Average Velocity and Angle of Inclination of a Slope

  1. What is the relationship between a ball rolling down a slope (ramp) and its average velocity.

    I know we are supposed to use: v^2 = ut + at/2 and F = mgsin(degree). But assume initial velocity is zero.

    Also if I do an experiment and I get results (make a graph between average velocity and cosine or sine of angle) how can I find the frictional force found within the slope? I'll know there is an error (friction) as the graph is linear but nor propotional.

    Thanks!
     
  2. jcsd
  3. jedishrfu

    Staff: Mentor

    It seems that this is an ideal problem and thus friction would be zero by definition.
     
  4. Sorry I should have clarified. I did an experiment with the aim of finding the relationship between average velocity and the angle of inclination. It turned out the average velocity squared was linear but not proportional (there was an y-inc).

    Given my data, how do I find out the frictional force acting on the ball? What equations and how can I solve this?

    Thanks
     
  5. jedishrfu

    Staff: Mentor

    You could compare the ideal case with your actual data and from the difference compute the magnitude of the frictional force.
     
  6. Ahh good thinking... However someone, in another forum, suggested this (attached) in finding the frictional force. Thoughts?
     

    Attached Files:

  7. jbriggs444

    jbriggs444 1,799
    Science Advisor

    So, as I understand this, you have raw data giving elapsed time versus angle for a ramp with a known length. From this you have computed average velocity (where the "average" is an average over time) and plotted average velocity squared versus (sine of?) angle. The theoretical expectation is that velocity squared will be proportional the sine of the angle. The graph approximately agrees with this. It is a straight-line graph. But extrapolating back to a zero angle yields a negative value for velocity squared.

    One model for this would be to assume that the primary error contribution is from rolling resistance and look for the point where the extrapolated graph crosses the x axis. This is the point where rolling resistance would be equal to friction so that velocity would be constant and zero.

    Given the angle where acceleration is zero, it is a simple high school physics exercise to compute the required rolling resistance.
     
  8. [//]
     
  9. You are correct in your assumptions. Your suggestion is actually much easier than having to compare the expected vs actual hundreds of times in excel, I didn't think of that.

    Alright, so lets say that the x-inc happens to be sin (0.2). I would just use that, and gravity on earth (9.81ms^-2, to simply calculate the frictional force? Correct? If so, thanks!

    What are your thoughts on the snapshot I attached above? It seems like an alternative to calculating the frictional force; although your method seems much easier.
     
  10. jbriggs444

    jbriggs444 1,799
    Science Advisor

    The figure I was calculating was rolling resistance. The figure that you seem to be intent on calculating in the middle of that snapshot as F is the force of static friction, i.e. the force that causes the ball to increase its rotation rate and retards its descent rate. Those are two completely different numbers -- apples and oranges.

    The bottom portion of the snapshot seems to conclude that g is 13.6 m/sec2. But I think that ignores static friction/the moment of inertia of the ball.
     
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