  does  positive  work f  does  negative work mg  does  negative work 1)  one force 2)  two forces 3)  three forces 4)  four forces 5)  no forces are doing work N   f   T   mg   displacement
ConcepTest 6.4   Lifting a Book You lift a book with your hand in such a way that it moves up at constant speed.  While it is moving, what is the total work done on the book? 1)  mg      r 2)  F HAND       r 3)  (F HAND  + mg)      r 4)  zero 5) none of the above mg  r F HAND v = const a = 0
ConcepTest 6.4   Lifting a Book You lift a book with your hand in such a way that it moves up at constant speed.  While it is moving, what is the total work done on the book? The  total work is zero  since the  net force  acting on the book is  zero .  The work done by the hand is positive, while the work done by gravity is negative.  The sum of the two is zero.  Note that the kinetic energy of the book does not change, either! 1)  mg      r 2)  F HAND       r 3)  (F HAND  + mg)      r 4)  zero 5) none of the above Follow-up:   What would happen if  F HAND  was greater than  mg ? mg  r F HAND v = const a = 0
ConcepTest 6.5a   Kinetic Energy I By what factor does the kinetic energy of a car change when its speed is tripled?   1)  no change at all  2)  factor of 3 3)  factor of 6 4)  factor of 9 5)  factor of 12
ConcepTest 6.5a   Kinetic Energy I By what factor does the kinetic energy of a car change when its speed is tripled?   1)  no change at all  2)  factor of 3 3)  factor of 6 4)  factor of 9 5)  factor of 12 Since the kinetic energy is  1/2  mv 2 , if the  speed increases by a factor of 3 , then the  KE will increase by a factor of 9 . Follow-up:   How would you achieve a KE increase of a factor of 2?
ConcepTest 6.5b   Kinetic Energy II Car #1 has twice the mass of car #2, but they both have the same kinetic energy.  How do their speeds compare?   1)  2 v 1   =  v 2 2)    2 v 1   =  v 2 3)  4 v 1   =  v 2 4)  v 1   =  v 2 5)  8 v 1   =  v 2
ConcepTest 6.5b   Kinetic Energy II Car #1 has twice the mass of car #2, but they both have the same kinetic energy.  How do their speeds compare?   Since the kinetic energy is  1/2  mv 2 , and the mass of car #1 is greater, then car #2 must be moving faster .  If the ratio of m 1 /m 2  is 2, then the ratio of v 2  values must also be 2 .  This means that the  ratio of v 2 /v 1  must be the square root of 2 .   1)  2 v 1   =  v 2 2)    2 v 1   =  v 2 3)  4 v 1   =  v 2 4)  v 1   =  v 2 5)  8 v 1   =  v 2
ConcepTest 6.6a   Free Fall I 1)   quarter as much 2)  half as much 3)  the same 4)  twice as much 5)  four times as much   Two stones, one twice the mass of the other, are dropped from a cliff.  Just before hitting the ground, what is the kinetic energy of the heavy stone compared to the light one?
ConcepTest 6.6a   Free Fall I Consider the work done by gravity to make the stone fall distance  d :  KE  =  W net   =  F d cos   KE  =  mg d Thus, the stone with the  greater mass  has the  greater KE , which is  twice  as big for the heavy stone. 1)   quarter as much 2)  half as much 3)  the same 4)  twice as much 5)  four times as much   Two stones, one twice the mass of the other, are dropped from a cliff.  Just before hitting the ground, what is the kinetic energy of the heavy stone compared to the light one?   Follow-up:   How do the initial values of gravitational PE compare?
ConcepTest 6.6b   Free Fall II In the previous question, just before hitting the ground, what is the final speed of the heavy stone compared to the light one?   1)  quarter as much  2)  half as much 3)  the same 4)  twice as much 5)  four times as much
ConcepTest 6.6b   Free Fall II In the previous question, just before hitting the ground, what is the final speed of the heavy stone compared to the light one?   1)  quarter as much  2)  half as much 3)  the same 4)  twice as much 5)  four times as much All freely falling objects fall at the same rate, which is  g .  Since the  acceleration is the same for both , and the  distance is the same , then the  final speeds will be the same  for both stones.
ConcepTest 6.7   Work and KE A child on a skateboard is moving at a speed of 2 m/s.  After a force acts on the child, her speed is 3 m/s.  What can you say about the work done by the external force on the child?   1)  positive work was done  2)  negative work was done  3)  zero work was done
ConcepTest 6.7   Work and KE A child on a skateboard is moving at a speed of 2 m/s.  After a force acts on the child, her speed is 3 m/s.  What can you say about the work done by the external force on the child?   1)  positive work was done  2)  negative work was done  3)  zero work was done   The kinetic energy of the child increased because her speed increased .  This  increase in KE  was the result of  positive work being done .  Or, from the definition of work, since  W  =   KE = KE f  – KE i  and we know that  KE f  > KE i  in this case, then the  work W must be positive . Follow-up:   What does it mean for negative work to be done on the child?
