Physics of pushing someone on a swing

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

M=30 kg

H₁=.5 m

H₂=2 m

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 

V_max=5.4 m/s

The max velocity at the bottom of the swing is 5.4 m/s