Backwards or Forwards?

A tricycle, photographed below, is "fixed" so that the steering wheel will not turn and the tricycle can only move forward or backward along a line. A rope is attached to the pedal, and the wheel rotated so the pedal is in its uppermost position, as seen in the photograph. When the rope is gently pulled the tricycle moves in the forward direction (to the left), which can be verified in this MPEG movie.

Now suppose that the wheel is rotated so that the pedal is in its lowest position, as seen in the photograph below.

Graphic - Bicycle Photo

When the rope is gently pulled with the pedal in its lowest position, what will the tricycle do?

Solution

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Solution

The answer is (a): the tricycle will move in the same direction as when the pedal is up, the forward direction, as seen in this MPEG Video.

One straightforward way to see this is to consider the torque around the point of contact of the wheel with the tabletop. In both cases the torque is in the same direction: counterclockwise when viewed as in the photographs, causing the wheel to rotate counterclockwise about the contact point and therefore causing the tricycle to move forward.

A more thorough analysis of this motion can be made by employing a "pedal extender," which extends the pedal downward so that the force can be applied at radii less than, equal to, or greater than the radius of the wheel. These cases can be seen in the following MPEG videos: