Dynamics: Finding force exerted on a box traveling down a slope

  1. 1. The problem statement, all variables and given/known data

    This is problem 13.70 from Beer and Johnston Vector Mechanics 9th ed.

    A 300-g pellet is released from rest at A and slides with friction
    along the surface shown. Determine the force exerted on the pellet
    by the surface (a) just before the pellet reaches B, (b) immediately
    after it has passed through B.

    The drawing shows a pellet A on a declining slope, distance 1.2 m to B which is almost at the bottom of the slope. C is a flat surface. The radius of curvature between B and C is 0.8 m and the angle between them is 30°

    2. Relevant equations

    PE = mgz
    KE = 1/2mv2
    Fr = muk*N
    Energy from Fr = FrΔx

    3. The attempt at a solution

    Since the pellet is at rest KEA = 0J, however PEA = (.3kg)(9.81m/s2)(1.2sin(30°))
    (The angle between the horizontal and the 1.2m hypotenuse isn't given, but I just found it using opposite interior angles.)

    so PEA = 1.7658 J

    At B we will have KE and PE. Assuming C is at z = 0m we can use the radius of curvature and angle given to find zb

    zB = 0.8 m - 0.8 m * cos(30°)
    zB = 0.10718 m

    so PEB = (.3kg)(9.81m/s2)(0.10718 m)
    PEB = 0.31543 J

    KEB = 1/2(.3 kg)vB2

    Plugging all of this into the law of conservation of energy where EA = EB

    1.7658 J = 0.31543 J + (1/2)(.3 kg)vB2
    vB = 3.109 m/s

    I got hung up here because I think that the work due to the frictional force should be subtracted from KEB + PEB in order to get the correct velocity the pellet would be traveling at. However, there is no coefficient of friction given in the problem.

    I feel like I'm just missing something small here and my brain is just dead..
     
  2. jcsd
  3. Would you sketch this?
     
  4. It is problem 13.70
     

    Attached Files:

  5. jhae2.718

    jhae2.718 1,160
    Gold Member

    From my reading of the problem, you're supposed to solve for the friction force on the block at the given points.
     
  6. Our teacher just posted an announcement that the problem should be a pellet sliding without friction.

    The answer is 2.55N, I'm just unsure how to get here..
     
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