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Force acting on an object

  1. Mar 10, 2016 #1
    1. The problem statement, all variables and given/known data

    http://imgur.com/WeZ2lSS

    If the image isn't clear, this is what it states:

    The speed of a particle of mass m increases at a constant rate as it moves along the path shown from location 1 to 2 and so on. The particle's speed is much less than c, the speed of light, throughout its motion.

    Problem:

    At which particle location/locations is the magnitude of the transverse component of the time rate of change of momentum ( mag. of dp / dt, perpendicular) the greatest?

    At which location is the magnitude of the net force acting on the particle smallest?


    2. Relevant equations

    F = dp/dt and F = mv^2 / r (I think)

    3. The attempt at a solution

    This question just stumped me during the exam. If the particle was speeding up at a constant rate, there was a constant force applied to it, but I do not understand how it goes tangential after a point and then makes a path with a smaller radius. Also, looking at the figure, since r was small and v was large at positions 3 and 4, I chose option E (3 and 4) for the first part since F perpendicular seemed the greatest there by mv^2/r. I also thought that since the path followed looks circular, the force experienced at 3 and 4 was the same. I do not understand how it could be circular if the speed at 4 was greater than the speed at 3.

    For the second part, I picked E (same at all points) since the speed was increasing at a constant rate and I figured this implied constant acceleration.
     
  2. jcsd
  3. Mar 10, 2016 #2

    haruspex

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    No. All that tells you is that the tangential component of the acceleration is constant in magnitude. The normal component of acceleration does not affect speed.
     
  4. Mar 10, 2016 #3
    Ahh, that makes a lot more sense. So for problem 1, since they are asking about the normal component of force, would that be the same at points 3 and 4 since the path is circular and the normal component of force would be the same at both points?

    And for problem 2, the least force would be at point 2 then since there is only a tangential component for the acceleration whereas at 1,3 and 4, there is also a normal component, and hence net force would be the vector sum of those 2. Is that right?
     
  5. Mar 10, 2016 #4

    SammyS

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    compare the centripetal force at 3 with that at 4.
     
  6. Mar 10, 2016 #5
    mv^2/r ... and v increases, which means there is a greater centripetal force at 4. Whoops! Looks like I messed up on this one :/

    Thanks guys!
     
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