Physics

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Physics  2201  Homework  III  part  2.  Fall  2015.  Due:  Tuesday  November  17,  2015      Show  all  work  with  clear  setup  and/or  explain  all  answers.  All  solutions  must  be   based  on  work  and/or  energy  methods.  10  points  each.  Partial  credit  is  available.       1)  A  1.4  kg  falling  object  (subject  to  the  effects  of  aerodynamic  drag)  is  1800  m  high,   traveling  at  34  m/s  and  has  not  yet  reached  terminal  speed.  It  first  reaches  terminal   speed  at  a  height  of  1340  m  and  the  terminal  speed  is  37.3  m/s.     a)  Determine  if  the  mechanical  energy  (

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E = K + Ug)  of  the  system  consisting  of  the   falling  object  and  Earth’s  gravity  field  has  been  conserved  during  the  fall  from       1800  m  to  500  m.   b)  How  much  work  (if  any)  including  the  correct  sign  (+  or  -­‐)  has  been  done  on  the   system  over  this  interval  (presumably  by  the  external  drag  force)?   c)  Will  the  energy  of  the  system  consisting  of  the  object,  the  gravity  field  and  the   surrounding  air  be  conserved  over  this  interval?  Explain  your  answer.  Is  there  an   additional  energy  that  must  be  accounted  for  in  this  analysis?    What  is  it  and  how   much  of  it  has  been  generated?  Note:  terminal  speed  is  a  constant  speed.     2)  The  0.2  kg  box  below  slides  down  a  curved  ramp,  jumps  a  small  gap  and  lands  on   a  flat  platform.  At  the  point  on  the  ramp  shown  it  is  1.5  m  above  the  floor  and  its   speed  is  2.0  m/s.  At  the  point  shown  on  the  platform  the  box  is  0.4  m  above  the  floor   and  sliding  at  4.2  m/s.     a)  If  we  consider  a  system  consisting  of  the  box  and  Earth’s  gravity  field  so  that  

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E = K + Ug ,  has  the  energy  of  this  system  been  conserved  during  the  described   process?  Explain  how  you  know.   b)  If  we  consider  the  exact  same  process  but  broaden  our  system  definition  so  that    

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E = K + Ug + Eother  and  

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Eother  includes  any  “other”  form  of  energy  that  might  have   been  produced  through  the  process  (most  of  it  is  thermal),  what  objects  are  included   in  this  system?  Discuss,  don’t  just  state  a  list.     c)  Determine  

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ΔEother  for  the  process  as  described.   d)  How  much  kinetic  energy  would  the  box  have  on  the  platform  if    

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ΔEother = 0  ?  

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3) The system below consists of two masses attached through a string of negligible mass over a pulley that turns with negligible friction.

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m1 > m2 and the sphere

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m2 is immersed in a viscous fluid that exerts a considerable drag force. Starting from rest the system is set into motion by releasing

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m1 which causes this mass to descend while the other rises (assume the string instantly becomes taut). In what follows analyze the motion by defining the “system” as both masses and Earth’s gravity field.

a) Once released each mass travels a distance

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h1 and somewhere during this interval both masses reach terminal speed

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VT . Write out (derive/formulate) a mathematical expression for the change of the potential energy of the system over this interval (Using the givens! Don’t make up numbers or define your own variable names.) Has the system gained or lost potential energy? Explain how you know. b) Write out (derive/formulate) a mathematical expression for the change in the kinetic energy of the system over the

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h1 interval (using the givens). Write out an expression for the work done by the drag force over this interval using the givens. c) Following the

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h1 interval the system moves a distance

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h2 while the sphere is still immersed in the fluid. Write out an expression for the work done by the drag force over this interval. Can you tell from this expression if the work done by drag is positive or negative? (You should.) Which is it and how do you know? d) If

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h1 = h2 over which interval does the drag force do more work in an absolute value sense? How do you know?

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4) A 48 kg diver jumps off a cliff (with a running start) into the ocean. The cliff is 50 m above the ocean below. Her coach, using a video of the dive, determines that at a point in flight when she has risen 0.7 m above the cliff, her speed1 (center of mass) is 0.5 m/s. Frictional effects such as drag are negligible. Formulate your solution using the diver and Earth’s gravity field as a system. Gravity does not do work on this system. It’s effects are captured in changes in potential energy. a) How much kinetic energy did she have at takeoff? What was her speed? b) How much kinetic energy will she have as she splashes into the ocean? c) What minimum amount of chemical energy needed to be consumed within the diver’s body in order for her to walk to the cliff, from ocean level, and then take off (jump)? Explain how you know.

1 Includes both x and y velocity components. This is not the highest point in the jump.