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Check work on simple Energy problem

  1. Oct 9, 2009 #1
    1. The problem statement, all variables and given/known data
    A particle of mass m starts at rest and slides down a frictionless track as shown. It leaves the track horizontally, striking the ground as indicated. At what height h did it start above the ground?
    Image: http://tinypic.com/view.php?pic=2irb03r&s=4


    2. Relevant equations



    3. The attempt at a solution
    To find h, I started by equating the energies at the top and bottom as PE=KE, mgh=1/2mv^2, and to solve for the height, I needed to solve for the velocity, v, at the bottom.
    I used a kinematic equation for the y-direction(Vf^2=Vo^2+2ad) where Vo=0, Vf= vsintheta, a=g, and d=1.25m and solved for v^2. I then plugged this v^2 into my energy equation and solved h to be 3.2m.

    I am just wondering whether setting Vf=vsintheta was correct, assuming the velocity needed at the bottom is the total resultant velocity, not just the vertical component of it.
    Can someone please verify this and my work and answer as well?

    PS: I realize the value of theta is required for calculation and I have found that to be equal to 38.66 degrees using tan of theta

    Thank you PF community!
     
  2. jcsd
  3. Oct 9, 2009 #2

    drizzle

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    Gold Member

    there are 3 different velocities, not just two;

    the initial velocity Vo where the particle starts at rest, another one [say Vf1] where it leaves the track horizontally [that means the angle is…?] and the last Vf2 where it strikes the ground [note that the path this particle takes once it leaves the track is the projectile motion,‏where you treat Vf1 as an initial velocity].
     
  4. Oct 9, 2009 #3

    rl.bhat

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    Homework Helper

    When the particle leaves the track horizontally, its vertical velocity is zero. Horizontal velocity is, say v. Find the time t taken by the particle to reach the ground at the depth h1. Horizontal distance traveled by the particle is given. From that find v by using the formula v = d/t. Find the height h2 through which the particle must fall to have velocity v. Finally find h = h1 + h2
     
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