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Translation motion question

Discussion in 'MCAT Study Question Q&A' started by kmcgrath, Jan 5, 2009.

  1. kmcgrath

    5+ Year Member

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    Please help...this problem below is bugging me and I cannot get to the correct answer (though known) going backwards or forwards. Could anyone, stepwise, walk me through it?

    Translational Motion:

    Q: Two different objects are dropped from rest off a 50-m-tall cliff. One lands going 30% faster than the other. The two objects have the same mass. How much more kinetic energy does one object have at the landing than the other?

    A: 69% more
     
  2. thatscorrect7

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    its way simple than i thought
    i tried a couple of equations, but it didnt work.
    try this

    A is moving at 13 m/s

    B is moving at 10 m/s

    13^2 = 169
    10^2 = 100

    1/2 m1v1^2 = 1/2 m2v2^2

    => v1^2 = v2^2

    diff is 70%
     
  3. swamprat

    Physician Classifieds Approved 10+ Year Member

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    nevermind!
     
  4. Charles_Carmichael

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    Yea, that's a pretty good way to go about it. The way I was looking at it was that for the slower object, KE = 1/2 mv^2 while for the faster moving object, the KE = 1/2 m (1.3v)^2.

    Since the velocity of the second object is 30% more than the first one, converting it to a decimal results in 1.3v (where v is the velocity of the first object).

    So if you do KE2/KE1 (where KE1 is the KE of the first, slower object and KE2 is the KE of the faster object), you'll get:

    [1/2 m(1.3v)^2] / [1/2 mv^2]

    This simplifies to 1.69/1 as the ratio of kinetic energies. So, the KE of the faster moving object is 1.69 times, or 69%, larger than the KE of the slower moving object.

    Hope this helps.

    Edit: So, the equation you use is still 1/2mv^2...the only thing that changes is the value of v. The v for object 1 is v and the velocity of object 2 is 1.3v. Remember when you square the velocity, the 1.3 gets squared also.
     
    #4 Charles_Carmichael, Jan 5, 2009
    Last edited: Jan 5, 2009
  5. Vihsadas

    Vihsadas No summer
    Moderator Emeritus Lifetime Donor Classifieds Approved 5+ Year Member

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    Yeah, you guys should try and get good at "short-cutting" these problems like Kaushik did above. If you do enough problems like this, you'll be able to get the answer in under 5 seconds. You'll eventually just think:

    Okay, KE goes like v^2.

    30% means a factor of 1.3 in v^2.

    1.3^2 = 1.69

    So it's 69% more energy.

    Practice and practice these shortcuts! You'll thank me later after your MCAT. :)
     
  6. kmcgrath

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    Thanks! Very simple. I made this entirely too difficult.
     

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