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anonymous

  • 4 years ago

a wooden block of mass 8 kg is tied to a string attatched to the bottom of the tank.In equilibrium the block is completely immersed in water. if relative density of wood is 0.8 and g=10m/s^2 then what is the value of tension in the string?

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  1. anonymous
    • 4 years ago
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    any 1 pleeeese help

  2. anonymous
    • 4 years ago
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    hey jamesj pleese help

  3. JamesJ
    • 4 years ago
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    There are three forces acting on the block of wood F_g = force of gravity (down) F_b = force of buoyancy (up) F_s = force from the string (down) The block is in equilibrium hence the sum of the three is zero. Use that to solve for F_s. The magnitude of F_s is the tension in the string.

  4. JamesJ
    • 4 years ago
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    Make sense?

  5. anonymous
    • 4 years ago
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    wow i am extremely convinced

  6. anonymous
    • 4 years ago
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    but for more convinciation can u pleese solve the problem for me

  7. JamesJ
    • 4 years ago
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    No ... I want you to take the next steps. What are expressions for \[ F_g \] and \[ F_b \] ?

  8. JamesJ
    • 4 years ago
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    F_g is particularly easy

  9. anonymous
    • 4 years ago
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    is f_g is mg?

  10. JamesJ
    • 4 years ago
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    yes

  11. anonymous
    • 4 years ago
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    so u dono the expressions?

  12. JamesJ
    • 4 years ago
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    I do know. Of course. But I want you to learn by doing, not watching.

  13. anonymous
    • 4 years ago
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    k pleese wait

  14. JamesJ
    • 4 years ago
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    To find F_b, go back to first principles and definitions The buoyant force is equal to the weight of water displaced. hence you need to find the weight of water displaced. The find the weight of water displaced, you'll need to find the volume of water displaced and multiply it by the density of water. Then to find the volume of water displaced ...

  15. anonymous
    • 4 years ago
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    buoyant force=weight of water displaced

  16. anonymous
    • 4 years ago
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    i.e F_b=mg

  17. JamesJ
    • 4 years ago
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    Ok, yes, where m here is the mass of the water displaced

  18. anonymous
    • 4 years ago
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    ya

  19. anonymous
    • 4 years ago
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    so now can u solve

  20. JamesJ
    • 4 years ago
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    We use rho, \( \rho \) for density. Hence you have by definition \[ \rho_{water} = \frac{m_{water}}{V_{water}} \] where V is volume. Hence \[ m_{water} = \rho_{water}.V_{water} \] Now find \( V_{water} \). It must be equal to \( V_{block} \). Hence you have to find \( V_{block} \). Use the same density principle. That's why the density of wood was given to you in the problem.

  21. anonymous
    • 4 years ago
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    so wat's the use of relative density

  22. JamesJ
    • 4 years ago
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    Tell me first what's the equation of the volume of the block?

  23. anonymous
    • 4 years ago
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    of cousre it is m/d

  24. anonymous
    • 4 years ago
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    d is the density

  25. JamesJ
    • 4 years ago
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    Hence \[ m_{water} = \rho_{water}.V_{water} \] \[ = \rho_{water} . V_{block} \] because the volume of water displaced must equal the volume of the block \[ = \rho_{water}.\frac{m_{block}}{\rho_{block}} \ \ \ \ \text{ by definition of density } \] \[ = \frac{\rho_{water}}{\rho_{block}}. m_{block} \] See what to do now?

  26. anonymous
    • 4 years ago
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    i cant understand the last equation

  27. anonymous
    • 4 years ago
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    k thanks for yor help iam really happy with the presence of u

  28. JamesJ
    • 4 years ago
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    what don't you understand about the last equation.

  29. anonymous
    • 4 years ago
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    no other guy was able to answer my qusetion

  30. anonymous
    • 4 years ago
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    i'll send u a frnd request in face book

  31. anonymous
    • 4 years ago
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    what is your fb username and i am nt big enough to misuse it

  32. JamesJ
    • 4 years ago
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    By definition \[ \rho_{block}/\rho_{water} \] is the relative density of the block, i.e., is equal to 0.8 Therefore \[ m_{water} = \rho_{water}/\rho_{block}.m_{block} \] \[ = (\rho_{block}/\rho_{water})^{-1}.m_block \] \[ = (0.8)^{-1}.m_block \] \[ = (5/4).m_block \] \[ = (5/4).(8 \ kg) \] \[ = 10 \ kg \] Now I want you to make an effort to finish the problem yourself, as I've now shown you 90% of it.

  33. JamesJ
    • 4 years ago
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    I should have written \[ m_{block} \] not \[ m_block \]

  34. anonymous
    • 4 years ago
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    wow wow wo o

  35. JamesJ
    • 4 years ago
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    I'm going to help someone else with a question. Try and figure it out while I'm gone. I'll keep an eye on what's going on over here.

  36. anonymous
    • 4 years ago
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    k by the way pleese tell yor fb username

  37. JamesJ
    • 4 years ago
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    No, I don't do that, sorry.

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