ConcepTest 6.8a   Slowing Down ,[object Object],1)   20 m 2)  30 m 3)  40 m 4)  60 m  5)  80 m
ConcepTest 6.8a   Slowing Down ,[object Object],F d   = W net  =   KE  =  0 –  1/2  mv 2 thus:  |F| d  =  1/2 mv 2   Therefore, if the speed  doubles ,  the stopping distance gets  four times larger . 1)   20 m 2)  30 m 3)  40 m 4)  60 m  5)  80 m
ConcepTest 6.8b   Speeding Up I ,[object Object],1)   0     30 mph 2)  30    60 mph 3)  both the same
ConcepTest 6.8b   Speeding Up I ,[object Object],The change in KE  ( 1/2 mv 2  )  involves the  velocity   squared . So in the first case, we have:  1/2 m (30 2  - 0 2 )  = 1/2 m (900) In the second case, we have:  1/2 m (60 2  - 30 2 )  = 1/2 m (2700) Thus, the  bigger energy change  occurs in the  second case . 1)   0     30 mph 2)  30    60 mph 3)  both the same Follow-up:   How much energy is required to stop the 60-mph car?
ConcepTest 6.8c   Speeding Up II The work  W 0  accelerates a car from 0 to 50 km/hr.  How much work is needed to accelerate the car from 50 km/hr to 150 km/hr?   1)  2  W 0 2)  3  W 0   3)  6  W 0 4)  8  W 0 5)  9  W 0
ConcepTest 6.8c   Speeding Up II The work  W 0  accelerates a car from 0 to 50 km/hr.  How much work is needed to accelerate the car from 50 km/hr to 150 km/hr?   1)  2  W 0 2)  3  W 0   3)  6  W 0 4)  8  W 0 5)  9  W 0 Let’s call the two speeds  v  and 3 v , for simplicity.  We know that the work is given by:  W  =   KE = KE f  – KE i   Case #1:  W 0  =  1/2  m  ( v 2   –   0 2 )  =  1/2 m  ( v 2 ) Case #2:  W  =  1/2  m  ( 3 v ) 2   –   v 2 )  =  1/2 m  ( 9 v 2   –   v 2 )  =  1/2  m  ( 8 v 2 )  =  8  W 0 Follow-up:   How much work is required to stop the 150-km/hr car?
ConcepTest 6.9a   Work and Energy I 1)   m 1   2)  m 2   3)  they will go the same distance   Two blocks of mass  m 1  and  m 2  ( m 1  >  m 2 ) slide on a frictionless floor and have the  same kinetic energy  when they hit a long rough stretch (   > 0 ), which slows them down to a stop.  Which one goes farther? m 1 m 2
ConcepTest 6.9a   Work and Energy I With the  same   KE , both blocks must have the  same work  done to them by friction.  The friction  force  is  less  for  m 2   so stopping  distance  must be  greater . 1)   m 1   2)  m 2   3)  they will go the same distance   Two blocks of mass  m 1  and  m 2  ( m 1  >  m 2 ) slide on a frictionless floor and have the  same kinetic energy  when they hit a long rough stretch (   > 0 ), which slows them down to a stop.  Which one goes farther? Follow-up:   Which block has the greater magnitude of acceleration? m 1 m 2
ConcepTest 6.9b   Work and Energy II A golfer making a putt gives the ball an initial velocity of  v 0 , but he has badly misjudged the putt, and the ball only travels one-quarter of the distance to the hole.  If the resistance force due to the grass is constant, what speed should he have given the ball (from its original position) in order to make it into the hole?   1)  2  v 0 2)  3  v 0 3)  4  v 0 4)  8  v 0 5)  16  v 0
ConcepTest 6.9b   Work and Energy II A golfer making a putt gives the ball an initial velocity of  v 0 , but he has badly misjudged the putt, and the ball only travels one-quarter of the distance to the hole.  If the resistance force due to the grass is constant, what speed should he have given the ball (from its original position) in order to make it into the hole?   1)  2  v 0 2)  3  v 0 3)  4  v 0 4)  8  v 0 5)  16  v 0 In traveling  4 times the distance , the resistive force will do  4 times the work .  Thus, the ball’s  initial KE must be 4 times greater  in order to just reach the hole  —  this requires an  increase in the initial speed by a factor of 2 , since  KE = 1/2  mv 2 .
