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Physics - Pressure

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  • bonkysleuth's Avatar
    266 posts since Mar '07
    • Water of depth 10 m exerts a pressure equal to atmospheric pressure. An air bubble rises to te surface of a lake which is 20 m deep. When the bubble reaches the surface, its volume is 6cm3. What was the volume of the air bubble at the bottom of the lake?

       

      How do you solve this question?

       

       

  • jiaxing2's Avatar
    15 posts since Jun '08
    • p inversely proportional to  v ( same temp)

      p1v1=p2v2

      at bottom pressure = 3 p (atm) compared to 1 atm at the top

      thus V bottom = 6/3 = 2 cm3

       

  • Moderator
    Darkness_hacker99's Avatar
    31,715 posts since Jun '05
  • Moderator
    Darkness_hacker99's Avatar
    31,715 posts since Jun '05
  • bonkysleuth's Avatar
    266 posts since Mar '07
    • In that post Darkness_hacker99 mentioned, eagle posted the solution as this:

       

       

       at surface:
      pressure, P1 = 1atm (atmospheric pressure equivalent to 10m of water), V1 = 6cm3

      at bottom of lake:
      pressure, P2 = 3 atm (atmospheric pressure + 20m of water), V2 = unknown

      Using Bolye's Law, P1V1 = P2V2

      V2 = 2cm3

      But the thing is, I haven't learnt about this Boyle's Law thing. Nor have I heard of it. My brother tried to teach me using this method but he told me not to attempt this question since I havent been taught about the law before. why is P1 = 1 atm and P2 = 3 atm?

  • Moderator
    eagle's Avatar
    16,324 posts since Aug '01
    • the equation means this

      original volume multiplied by original pressure equals to final volume multiplied by final pressure

      or vice versa

      Do you understand the above part first? Understand then we proceed to the next step

  • Moderator
    Darkness_hacker99's Avatar
    31,715 posts since Jun '05
    • P1V1 = P2V2

      This formula is taught in your syllabus under the chapter Pressure:Pressure changes. icon_smile.gif

  • Moderator
    UltimaOnline's Avatar
    548 posts since May '05
  • bonkysleuth's Avatar
    266 posts since Mar '07
    • Originally posted by eagle:

      the equation means this

      original volume multiplied by original pressure equals to final volume multiplied by final pressure

      or vice versa

      Do you understand the above part first? Understand then we proceed to the next step


      So how do you get 1 atm and 3atm? I don't understand this because I havent learnt this before. But I am interested to find out.

  • bonkysleuth's Avatar
    266 posts since Mar '07
    • Oh yea and there's this question from the Ten Years series.

       

      2 cubes are made form the same material. one cube has sides that are twice as long as the other. standing on one face, the small cube exerts a pressure p = w/a, where a is the area of the face. what is the pressure exerted by the larger cube standing on ONE of its faces?

       

      I got this answer as 4p but the answer booklet writes 2p. can anyone explain?

  • Moderator
    eagle's Avatar
    16,324 posts since Aug '01
    • Originally posted by bonkysleuth:


      So how do you get 1 atm and 3atm? I don't understand this because I havent learnt this before. But I am interested to find out.

      1 atm is pressure at the water surface. That's because it is the air pressure.

      and at depth of 20m, the total pressure comes from 1atm (at water surface) + 20m of water. Since 10m of water = 1atm, that means total pressure = 3atm

       

  • Moderator
    eagle's Avatar
    16,324 posts since Aug '01
    • Originally posted by bonkysleuth:

      Oh yea and there's this question from the Ten Years series.

       

      2 cubes are made form the same material. one cube has sides that are twice as long as the other. standing on one face, the small cube exerts a pressure p = w/a, where a is the area of the face. what is the pressure exerted by the larger cube standing on ONE of its faces?

       

      I got this answer as 4p but the answer booklet writes 2p. can anyone explain?

      if the small cube has face area a, the large cube has area 4a.

      Also, if the small cube has weight w, the large cube has weight 8w, since weight is proportional to volume (same material means same density).

      Thus, pressure exerted by larger cube = 8w / 4a = 2 w/a = 2p

  • bonkysleuth's Avatar
    266 posts since Mar '07
    • Originally posted by eagle:

      if the small cube has face area a, the large cube has area 4a.

      Also, if the small cube has weight w, the large cube has weight 8w, since weight is proportional to volume (same material means same density).

      Thus, pressure exerted by larger cube = 8w / 4a = 2 w/a = 2p


      Thanks. But I somehow dont get this part:

       

      if the small cube has weight w, the large cube has weight 8w, since weight is proportional to volume (same material means same density).

      Thus, pressure exerted by larger cube = 8w / 4a = 2 w/a = 2p

       

      i still dont know why weight is proportional to volume. havent heard of that before.

       

  • Moderator
    eagle's Avatar
    16,324 posts since Aug '01
    • Originally posted by bonkysleuth:


      Thanks. But I somehow dont get this part:

       

      if the small cube has weight w, the large cube has weight 8w, since weight is proportional to volume (same material means same density).

      Thus, pressure exerted by larger cube = 8w / 4a = 2 w/a = 2p

       

      i still dont know why weight is proportional to volume. havent heard of that before.

       

      Ok.

      One of the ways to see it is:

      Weight is proportional to mass.
      Mass is proportional to volume (since mass = density * volume)

      Therefore, Weight is proportional to volume.

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