The physics of rah-rah

Classical Mechanics Level 5

Cheerleaders at sporting events will often use a bullhorn to make themselves louder. A bullhorn is simply a hollowed out cone - you speak into the narrow end and your voice comes out the wide end, channeled by the cone so it is louder than it would be otherwise. At a sporting event, a cheerleader holds a bullhorn up to their mouth as in the figure below. The very tip of the bullhorn rests on their mouth and they use their hand on the other end to hold the bullhorn horizontal and still. We model the bullhorn as the rigid 2-d hollow cone of horizontal length \(0.75~\mbox{m}\), opening angle \(30^\circ\), and (surface) mass density of \(0.4~\mbox{kg/m}^2\) (see figure). How much force in Newtons does the cheerleader exert at point A?

Details and assumptions

  • You may take \(g\) to be \(9.8~\mbox{m/s}^2\).
  • Assume the force at point A is directed straight up.

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