ConcepTest 6.10   Sign of the Energy I Is it possible for the kinetic energy of an object to be negative? 1)  yes 2)  no
ConcepTest 6.10   Sign of the Energy I Is it possible for the kinetic energy of an object to be negative? 1)  yes 2)  no The  kinetic energy is  1/2 mv 2 .  The  mass  and the  velocity squared  will always be  positive , so  KE must always be positive .
ConcepTest 6.11   Sign of the Energy II Is it possible for the gravitational potential energy of an object to be negative? 1)  yes 2)  no
ConcepTest 6.11   Sign of the Energy II Is it possible for the gravitational potential energy of an object to be negative? 1)  yes 2)  no Gravitational PE is  mgh , where  height  h  is measured relative to some arbitrary reference level where PE = 0 .  For example, a b ook on a table has positive PE if the zero reference level is chosen to be the floor.  However, if the  ceiling is the zero level , then the  book has negative PE on the table .  It is only  differences  (or changes) in PE that have any physical meaning.
ConcepTest 6.12   KE and PE You and your friend both solve a problem involving a skier going down a slope, starting from rest. The two of you have chosen  different levels for  y  = 0  in this problem.  Which of the following quantities will you and your friend agree on? 1)  only B 2)  only C 3)  A, B, and C 4)  only A and C 5)  only B and C A) skier’s PE  B) skier’s change in PE  C) skier’s final KE
ConcepTest 6.12   KE and PE You and your friend both solve a problem involving a skier going down a slope, starting from rest. The two of you have chosen  different levels for  y  = 0  in this problem.  Which of the following quantities will you and your friend agree on? 1)  only B 2)  only C 3)  A, B, and C 4)  only A and C 5)  only B and C The  gravitational PE depends upon the reference level , but the  difference    PE does not !  The work done by gravity must be the same in the two solutions, so   PE and   KE should be the same . A) skier’s PE  B) skier’s change in PE  C) skier’s final KE Follow-up:   Does anything change  physically  by the choice of  y  = 0?
ConcepTest 6.13   Up the Hill ,[object Object],1)   the same 2)  twice as much 3)  four times as much 4)  half as much 5)  you gain no PE in either case
ConcepTest 6.13   Up the Hill ,[object Object],Since your vertical position (height) changes by the same amount in each case, the gain in potential energy is the same.  1)   the same 2)  twice as much 3)  four times as much 4)  half as much 5)  you gain no PE in either case Follow-up:   How much more work do you do in taking the steeper path? Follow-up:   Which path would you rather take?  Why?
ConcepTest 6.14   Elastic Potential Energy How does the work required to stretch a spring 2 cm compare with the work required to stretch it 1 cm? 1)  same amount of work 2)  twice the work 3)  4 times the work 4)  8 times the work
ConcepTest 6.14   Elastic Potential Energy How does the work required to stretch a spring 2 cm compare with the work required to stretch it 1 cm? 1)  same amount of work 2)  twice the work 3)  4 times the work 4)  8 times the work The elastic potential energy is  1/2  kx 2 .   So in the second case, the  elastic PE is 4 times greater  than in the first case.  Thus, the  work required to stretch the spring is also 4 times greater .
ConcepTest 6.15   Springs and Gravity A mass attached to a vertical spring causes the spring to stretch and the mass to move downwards.  What can you say about the spring’s potential energy (PE s ) and the gravitational potential energy (PE g ) of the mass? 1)  both PE s  and PE g  decrease  2)  PE s  increases and PE g  decreases  3)  both PE s  and PE g  increase  4)  PE s  decreases and PE g  increases  5)  PE s  increases and PE g  is constant
ConcepTest 6.15   Springs and Gravity A mass attached to a vertical spring causes the spring to stretch and the mass to move downwards.  What can you say about the spring’s potential energy (PE s ) and the gravitational potential energy (PE g ) of the mass? 1)  both PE s  and PE g  decrease  2)  PE s  increases and PE g  decreases  3)  both PE s  and PE g  increase  4)  PE s  decreases and PE g  increases  5)  PE s  increases and PE g  is constant   The spring is  stretched , so its  elastic PE increases , since  PE s  =  1/2  kx 2 .  The mass moves down to a  lower position , so its  gravitational PE decreases , since  PE g  =  mgh .
ConcepTest 6.16   Down the Hill ,[object Object],1 4)  same speed for all balls 2 3
ConcepTest 6.16   Down the Hill ,[object Object],All of the balls have the  same initial gravitational PE , since they are all at the  same height   (PE =  mgh ).  Thus, when they get to the bottom, they all have the  same final KE , and hence the  same speed  (KE = 1/2  mv 2 ). 1 4)  same speed for all balls 2 3 Follow-up:   Which ball takes longer to get down the ramp?
