1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Block slides 4ft down a smooth plane & then slides on a rough surface (0.6) - s = ?

  1. Jun 21, 2006 #1
    The 30 lb box A is released from rest and slides down along the smooth ramp and onto the surface. Determine the distance s from the end of the surface to where the box stops. The coefficient of kinetic friction between the cart and the box is [itex]\mu_k\,=\,0.6[/itex].

    [​IMG]


    Here is what I have so far:


    [tex]-W\,\Delta\,y\,=\,(-30\,lb)\,(-4\,ft)\,=\,120\,ft\,lb[/tex]

    [tex]\sum\,F_y\,=\,N\,-\,W\,=\,0\,\Rightarrow\,N\,=\,W\,=\,30\,lb[/tex]

    [tex]\sum\,F_x\,=\,-f_k\,=\,m\,a_x\,\Rightarrow\,-\mu_k\,N\,=\,m\,a_x[/tex]

    [tex](-0.6)\,(30\,lb)\,=\,(0.932)\,a_x[/tex]

    [tex]a_x\,=\,\frac{-18.6}{0.932}\,=\,-19.3\,\frac{ft}{s^2}[/tex]

    Now what?

    I know I need to find [itex]v_f[/itex] and the bottom of the hill and I am probably supposed to use a work-energy equation?

    [tex]\sum\,T_1\,+\,\sum\,U_{1\,-\,2}\,=\,\sum\,T_2[/tex]

    Please help, thanks.
     
    Last edited: Jun 21, 2006
  2. jcsd
  3. Jun 21, 2006 #2

    Hootenanny

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Yes, as the ramp is frictionless the kinetic energy gained by the block will equal the work done by gravity; 1/2mv2 = mgh. A good point to note for future reference is that the velocity of the object is independent of the mass.
     
    Last edited: Jun 21, 2006
  4. Jun 21, 2006 #3
    Using that, I get this:

    [tex]V_f^2\,=\,2\,g\,h\,=\,2\,(32.2)\,(4)\,=\,257.6[/tex]

    [tex]V_f\,=\,\sqrt{257.6}\,=\,16.05\,\frac{ft}{s}[/tex]

    [tex]v\,=\,v_0\,+\,a\,t[/tex]

    [tex]0\,=\,16.05\,+(-19.3)\,t[/tex]

    [tex]t\,=\,0.832\,s[/tex]

    [tex]s\,=\,s_0\,+\,v_0\,t\,+\,\frac{1}{2}\,a\,t^2[/tex]

    [tex]s\,=\,0\,+\,(16.05)\,(0.832)\,+\,\frac{1}{2}\,a\,t^2[/tex]

    [tex]s\,=\,6.67\,ft[/tex]

    The real answer is 3.33 ft though! What did I do wrong?
     
  5. Jun 21, 2006 #4

    Hootenanny

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Your going to kick yourself for this one. You have calculated the distance travelled, not the distance from the end of the platform. HINT: What does 10 - 6.67 equal? :wink:
     
    Last edited: Jun 21, 2006
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Block slides 4ft down a smooth plane & then slides on a rough surface (0.6) - s = ?
Loading...