Re: What law of physics is represented by someone on a swing?

Amy,

The person on a swing primarily involves conservation of momentum 
(Newton's second law), which states "an object in motion will continue 
it's motion until acted on by an outside force."  The outside force is 
gravity.  
When starting at the highest point in the swinging motion, the person is 
stationary for a brief moment.  At this point they have no kinetic 
(moving) energy, but they have potential energy stored in the form of 
height.  The only force acting on them is gravity which pulls them 
downward and accelerates them.  As they lose altitude, they have less 
potential energy (height), but they are going faster because they have 
traded for kinetic energy.
When they are at the bottom of the swinging motion, they are moving as 
fast as they can because all the energy is now in the form of kinetic 
energy (momentum).  The ropes of the swing prevent them from going any 
lower, so they have no more potential energy.  Now as they start moving up 
the other side of their trajectory, they reverse the process and exchange 
kinetic energy for potential until they stop at the top and go back the 
other way.
On a side note, the reason you have to swing your legs to keep moving is 
to add energy back that gets lost due to wind resistance.  If you don't, 
each swing will get lower and lower until you stop.  This is still 
following the second law of motion, but accounts for both outside forces, 
drag and gravity.

The person being fired from a cannon is also using Newton's second law.  
In this case, when they come out of the cannon they start with lots of 
kinetic energy, but no potential energy (height).  When they hit the top 
of their trajectory, they have traded all of the upward component of their 
initial kinetic energy for the potential energy of being higher up.  
(However, 
because they get shot out at an angle, they still have almost all of their 
forward kinetic energy component since the only thing opposing that 
movement is wind resistance.)  Then gravity continues to accelerate them 
downward as the vertical component of the energy converts back to 
kinetic.  When they land, they should still have all of the energy they 
had when they came out of the cannon (except for losses to the air).

Hope this helps you out.
Todd