ConcepTest 6.17a   Runaway Truck ,[object Object],1)   half the height 2) the same height 3)    2  times the height 4)  twice the height 5)  four times the height
ConcepTest 6.17a   Runaway Truck ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],1)   half the height 2) the same height 3)    2  times the height 4)  twice the height 5)  four times the height
ConcepTest 6.17b   Runaway Box ,[object Object],x 1)   half as much 2) the same amount 3)    2  times as much 4)  twice as much 5)  four times as much
ConcepTest 6.17b   Runaway Box ,[object Object],Use  energy conservation : initial energy:  E i   =  KE   =  1/2   mv 2 final energy:  E f   = PE s  =  1/2   kx 2 Conservation of Energy: E i   = 1/2   mv 2   = E f   = 1/2   kx 2   therefore:  mv 2   = kx 2 So if  v  doubles,  x  doubles! x 1)   half as much 2) the same amount 3)    2  times as much 4)  twice as much 5)  four times as much
ConcepTest 6.18a   Water Slide I ,[object Object],1)   Paul 2)  Kathleen 3)  both the same
ConcepTest 6.18a   Water Slide I ,[object Object],1)   Paul 2)  Kathleen 3)  both the same Conservation of Energy:   E i   =  mgH   =  E f   = 1/2   mv 2   therefore:  gH   = 1/2   v 2 Since they both start from the  same height , they have the  same velocity  at the bottom.
ConcepTest 6.18b   Water Slide II ,[object Object],1)   Paul 2)  Kathleen 3)  both the same
ConcepTest 6.18b   Water Slide II ,[object Object],Even though they both have the same  final velocity ,  Kathleen is at a lower height than Paul for most of her ride .  Thus she always has a  larger velocity  during her ride and therefore arrives earlier! 1)   Paul 2)  Kathleen 3)  both the same
ConcepTest 6.19   Cart on a Hill ,[object Object],1)   4 m/s 2)  5 m/s 3)  6 m/s 4)  7 m/s 5)  25 m/s
ConcepTest 6.19   Cart on a Hill ,[object Object],[object Object],[object Object],1)   4 m/s 2)  5 m/s 3)  6 m/s 4)  7 m/s 5)  25 m/s When starting from 3 m/s, the final KE is: KE f   =  KE i   +   KE =  1/2 m(3) 2   +  1/2  m(4) 2 =  1/2 m(25)   =  1/2 m(5) 2 Speed is not the same as kinetic energy
ConcepTest 6.20a   Falling Leaves You see a leaf falling to the ground with  constant speed .  When you first notice it, the leaf has initial total energy PE i  + KE i .  You watch the leaf until just before it hits the ground, at which point it has final total energy PE f  + KE f .  How do these total energies compare?  1)  PE i  + KE i   >  PE f  + KE f 2)  PE i  + KE i   =  PE f  + KE f 3)  PE i  + KE i   <  PE f  + KE f 4)  impossible to tell from    the information provided
ConcepTest 6.20a   Falling Leaves You see a leaf falling to the ground with  constant speed .  When you first notice it, the leaf has initial total energy PE i  + KE i .  You watch the leaf until just before it hits the ground, at which point it has final total energy PE f  + KE f .  How do these total energies compare?  1)  PE i  + KE i   >  PE f  + KE f 2)  PE i  + KE i   =  PE f  + KE f 3)  PE i  + KE i   <  PE f  + KE f 4)  impossible to tell from    the information provided As the leaf falls,  air resistance exerts a force on it opposite to its direction of motion .  This  force does negative work , which prevents the leaf from accelerating.  This frictional force is a non-conservative force, so the  leaf loses energy as it falls , and its  final total energy is less than its initial total energy . Follow-up:   What happens to leaf’s KE as it falls?  What is net work done?
ConcepTest 6.20b   Falling Balls ,[object Object],1)   smaller 2)  the same 3)  greater
ConcepTest 6.20b   Falling Balls ,[object Object],Due to air friction, the ball is  continuously losing mechanical energy .  Therefore it has  less KE  (and consequently a  lower speed ) on the way down.  This means it will take more time on the way down  !! 1)   smaller 2)  the same 3)  greater   Follow-up:   How does the force of air resistance compare to gravity when the ball reaches terminal velocity?
