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Math Help - Ball rolling on ramp

  1. #1
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    Ball rolling on ramp

    Consider the motion of the red ball in the figure. Ignore friction and all other losses. The ball accelerates down under the action of gravity, it travels over the 6-m horizontal segment at constant speed, and then decelerates while moving up the incline on the right.

    If the value of the inclination angle is as given below, calculate the time it will take for the red ball to cover the entire distance from left to right.

    http://micko.dyndns.org/canyon.jpg
    Theta = 16

    Can someone show me how to solve this please. It seems trivial, however I think I am missing a small detail
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  2. #2
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    Quote Originally Posted by m_i_k_o View Post
    Consider the motion of the red ball in the figure. Ignore friction and all other losses. The ball accelerates down under the action of gravity, it travels over the 6-m horizontal segment at constant speed, and then decelerates while moving up the incline on the right.

    If the value of the inclination angle is as given below, calculate the time it will take for the red ball to cover the entire distance from left to right.

    http://micko.dyndns.org/canyon.jpg
    Theta = 16

    Can someone show me how to solve this please. It seems trivial, however I think I am missing a small detail
    I'm not an expert in physics - so check my considerations and calculations!
    1.
    • v = a \cdot t
      F=m \cdot a
      a = g \cdot \sin(16^\circ)
      d = \dfrac12 \cdot a \cdot t^2


    2. The height of the ramp is h = 3 \cdot \tan(16^\circ). Use Pythagorean theorem to calculate the length of the ramp. I got l \approx 3.121\ m

    3. Using the formula for d I got t \approx 1.52\ s as the acceleration time. Since the motion is symmetric this is the time for deceleration too.

    4. The speed of the ball at the foot of the ramp is v \approx 4.11\ \frac ms. With this speed the ball needs 1.46 s to pass the 6 m horizontal distance.

    5. The total time of the complete movement is therefore 4.5 s.
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