Physics of pushing someone on a swing
Over thanksgiving break, I spent time with my entire family, and took my little cousin to the park. When I was giving her a push on the swings, I started thinking about how the physics of pushing someone on a swing are a lot like the physics of a pendulum. When holding my cousin up behind the swing as far as I could, there was only potential energy in the system, and when she reached the bottom of the swing she reached a maximum velocity and only had kinetic energy.
Treating the bottom of her push as the y=0 point
H1 corresponds to the swings height above the ground at its zero point, and h2 corresponds to the max height when I’m holding my cousin up over my head.
PE=mgh = (30 kg)(1.5 m)(9.8 m/s2)= 441 J
E1=E2 mgh= ½ mv2
The max velocity at the bottom of the swing is 5.4 m/s