ConcepTest 6.21a   Time for Work I ,[object Object],1)   Mike 2)  Joe 3)  both did the same work
ConcepTest 6.21a   Time for Work I ,[object Object],Both exerted the  same force  over the  same displacement .  Therefore, both did the  same amount of work .  Time does not matter for determining the work done .   1)   Mike 2)  Joe 3)  both did the same work
ConcepTest 6.21b   Time for Work II Mike  performed  5 J  of work in  10 secs .  Joe  did  3 J  of work in  5 secs .  Who produced the greater power? 1)  Mike produced more power  2)  Joe produced more power  3)  both produced the same  amount of power
ConcepTest 6.21b   Time for Work II Mike  performed  5 J  of work in  10 secs .  Joe  did  3 J  of work in  5 secs .  Who produced the greater power? 1)  Mike produced more power  2)  Joe produced more power  3)  both produced the same  amount of power Since power  =  work / time, we see that  Mike produced 0.5 W  and  Joe produced 0.6 W  of power.  Thus, even though Mike did more work, he required twice the time to do the work, and therefore his power output was lower.
ConcepTest 6.21c   Power Engine #1 produces twice the power of engine #2.  Can we conclude that engine #1 does twice as much work as engine #2? 1)  yes  2)  no
ConcepTest 6.21c   Power Engine #1 produces twice the power of engine #2.  Can we conclude that engine #1 does twice as much work as engine #2? 1)  yes  2)  no   No!!  We cannot conclude anything about how much work each engine does.   Given the power output, the  work will depend upon how much time is used .  For example, engine #1 may do the same amount of work as engine #2, but in half the time.
ConcepTest 6.22a   Electric Bill ,[object Object],1)   energy 2)  power 3)  current 4)  voltage 5)  none of the above
ConcepTest 6.22a   Electric Bill ,[object Object],(1)   energy (2)  power (3)  current (4)  voltage (5)  none of the above   We have defined:  Power   =  energy  / time   So we see that:  Energy   =  power  x time  This means that the unit of  power  x time (watt-hour) is a unit of  energy  !!
ConcepTest 6.22b   Energy Consumption ,[object Object],1)   hair dryer 2)  microwave oven 3)  both contribute equally 4)  depends upon what you cook in the oven 5)  depends upon how long each one is on   1500 W 600 W
ConcepTest 6.22b   Energy Consumption ,[object Object],We already saw that what you actually pay for is  energy .  To find the energy consumption of an appliance, you must know more than just the power rating  —  you have to know how long it was running . (1)   hair dryer (2)  microwave oven (3)  both contribute equally (4)  depends upon what you cook in the oven (5)  depends upon how long each one is on   1500 W 600 W

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P P A6 Concep Tests Ch 06

  • 1. © 2005 Pearson Prentice Hall This work is protected by United States copyright laws and is provided solely for the use of instructors in teaching their courses and assessing student learning. Dissemination or sale of any part of this work (including on the World Wide Web) will destroy the integrity of the work and is not permitted. The work and materials from it should never be made available to students except by instructors using the accompanying text in their classes. All recipients of this work are expected to abide by these restrictions and to honor the intended pedagogical purposes and the needs of other instructors who rely on these materials. ConcepTest PowerPoints Chapter 6 Physics: Principles with Applications, 6 th edition Giancoli
  • 2. ConcepTest 6.1 To Work or Not to Work Is it possible to do work on an object that remains at rest? 1) yes 2) no
  • 3. ConcepTest 6.1 To Work or Not to Work Is it possible to do work on an object that remains at rest? 1) yes 2) no Work requires that a force acts over a distance . If an object does not move at all, there is no displacement , and therefore no work done .
  • 4.
  • 5.
  • 6. ConcepTest 6.2b Friction and Work II Can friction ever do positive work? 1) yes 2) no
  • 7. ConcepTest 6.2b Friction and Work II Can friction ever do positive work? 1) yes 2) no Consider the case of a box on the back of a pickup truck. If the box moves along with the truck , then it is actually the force of friction that is making the box move .
  • 8. ConcepTest 6.2c Play Ball! In a baseball game, the catcher stops a 90-mph pitch. What can you say about the work done by the catcher on the ball? 1) catcher has done positive work 2) catcher has done negative work 3) catcher has done zero work
  • 9. ConcepTest 6.2c Play Ball! In a baseball game, the catcher stops a 90-mph pitch. What can you say about the work done by the catcher on the ball? 1) catcher has done positive work 2) catcher has done negative work 3) catcher has done zero work The force exerted by the catcher is opposite in direction to the displacement of the ball, so the work is negative . Or using the definition of work ( W = F d cos  ), since  = 180 o , then W < 0 . Note that because the work done on the ball is negative, its speed decreases. Follow-up: What about the work done by the ball on the catcher?
