6.6 Conservation of Mechanical Energy Racing Balls |
| Instructions: Click on the "Start Simulation" button to open the applet window. The applet is an illustration of a race between two balls following different paths. You start the simulation by selecting your guess from the pull-down menu. Note that the final vertical displacement is the same for both balls. Once the race is completed you should try to understand the result. You can get some help by selecting the "more information" checkbox. In this set-up the path is color-coded and the horizontal component of the velocity of each of the balls is shown. Navigation: You can come back to this window by pressing the "Close Simulation" button on the bottom frame of the utility. |
| Explanation: There is a distinction between asking about the final speed and asking about the time of travel. As explained in section 6.6 when discussing amusement park rides, the only factor affecting the final speed is the change in height. Since the vertical displacement is the same, we know that both balls will have the same final speed. However, to find the time of travel we will focus on the horizontal component of the velocity. The displacement along the horizontal dH is related to the average velocity along the horizontal vH and time t by: dH = vH t The ball with the larger average horizontal velocity arrives first. As shown in the velocity time graph made by the applet, the first ball accelerates for a short time then moves at a constant velocity. Except for a small region, the horizontal component of the velocity of the second ball is similar to the first. However, in the region of the path drawn in red, ball 2 accelerates beyond the maximum value reached by ball 1 then slows down to reach the final speed. Since the second ball never moves slower than the first, we can deduce that its average velocity along the horizontal is greater. Thus, it arrives first. |
| Source: Fu-Kwun Hwang Go to the web site and link to the Online Library for further information. |