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!

Newton's Laws Problem- Question on upcoming TEST

  1. Oct 17, 2008 #1
    Newton's Laws Problem- Question on upcoming TEST!!

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

    A small block is placed at height h on a frictionless 30 degree ramp. Upon being released, the block slides down the ramp then falls 1.0 m to the floor. A small hole is located 1.0 m from the end of the ramp. From what height h should the block be released in order to land in the hole?

    [​IMG]


    2. Relevant equations
    Newton's Laws
    Kinematics Equations


    3. The attempt at a solution
    I did the problem assuming there would be no initial Y-velocity.
    And figured out the time it would take for the object to fall to the ground after leaving the ramp, and the X-velocity it would need to get to the whole.
    The time was .45 seconds and the X-velocity was 2.21 m/s.
    With that it should be really easy to find the time to get to that velocity, and then the height needed to start from....

    But I realized there would be an initial velocity in the y direction when it reaches the end of the ramp. I've spent nearly 3 hours trying to solve this problem, and it might be on an upcoming test. I have tried the problem with different axis, and I just can not figure it out. Please help, my test is this week!
     
    Last edited: Oct 17, 2008
  2. jcsd
  3. Oct 17, 2008 #2
    Re: Newton's Laws Problem- Question on upcoming TEST!!

    After leaving the plane, the block will have an unknown speed (S), which can be broken into x,y components. The x,y kinematics are:

    x - 1
    x0 - 0
    V - ?
    V0 - Scos(-30)
    a - 0
    t - t

    y - 0
    y0 - 1
    V - ?
    V0 - Ssin(-30)
    a - -9.8
    t - t
    (note: time will be the same in both)

    In both cases, V is what we don't care about. We then use x=x0+v0t+.5at2
    in the x case:
    1=0+Scos(-30)+.5(0)t2
    Solving for t gives t=1/Scos(-30)

    in the y case, with t-substitution:
    0=1+Ssin(-30)*1/Scos(-30)+.5(-9.8)(1/Scos(-30))2

    In the middle velocity term, S cancels out. Multiplying all known numbers as well as squaring the third term gives:
    0=1-.5774-6.5333/S2

    Solving for S gives S = 3.9319 m/s

    Now with a target final ramp speed, we can set up a 3rd kinematics equation for the slide. The acceleration will be modified from gravity: Slide force = 9.8*sin(30) = 4.9 m/s2.
    x - ?
    x0 - 0
    V - 3.9319
    V0 - 0
    a - 4.9
    t - ?
    We don't care about time in this one, so the equation we use is V2 = V02+2a(x-x0).
    3.93192=0+2*4.9*(x-0)
    Solving for x gives x=1.5775 m up the ramp. They said they wanted height and not ramp distance, so we find the y component of the ramp length: 1.5775*sin(30) = .78875 m 'high' on the ramp.

    Brutal!
     
  4. Oct 17, 2008 #3
    Re: Newton's Laws Problem- Question on upcoming TEST!!

    Yes! That was totally it. Brutal problem, indeed!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?