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Collision with projectile and block attached to spring

  1. Nov 20, 2015 #1
    1. The problem statement, all variables and given/known data
    A projectile of mass m = 50g traveling at v0 = 20m/s hits a block of mass M = 450g. The block rests on
    a frictionless horizontal surface and is attached to a spring of force constant k = 2000N/m. The projectile
    ricochets backward off the block with speed v’ = 0.6v0. The collision lasts for 4ms.
    (In the picture, the spring is attached to the block and the wall)
    a) What impulse is delivered to the block and what is the average force for the collision?
    b) Is the collision elastic? Justify your answer.
    c) What is the maximum compression of the spring?
    d) Suppose the surface has a “small” coefficient of friction μk = 0.1. Estimate the total distance the block
    traverses from the moment it is struck to when it comes finally to rest. Why is this only an estimate? For
    such an estimate to be accurate what is the criterion for “small” friction coefficient?
    2. Relevant equations
    p=mv
    J=Δp
    fav= Δp/Δt
    KE=1/2mv2
    Us=1/2kd2
    (maybe?) vrel=-v'rel

    3. The attempt at a solution
    a)
    momentum: mv0=mv'+Mv2'

    impulse on block: J=Δp=p2-p1 --> p2= mv0 - mv' = .4mv0 = .4 N⋅s

    fav= Δp/Δt = 100 N

    b)
    KE= 1/2 m v2
    KE' +1/2mv'2+1/2Mv2'2

    KE'/KE = [m(.6v0)+M(v0-.6v0)2] / mv02

    =(.6)2 + (.450)(.4)2(.05) =>.40 --> 60% KE loss. non- elastic


    and this is where I am second guessing myself.
     
    Last edited: Nov 20, 2015
  2. jcsd
  3. Nov 20, 2015 #2
  4. Nov 20, 2015 #3

    haruspex

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    Can't follow your working if you make up variables like p1, p2 etc. and don't define them.
    Your answer to a) is wrong. Please explain your working in detail.
    For part b), how are you calculating v2'?
     
  5. Nov 20, 2015 #4
    a) While the idea is not wrong here, you have forgotten to take into account that momentum is a vector quantity, which means that direction is important. Hence, it is important to define what direction you will be taking as positive and stick with that convention throughout your working. A diagram will help you here if you have trouble visualizing.

    b) The problem that I mentioned above manifests in your working for part (b) as well. Look through the directions and signs of your vector quantities again.
     
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