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  • 14. ConcepTest 6.4 Lifting a Book You lift a book with your hand in such a way that it moves up at constant speed. While it is moving, what is the total work done on the book? 1) mg   r 2) F HAND   r 3) (F HAND + mg)   r 4) zero 5) none of the above mg  r F HAND v = const a = 0
  • 15. ConcepTest 6.4 Lifting a Book You lift a book with your hand in such a way that it moves up at constant speed. While it is moving, what is the total work done on the book? The total work is zero since the net force acting on the book is zero . The work done by the hand is positive, while the work done by gravity is negative. The sum of the two is zero. Note that the kinetic energy of the book does not change, either! 1) mg   r 2) F HAND   r 3) (F HAND + mg)   r 4) zero 5) none of the above Follow-up: What would happen if F HAND was greater than mg ? mg  r F HAND v = const a = 0
  • 16. ConcepTest 6.5a Kinetic Energy I By what factor does the kinetic energy of a car change when its speed is tripled? 1) no change at all 2) factor of 3 3) factor of 6 4) factor of 9 5) factor of 12
  • 17. ConcepTest 6.5a Kinetic Energy I By what factor does the kinetic energy of a car change when its speed is tripled? 1) no change at all 2) factor of 3 3) factor of 6 4) factor of 9 5) factor of 12 Since the kinetic energy is 1/2 mv 2 , if the speed increases by a factor of 3 , then the KE will increase by a factor of 9 . Follow-up: How would you achieve a KE increase of a factor of 2?
  • 18. ConcepTest 6.5b Kinetic Energy II Car #1 has twice the mass of car #2, but they both have the same kinetic energy. How do their speeds compare? 1) 2 v 1 = v 2 2)  2 v 1 = v 2 3) 4 v 1 = v 2 4) v 1 = v 2 5) 8 v 1 = v 2
  • 19. ConcepTest 6.5b Kinetic Energy II Car #1 has twice the mass of car #2, but they both have the same kinetic energy. How do their speeds compare? Since the kinetic energy is 1/2 mv 2 , and the mass of car #1 is greater, then car #2 must be moving faster . If the ratio of m 1 /m 2 is 2, then the ratio of v 2 values must also be 2 . This means that the ratio of v 2 /v 1 must be the square root of 2 . 1) 2 v 1 = v 2 2)  2 v 1 = v 2 3) 4 v 1 = v 2 4) v 1 = v 2 5) 8 v 1 = v 2
  • 20. ConcepTest 6.6a Free Fall I 1) quarter as much 2) half as much 3) the same 4) twice as much 5) four times as much Two stones, one twice the mass of the other, are dropped from a cliff. Just before hitting the ground, what is the kinetic energy of the heavy stone compared to the light one?
  • 21. ConcepTest 6.6a Free Fall I Consider the work done by gravity to make the stone fall distance d :  KE = W net = F d cos   KE = mg d Thus, the stone with the greater mass has the greater KE , which is twice as big for the heavy stone. 1) quarter as much 2) half as much 3) the same 4) twice as much 5) four times as much Two stones, one twice the mass of the other, are dropped from a cliff. Just before hitting the ground, what is the kinetic energy of the heavy stone compared to the light one? Follow-up: How do the initial values of gravitational PE compare?
  • 22. ConcepTest 6.6b Free Fall II In the previous question, just before hitting the ground, what is the final speed of the heavy stone compared to the light one? 1) quarter as much 2) half as much 3) the same 4) twice as much 5) four times as much
  • 23. ConcepTest 6.6b Free Fall II In the previous question, just before hitting the ground, what is the final speed of the heavy stone compared to the light one? 1) quarter as much 2) half as much 3) the same 4) twice as much 5) four times as much All freely falling objects fall at the same rate, which is g . Since the acceleration is the same for both , and the distance is the same , then the final speeds will be the same for both stones.
  • 24. ConcepTest 6.7 Work and KE A child on a skateboard is moving at a speed of 2 m/s. After a force acts on the child, her speed is 3 m/s. What can you say about the work done by the external force on the child? 1) positive work was done 2) negative work was done 3) zero work was done
  • 25. ConcepTest 6.7 Work and KE A child on a skateboard is moving at a speed of 2 m/s. After a force acts on the child, her speed is 3 m/s. What can you say about the work done by the external force on the child? 1) positive work was done 2) negative work was done 3) zero work was done The kinetic energy of the child increased because her speed increased . This increase in KE was the result of positive work being done . Or, from the definition of work, since W =  KE = KE f – KE i and we know that KE f > KE i in this case, then the work W must be positive . Follow-up: What does it mean for negative work to be done on the child?
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  • 30. ConcepTest 6.8c Speeding Up II The work W 0 accelerates a car from 0 to 50 km/hr. How much work is needed to accelerate the car from 50 km/hr to 150 km/hr? 1) 2 W 0 2) 3 W 0 3) 6 W 0 4) 8 W 0 5) 9 W 0
  • 31. ConcepTest 6.8c Speeding Up II The work W 0 accelerates a car from 0 to 50 km/hr. How much work is needed to accelerate the car from 50 km/hr to 150 km/hr? 1) 2 W 0 2) 3 W 0 3) 6 W 0 4) 8 W 0 5) 9 W 0 Let’s call the two speeds v and 3 v , for simplicity. We know that the work is given by: W =  KE = KE f – KE i Case #1: W 0 = 1/2 m ( v 2 – 0 2 ) = 1/2 m ( v 2 ) Case #2: W = 1/2 m ( 3 v ) 2 – v 2 ) = 1/2 m ( 9 v 2 – v 2 ) = 1/2 m ( 8 v 2 ) = 8 W 0 Follow-up: How much work is required to stop the 150-km/hr car?
  • 32. ConcepTest 6.9a Work and Energy I 1) m 1 2) m 2 3) they will go the same distance Two blocks of mass m 1 and m 2 ( m 1 > m 2 ) slide on a frictionless floor and have the same kinetic energy when they hit a long rough stretch (  > 0 ), which slows them down to a stop. Which one goes farther? m 1 m 2
  • 33. ConcepTest 6.9a Work and Energy I With the same  KE , both blocks must have the same work done to them by friction. The friction force is less for m 2 so stopping distance must be greater . 1) m 1 2) m 2 3) they will go the same distance Two blocks of mass m 1 and m 2 ( m 1 > m 2 ) slide on a frictionless floor and have the same kinetic energy when they hit a long rough stretch (  > 0 ), which slows them down to a stop. Which one goes farther? Follow-up: Which block has the greater magnitude of acceleration? m 1 m 2
  • 34. ConcepTest 6.9b Work and Energy II A golfer making a putt gives the ball an initial velocity of v 0 , but he has badly misjudged the putt, and the ball only travels one-quarter of the distance to the hole. If the resistance force due to the grass is constant, what speed should he have given the ball (from its original position) in order to make it into the hole? 1) 2 v 0 2) 3 v 0 3) 4 v 0 4) 8 v 0 5) 16 v 0
  • 35. ConcepTest 6.9b Work and Energy II A golfer making a putt gives the ball an initial velocity of v 0 , but he has badly misjudged the putt, and the ball only travels one-quarter of the distance to the hole. If the resistance force due to the grass is constant, what speed should he have given the ball (from its original position) in order to make it into the hole? 1) 2 v 0 2) 3 v 0 3) 4 v 0 4) 8 v 0 5) 16 v 0 In traveling 4 times the distance , the resistive force will do 4 times the work . Thus, the ball’s initial KE must be 4 times greater in order to just reach the hole — this requires an increase in the initial speed by a factor of 2 , since KE = 1/2 mv 2 .
  • 36. ConcepTest 6.10 Sign of the Energy I Is it possible for the kinetic energy of an object to be negative? 1) yes 2) no
  • 37. ConcepTest 6.10 Sign of the Energy I Is it possible for the kinetic energy of an object to be negative? 1) yes 2) no The kinetic energy is 1/2 mv 2 . The mass and the velocity squared will always be positive , so KE must always be positive .
  • 38. ConcepTest 6.11 Sign of the Energy II Is it possible for the gravitational potential energy of an object to be negative? 1) yes 2) no
  • 39. ConcepTest 6.11 Sign of the Energy II Is it possible for the gravitational potential energy of an object to be negative? 1) yes 2) no Gravitational PE is mgh , where height h is measured relative to some arbitrary reference level where PE = 0 . For example, a b ook on a table has positive PE if the zero reference level is chosen to be the floor. However, if the ceiling is the zero level , then the book has negative PE on the table . It is only differences (or changes) in PE that have any physical meaning.
  • 40. ConcepTest 6.12 KE and PE You and your friend both solve a problem involving a skier going down a slope, starting from rest. The two of you have chosen different levels for y = 0 in this problem. Which of the following quantities will you and your friend agree on? 1) only B 2) only C 3) A, B, and C 4) only A and C 5) only B and C A) skier’s PE B) skier’s change in PE C) skier’s final KE
  • 41. ConcepTest 6.12 KE and PE You and your friend both solve a problem involving a skier going down a slope, starting from rest. The two of you have chosen different levels for y = 0 in this problem. Which of the following quantities will you and your friend agree on? 1) only B 2) only C 3) A, B, and C 4) only A and C 5) only B and C The gravitational PE depends upon the reference level , but the difference  PE does not ! The work done by gravity must be the same in the two solutions, so  PE and  KE should be the same . A) skier’s PE B) skier’s change in PE C) skier’s final KE Follow-up: Does anything change physically by the choice of y = 0?
