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Why Does the Lap Time Get Shorter Each Lap?

  1. Jun 14, 2016 #1
    • Member advised to use the homework template for posts in the homework sections of PF.
    This is a multiple choice question where no numbers or values are give; however, I sure it can be deduced through logic.
    The question: The mass in the race consists of the mass of the car and the mass of the fuel.
    The mass of the fuel decreases as the car completes its journey around the lap.
    Why does the lap time decrease with each consecutive lap.


    The question never stated that there was friction between the car and the track, so I assumed it wasn't the correct answer.
    Therefore, I managed to reduce it down to two solutions, those being
    Both the acceleration and deceleration increase
    The maximum velocity of the race car increases
    I've reasoned that the maximum velocity of the race must increase in order that momentum is conserved. However, some of my classmates have said that the other solution is correct.
    So, hopefully someone here can clear things up for me-thanks for any help!
     
  2. jcsd
  3. Jun 14, 2016 #2

    andrevdh

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    If the lap time decreased then it went faster with each lap. Why would it go faster for each subsequent lap? Surely the car's power didn't increase.
     
  4. Jun 14, 2016 #3

    CWatters

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    Find out what effects the maximum speed.
     
  5. Jun 14, 2016 #4
    As the mass of the fuel decreases, the mass of the fuel-car system also decreases. F=ma so, if the force from the engine is the same, it would have a larger acceleration.
     
    Last edited: Jun 14, 2016
  6. Jun 14, 2016 #5

    CWatters

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    Larger acceleration.
     
  7. Jun 14, 2016 #6
    Acceleration :smile:
     
  8. Jun 14, 2016 #7
    So, the correct answer would be both large acceleration and deceleration or just an increase in maximum velocity?
    The question seems that both hold true-but there can only be one.
     
  9. Jun 14, 2016 #8
    That's exactly what I'm trying to get my head around, but that's what the question said-it's poorly worded I think.
    I though it was just a basic system of decreasing mass type question, therefore momentum needs to be conserved.
    But yeah, if power was held constant, then the driving force would decrease which means the acceleration will also need to increase, therefore so will the speed in order to maintain a constant power. The thing is this means that both of them apply.
     
  10. Jun 14, 2016 #9

    CWatters

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    Earlier I suggested finding out what limits the maximum velocity. On short straights it might well be the acceleration. On long straights I believe it's air resistance/drag.
     
  11. Jun 14, 2016 #10

    CWatters

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    I'm not sure why you think this is a question about conservation of momentum? A light car accelerates faster but that's not due to conservation of momentum.
     
  12. Jun 14, 2016 #11
    What would affect the maximum speed other than air resistance? The question is paraphrased slightly as I do not have the paper with me currently, but the question never implied that there was any form of resistance, so I assumed there was none.
     
  13. Jun 14, 2016 #12
    OK, so would the deceleration decrease also?
    And why would momentum not be conserved if the system's mass decreases and the fuel move in an opposite direction to that of the car with some velocity, so the car's velocity will also need to increase to negate this change?
     
  14. Jun 14, 2016 #13
    Sorry, I meant to say would the deceleration increase also
     
  15. Jun 14, 2016 #14

    CWatters

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    What do you think? A car with less mass has less inertia so is it easier or harder to stop?.

    Only a rocket car pushes itself along by throwing fuel out of the back. All other cars work by pushing the ground backwards. Momentum is conserved but you have to take into account the effect the car has on the rotation of the planet. We could discuss this but conservation of momentum isn't relevant to this problem.
     
  16. Jun 14, 2016 #15
    I definitely agree that the final velocity increases, like you said because momentum in conserved. Intuitively the acceleration would also increase, but why would it decrease? And if acceleration decreases and increases why don't the effects cancel out? That one just doesn't make any sense to me, hopefully I'm not missing anything important.
     
  17. Jun 14, 2016 #16
    My thoughts are that it is easier to stop, since a smaller force is required to produce the same acceleration/deceleration
     
  18. Jun 14, 2016 #17
    So
    Yeah, it doesn't make sense to me. The thing I think is missing from a lot of these answers is that would both the acceleration and deceleration decrease.
     
  19. Jun 14, 2016 #18
    Sorry, would both increase.
     
  20. Jun 14, 2016 #19
    Yeah, my understanding of physics is only elementary at this point, I am a first year A-level student, this seems more like undergraduate level stuff. Regardless, it seems to me that this question in unanswerable as both potential answers apply to the situation.
     
  21. Jun 14, 2016 #20

    CWatters

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    Ok so I agree. A lighter car accelerates and decelerates faster than a heavy one.

    More in a moment.
     
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