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Collisions and relative energy loss

  1. Mar 12, 2012 #1
    1. The problem statement, all variables and given/known data
    I am working on a simulated lab in which we have a single particle projectile launched at a target particle (located at the center of the circular chamber) of similar weight. Once the collision takes place, I record the time it takes for the scattered projectile to travel the radius of the circular chamber AND the scattering angle of the projectile. The purpose is to calculate the mass, M, of the target. I am given the mass, m, of the projectile. Before the trials took place, I measured the crossing time that the projectile (before the collision) took to cross the radius of the chamber. I took this measurement several times and I used the average value. The projectile is launched at an unchanging constant speed each time.

    (a) I am being asked to find the largest and smallest relative energy losses among the ten collisions I studied. I know that [itex]KE=\frac{1}{2}mv^{2}[/itex] but I am not given the radius of the chamber, so I can't find the initial velocity of the projectile before the collision. Once the collision has taken place, I record the post-collision crossing time and the scattering angle of the projectile. My program then gives me a "V" and a ratio of "M/m" from the following formula:

    [itex]\frac{M}{m}=\frac{1+V^{2}-2V*cos\theta_{p}}{1-V^{2}}[/itex]

    where V=[itex]\frac{v_{p}}{v_{0}}[/itex]

    [itex]v_{0}[/itex] is the pre-collision speed of the particle, [itex]v_{p}[/itex] is the post-collision speed, and [itex]\theta_{p}[/itex] is the scattering angle.

    (b) I am also being asked to express the relative energy loss [itex]\delta[/itex] as a function of V. Here is the given formula for energy loss:

    [itex]\delta=\frac{E_{0}-E_{p}}{E_{0}}[/itex]

    (c) The previous two questions consider energy loss. But we have assumed that the energy is conserved in the collision. Is energy actually lost, and if not, where does it go?


    2. Relevant equations

    [itex]KE=\frac{1}{2}mv^{2}[/itex]

    [itex]\frac{M}{m}=\frac{1+V^{2}-2V*cos\theta_{p}}{1-V^{2}}[/itex]

    [itex]\delta=\frac{E_{0}-E_{p}}{E_{0}}[/itex]



    3. The attempt at a solution

    (a) I have no idea where to start on this part. I'm thinking that if I understood this part, the the question in part b might be easier...?

    (b) I am not sure where to start on this part because I don't know the radius of the chamber so I can't calculate the the velocities directly. I am, however, given the V for each trial run when I enter the scattering angle and crossing time post collision. I'm guessing that there is a way to use this V to figure out the relative energy loss, however, I can't see it. Can someone give me a clue?

    (c) I think that the energy is not lost because it is an elastic collision. If this is true, then the energy must be converted to some other type of energy??

    Please help. I apologize for the long post but I felt it was necessary to describe the experiment in complete detail. Thanks
     
  2. jcsd
  3. Mar 13, 2012 #2
    I think I may have figured out the answer to question (b)

    If [itex]\delta=\frac{E_{0}-E_{p}}{E_{0}}[/itex]

    and [itex]E_{o}[/itex] = Initial Kinetic Energy, which = [itex]\frac{1}{2}*m*{v_{0}}^{2}[/itex]

    then [itex]\delta=\frac{E_{0}}{E_{0}}-\frac{E_{p}}{E_{0}}[/itex] = [itex]1-\frac{E_{p}}{E_{0}}[/itex] = [itex]1-\frac{v_{p}}{v_{0}}[/itex] = [itex]1-V[/itex]

    Is this right? If so then part (a) should become pretty easy to calculate. Please let me know if you see any errors. Thanks
     
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