1) You are avoiding your physics homework by doing a little physics experiment on the swing set near your home. You make sure you pick a swing that has recently been greased so that friction will be minimal. By pumping your legs back and forth, you manage to get swinging from an initial height of about 4 feet above the ground (when the swing is at rest) to a maximum height of 5 feet above the ground. You estimate that the swing seat has a mass of about 2 kg. How much energy have you transferred into the swing seat?
2) When you've swung to about half the maximum height, how fast do you estimate you're moving?
3) You happen to remember someone telling you that for small enough angles, the function sin(x) is well approximated by the value of x. You realize that a frictionless swing acts a lot like a spring---the net force behaves like a restoring force. You estimate your swing's chain to have a length of about 17 feet. By thinking through the forces that yield a net force on you and the swing seat, and treating the angle that the swing's chain makes with the vertical as small, you try to develop a model of the net force from the swing as a simple restoring force. What would the associated restoring force constant be assuming your mass is about 70 kg?