Motion along different paths



Description

Two identical balls race down a slide along different paths as seen in the picture above. Which one will win - the one on the shorter, straight path or the one on the longer, curved path? If the velocities are equal and constant, the ball on the shorter path will take less time, but in order to deduce the correct path in our case, we need to examine the velocity and acceleration vectors of the balls when they are on the different paths.

When the acceleration vector is in the direction of the velocity vector of an object, that object will speed up (the velocity increases). Notice in the picture above that when the two balls first start out, the vector representing the acceleration due to gravity (g) is nearly in the same direction as the velocity vector of the ball on the curved track. However, it is oriented as some angle with respect to the velocity vector of the ball on the straight track. This means that the component of the acceleration in the direction of the velocity is GREATER for the ball on the curved track compared to the ball on the straight track. This means that the ball on the curved track speeds up more than the ball on the straight track.

A movie of the race shows that the extra speed allows the ball on the curved track to win the race even though it travels a farther distance.





Questions/Exercises:
  1. What kind of motion do you get when the acceleration vector is pointing in the opposite direction of the velocity vector?
  2. In what directions are the acceleration and velocity vectors pointing for a ball that is thrown straight up in the air?
  3. In what directions are the acceleration and velocity vectors pointing for a ball that is dropped?



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Please direct all comments or suggestions to Dr. David Tedeschi via e-mail.
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