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Several step problem

  1. Oct 15, 2008 #1
    1. The problem statement, all variables and given/known data

    Consider the track shown in the figure. The section AB is one quadrant of a circle of radius r = 2.0 m and is frictionless. B to C is a horizontal span 3.3 m long with a coefficient of kinetic friction µk = 0.25. The section CD under the spring is frictionless. A block of mass 1 kg is released from rest at A. After sliding on the track, it compresses the spring by 0.20 m.

    a)Determine the velocity of the block at point B.
    b)Determine the thermal energy produced as the block slides from B to C.
    c)Determine the velocity of the block at point C.
    d)Determine the stiffness constant k for the spring.

    2. Relevant equations

    http://www.webassign.net/gianpse3/8-32alt.gif

    3. The attempt at a solution
    I am not sure how to begin. I know the conservation of energy equation comes in to play....
     
    Last edited: Oct 15, 2008
  2. jcsd
  3. Oct 15, 2008 #2
    At first, there is only potential energy. Once at the bottom, it has all turned to kinetic energy. These energies will be equal.

    Potential = 9.8*Mass*Height
    Kinetic = 1/2*Mass*Velocity2

    This allows you to solve for velocity. Once on the track, it will experience a deceleration due to friction, with no other horizontal forces acting on it, seemingly. Friction force = normal force*coeff of friction. Turn the friction force into an acceleration and use kinematics to find it's final velocity. At the spring, use the velocity to find it's kinetic energy again. Energy and work interchange, and the work to compress a spring is 1/2*Spring constant*Compression distance2

    What is the ultimate question?
     
  4. Oct 15, 2008 #3
    Consider the track shown in the figure. The section AB is one quadrant of a circle of radius r = 2.0 m and is frictionless. B to C is a horizontal span 3.3 m long with a coefficient of kinetic friction µk = 0.25. The section CD under the spring is frictionless. A block of mass 1 kg is released from rest at A. After sliding on the track, it compresses the spring by 0.20 m.

    a)Determine the velocity of the block at point B.
    b)Determine the thermal energy produced as the block slides from B to C.
    c)Determine the velocity of the block at point C.
    d)Determine the stiffness constant k for the spring.

    Sorry, I forgot the actual questions in the first post.
     
    Last edited: Oct 15, 2008
  5. Oct 15, 2008 #4
    I have been trying to solve this all night and have gotten this far:

    a) V=square root of 2(9.8m/s^2)(2m) V=6.26m/s
    b) (.25)(9.8m/s^2)(3.3m)(1kg)=8.09 J
    c) 1/2(1kg)V^2-1/2(1kg)6.25m/s)=0 V=2.50m/s
    Are these correct? How do I do part d. I know part d involves 1/2(-k)x, but I am not sure what information is important form parts a, b, and c.
     
    Last edited: Oct 15, 2008
  6. Oct 16, 2008 #5
    It worked out, thanks for the pointers ;)
     
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