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Object sliding with friction into a spring Find compression

  1. May 13, 2012 #1
    1. The problem statement, all variables and given/known data
    A 1.18 kg block slides across a horizontal surface directly toward a massless spring with spring constant 5,803 N/m. The surface is frictionless except for a rough patch of length 0.42 m that has coefficient of kinetic friction 0.367. The initial velocity of the block is 2.49 m/s directed straight toward the spring. What is the maximum compression of the spring?

    What i obtained form the question:
    v0 = 2.49
    friction coefficient 0.367
    m=1.18
    d=0.42
    Spring constant = 5803


    2. Relevant equations
    W=Fd
    W=Δk
    k=1/2mv^2



    3. The attempt at a solution
    What I first did was find the knetic energy before the object hit the spring so i got
    kf = .5(1.18)(vf)
    ki = .5(1.18)(2.49)

    i replaced vf with the equation to obtain equation is vf^2 = vi^2 + 2ax

    kf = .5*(1.18)(2.49^2+2a(0.42))
    Now i have W=Fd which i made W=(1.18)(a)(.42)

    then i set the equations equal to each other

    .5(1.18)(2.49^2+2a(.42))-.5(1.18)(2.49)=(1.18)(a)(.42)

    solved for a = -1.029188469

    used this a to find vf = 2.309887808

    now i have the velocity it hits the spring with I then again brought back the work equation to find

    W = kf-ki since final knetific force is 0 i have
    W = -.5(1.18)vf^2 = Fd = ((-5803x)x)

    then i solved for x as 0.0232911326
    as demanded I entered 2.33 cm. But i was marked wrong. Can anyone help? That'll be greatly appreciated.
     
  2. jcsd
  3. May 13, 2012 #2
    You are getting confused with your initial and final velocities. You need to break your problem into two separate problems.

    I. Block slows down on friction section.

    II. Block compresses spring.


    The final velocity for section I will become the initial velocity for section II of the problem.
     
  4. May 13, 2012 #3
    That is what I did. If you follow my work.
    Is the procedures right? I did i simply do my math wrong?
     
  5. May 13, 2012 #4
    Ok, I think I found your mistake. In general, it's best to leave everything as variables and put numbers in at the end. otherwise, you end up with a jumble of numbers and no idea where they came from.

    You weren't allowed to do this step.

    ".5(1.18)(2.49^2+2a(.42))-.5(1.18)(2.49)=(1.18)(a)(.42)"

    The LHS is the kenitic energy after going through the rough patch. The RHS is the energy LOST to the friction.

    Go back to vf^2 = vi^2 + 2ax. You will use this to find the velocity after the rough section. However, you still need to find the acceleration. Look up your equations for the force of friction. you will use this equation and F=ma to get the acceleration.
     
  6. May 13, 2012 #5
    Thanks for the response, but I am a bit confused as to what to do, and what you said.
    First of all I'm curious as to why the RHS is the energy LOSt to friction.
    Secondly, to find the acceleration I assume i must make 1.18(a)*.42 = uk(N) which is

    1.18a(0.42)= 0.367(1.18)(9.8)
    is that correct?
    Once again thanks for taking the time to help me out.
     
  7. May 14, 2012 #6
    You're close, but you multiplied by the distance for some reason.

    We need to find the acceleration in the rough area. Start with Newton's Second law. We might as well solve for acceleration.

    F=ma.

    a = F/m

    In this area, we know that the force is being caused by friction.

    F = uN = umg

    Where u is the coefficient of friction and N is the normal force.

    Now plur this into the above equation.

    a = umg/m

    At this point, what can you do with the term for mass in the equation?

    Notice that I didn't type any actual numbers. When working a problem, keep all your numbers as variables untill the end.
     
  8. May 14, 2012 #7
    So I tried again using the a from that equation and I was still unfruitful. What I did was
    found a = ug

    vf = √(vi^2-2aΔx)

    i used the minus because when i used the plus the velocity actually went up, and i assumed because it was the deceleration caused by the friction it should be a negative number for a.

    and using that i have

    x = √(.5 *m *vf^2 /5986)

    the answer was still incorrect.
     
  9. May 14, 2012 #8
    I prefer to solve this kind of problem by work-energy theorem rather than kinematic.
    By work-energy theorem single equation can be formed to solve the problem.

    ΔKE +ΔPE= Work done.
     
  10. May 21, 2012 #9
    If you follow a simple law , the law of conservation of energy, you'll get the answer.
    The initial energy of object is 1/2mv^2.
    When it moves over distance "d" having friction force coefficient as "k", the friction force does the work and reduced its energy by same amount as work and is given by - mg*k*d.
    Finally the block will compress the spring and will come to rest, but since energy must be conserved, the energy must remain there.
    But actually what happens is that the energy gets stored in the spring as potential energy.
    This energy (given by 1/2kx^2, k is stiffness constant of spring ) is equal to energy left out with block after it crossed the distance with friction.
    Just do the mathematical calculations with these pictures in mind and you'll get the answer.
    Zubeen
     
  11. May 21, 2012 #10
    Yeah...I don't think there's any need to find acceleration.
     
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