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## 05 February 2014

### Paper Football and a force exercise

Ever play Paper Football?  Only one student out of my 45 freshmen had not.  As today was our first day
back to school after the Superb Owl, my colleague Alex Tisch created a force-and-motion exercise based on the game of Paper Football.

How do you play:  You get four tries to tab the triangular "football" (pictured) across the table such that it comes to rest with part hanging off the edge of the table.  After scoring, a team may attempt an "extra point" by flicking the ball such that it becomes a projectile that soars between the "goalposts" created by the opponent's fingers.

What does this have to do with physics?  Consider the football in four situations:

(1) While your finger is in contact with the football during the tap
(2) After your finger loses contact, but while the football still slides forward
(3) When the football is in position for a score, at rest with part off the table's edge
(4) While the football is in the air during an extra point attempt

In each situation, students are asked:

(a) Draw a free body diagram of the football.
(b) What is the direction of the net force on the football?
(c) What is the direction of the football's acceleration?

This produces some fascinating responses.  This is a good exercise for continuing to bust silly misconceptions such as "the acceleration is to the right, because the football moves to the right."  But the four situations provide ample opportunity to work on advanced problem solving skills, too...

In situation (1), the acceleration direction must be determined through the motion (speeding up, so acceleration is forward).  Only then can the direction of net force be justified as the same as the acceleration.  Many students started with the net force being forward because "the force of the finger is greater than the force of friction."  But how do we know?  The problem never gives values, and there's no way to know a priori which horizontal force is bigger.  Only facts about motion and acceleration lead to the net force direction.

But in situation (2), only one horizontal force -- friction -- acts on the football.  So it's entirely legitimate to start with the direction of the net force straight from the free body diagram.  Then, the acceleration must be in the same direction as the net force.

These two similar situations must be approached with opposite-ordered logic.  Cool...

When a student finishes answering all four situations correctly, I hand him a paper football and assign him an opponent.  They play a game in the remaining few minutes of class.  Winners get candy...  Thanks to Alex for creating this activity.