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  • 44. ConcepTest 6.14 Elastic Potential Energy How does the work required to stretch a spring 2 cm compare with the work required to stretch it 1 cm? 1) same amount of work 2) twice the work 3) 4 times the work 4) 8 times the work
  • 45. ConcepTest 6.14 Elastic Potential Energy How does the work required to stretch a spring 2 cm compare with the work required to stretch it 1 cm? 1) same amount of work 2) twice the work 3) 4 times the work 4) 8 times the work The elastic potential energy is 1/2 kx 2 . So in the second case, the elastic PE is 4 times greater than in the first case. Thus, the work required to stretch the spring is also 4 times greater .
  • 46. ConcepTest 6.15 Springs and Gravity A mass attached to a vertical spring causes the spring to stretch and the mass to move downwards. What can you say about the spring’s potential energy (PE s ) and the gravitational potential energy (PE g ) of the mass? 1) both PE s and PE g decrease 2) PE s increases and PE g decreases 3) both PE s and PE g increase 4) PE s decreases and PE g increases 5) PE s increases and PE g is constant
  • 47. ConcepTest 6.15 Springs and Gravity A mass attached to a vertical spring causes the spring to stretch and the mass to move downwards. What can you say about the spring’s potential energy (PE s ) and the gravitational potential energy (PE g ) of the mass? 1) both PE s and PE g decrease 2) PE s increases and PE g decreases 3) both PE s and PE g increase 4) PE s decreases and PE g increases 5) PE s increases and PE g is constant The spring is stretched , so its elastic PE increases , since PE s = 1/2 kx 2 . The mass moves down to a lower position , so its gravitational PE decreases , since PE g = mgh .
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  • 60. ConcepTest 6.20a Falling Leaves You see a leaf falling to the ground with constant speed . When you first notice it, the leaf has initial total energy PE i + KE i . You watch the leaf until just before it hits the ground, at which point it has final total energy PE f + KE f . How do these total energies compare? 1) PE i + KE i > PE f + KE f 2) PE i + KE i = PE f + KE f 3) PE i + KE i < PE f + KE f 4) impossible to tell from the information provided
  • 61. ConcepTest 6.20a Falling Leaves You see a leaf falling to the ground with constant speed . When you first notice it, the leaf has initial total energy PE i + KE i . You watch the leaf until just before it hits the ground, at which point it has final total energy PE f + KE f . How do these total energies compare? 1) PE i + KE i > PE f + KE f 2) PE i + KE i = PE f + KE f 3) PE i + KE i < PE f + KE f 4) impossible to tell from the information provided As the leaf falls, air resistance exerts a force on it opposite to its direction of motion . This force does negative work , which prevents the leaf from accelerating. This frictional force is a non-conservative force, so the leaf loses energy as it falls , and its final total energy is less than its initial total energy . Follow-up: What happens to leaf’s KE as it falls? What is net work done?
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  • 66. ConcepTest 6.21b Time for Work II Mike performed 5 J of work in 10 secs . Joe did 3 J of work in 5 secs . Who produced the greater power? 1) Mike produced more power 2) Joe produced more power 3) both produced the same amount of power
  • 67. ConcepTest 6.21b Time for Work II Mike performed 5 J of work in 10 secs . Joe did 3 J of work in 5 secs . Who produced the greater power? 1) Mike produced more power 2) Joe produced more power 3) both produced the same amount of power Since power = work / time, we see that Mike produced 0.5 W and Joe produced 0.6 W of power. Thus, even though Mike did more work, he required twice the time to do the work, and therefore his power output was lower.
  • 68. ConcepTest 6.21c Power Engine #1 produces twice the power of engine #2. Can we conclude that engine #1 does twice as much work as engine #2? 1) yes 2) no
  • 69. ConcepTest 6.21c Power Engine #1 produces twice the power of engine #2. Can we conclude that engine #1 does twice as much work as engine #2? 1) yes 2) no No!! We cannot conclude anything about how much work each engine does. Given the power output, the work will depend upon how much time is used . For example, engine #1 may do the same amount of work as engine #2, but in half the time.
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Editor's Notes

  1. [CORRECT 5 ANSWER]