Force Needed for Child Toss

Since posting a piece on tossing a child in a swimming pool, I've gotten several flattering comments and e-mails from family, friends, and colleagues.  The consensus seems to be that though child tossing will never appear in the Summer Olympics, it is highly recommended as something fun to do in a swimming pool.  A few people asked that I compute the force I needed to propel my younger daughter into the air.  That is the subject of this post.

The animated GIF below shows the portion of my vacation movie that involves my daughter being pushed upward (click on the image for a larger view).

The red data points show the position of my daughter's left shoulder, which is the same reference I used in my previous post.  My daughter's weight is 37 lbs (165 N), which corresponds to a mass of 1.15 slugs (16.8 kg).  What a terrible name for a mass unit!  Using Newton's second law, I came up with the force plot you see below (click on the image for a larger view).

The force I applied to propel my daughter is on the vertical axis; time is on the horizontal.  During the nearly half second it took to launch my daughter, my maximum force reached about 70 lbs (311 N).  During the strongest part of my push, I shoved my daughter with a force roughly twice her weight.

One must be cautious with force calculations that originate with position/time data, as mine do.  Acceleration requires two time derivatives of position, and those derivatives must be calculated numerically.  That is why you see a large force for the first datum and a nonzero force for the last datum.  If I wasn't trying to propel my daughter, my force should be her weight.  But the graph's first datum shows a force about twice her weight.  The reason is that the first couple of times are left off because they are needed to compute the first force datum shown in the graph.   The force calculations for the data away from the edges in the above plot should be good.

Okay, that's enough about child tossing from me.  With the 100th Tour de France starting on Saturday, I've got plenty of other physics goodies to keep me busy!