The Physics Of a Swing

What makes a swing...........swing????
We start from rest and then begin to pump our legs.  This helps us build momentum which makes the swing take us higher.
Opposing this force is gravity which pulls the swing back toward the ground on its downward path.
At the two peaks, the swinger has potential energy and when the swing is in motion, the swinger has kinetic energy.  When the swing moves from the lowest point up to either peak, the main force acting is momentum; and when the swing falls from either peak to its lowest point, the main force acting is gravity.  If you do not pump your legs fast enough, air resistance along with gravity will keep you down.
So, the harder you pump your legs, the higher you will go!  And when you are done swinging, stop pumping and let gravity take you down.

The kid on the right has a lot of momentum!                                                                                 When playing on a swing set, you are really working a pendulum.

When sitting stationary on the swing, like the kid on the left, the only force acting is gravity, and there is tension coming from the chains connected to the swing.  As momentum builds, the swing......swings and the forces acting on the swing look like figure 2.  Where m = mass g = gravity, T = tension, and F = the force due to pumping your legs.
Figure 1                                                                          Figure 2