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Simple and basic momentum and work done Qs!

  1. Mar 10, 2012 #1
    Mr Green, mass 80 kg, stepped off a boat of mass 35 kg at a speed of 3m/s. how fast did the boat move in the opposite direction?
     
  2. jcsd
  3. Mar 10, 2012 #2
    As this sounds like a homework problems I'll just give you a few hints abut the problem.

    Conservation of momentum for the total system states that the momentum before and after must be equal as there are no external forces acting upon the system.

    So before he steps off as I'm assuming the boat is at rest, the total momentum of the system will be 0.

    So after the man steps off the boat his momentum will be equal and opposite to that of the boat as the 2 momentums will cancel out to be zero.
     
  4. Mar 10, 2012 #3
    thanks which formulae do i use?

    m = mass x v

    or

    mom before = mom after

    ?
     
  5. Mar 10, 2012 #4
    You can use either but probably working out the momentum of the man using p = m * v, then use that value of p to work out the momentum of the boat, v = m / p. If you were working out the velocity of the boat afterwards you would need to make momentum negative but as it only asks for the speed you can keep momentum positive.
     
  6. Mar 10, 2012 #5
    is this correct?

    80 x 3 = 240

    80/240 = 0.3 (which is the velocity) so it's 0.3m/s^2
     
  7. Mar 10, 2012 #6
    please help
     
  8. Mar 10, 2012 #7
    Sorry I made a mistake rearranging the formula for velocity.

    It should be v=p/m

    Your calculation for the momentum is correct and you should get the right answer if you use the right formula for the velocity.
     
  9. Mar 10, 2012 #8
    how can it be 3m/s^2 because that ids already given in the question.

    i think i remeber my teacher saying that it's: 80 + 35= 115
    115 x 3 = 375
    375/35 = 1.3...m/s

    is that correct?
     
  10. Mar 10, 2012 #9
    Thats how you would calculate the initial momentum for the system as the 2 masses are together and have the same velocity.

    Initial momentum for the system = m * v = (80 + 35) * 0


    Then you need to treat the 2 masses separate for the after stage as the 2 masses are not together anymore and will be moving in opposite directions (Newtons 3rd Law)
     
  11. Mar 10, 2012 #10

    ok thanks so what would i have to do to find how fast the boat moved in the opposite direction?
     
  12. Mar 10, 2012 #11
    Work out the momentum for Mr Green.

    p = m * v

    Then use this value as the momentum for the boat (You can ignore the fact it should be opposite as we are only working out speed not velocity) Rearrange the momentum formula to work out velocity (or speed in this case).

    p = m * v
    v = p / m
     
  13. Mar 10, 2012 #12
    3 m/s is it squared but how can that be the answer when it's already written in the question?
     
  14. Mar 10, 2012 #13
    For the second step you need to use the mass of the boat.
     
  15. Mar 10, 2012 #14
    so it's 240/35 ? = 6.9m/s is that the final answer and it's not squared?
     
  16. Mar 10, 2012 #15
    did i get the question right?
     
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