Shifty Swings

Why does swinging your legs on a swing make you go higher?

This is a familiar scene for most people. At a playground, you sit on a swing and begin the movement without much thought. On the way up, you straighten out your legs. As you fall back down, your legs curl back close to the seat. This motion usually goes without saying. It just works. Today we will find out exactly why this method is effective.

We'll begin by talking about energy. Energy is difficult to define because different types of energy can be represented in different ways (Figure 2). Today, we will talk about two types of energy: kinetic and potential energy. Kinetic energy is associated with movement, but no movement is necessary for potential energy. These discrepancies actually make our definition of energy a simple one. Energy is purely an abstract mathematical concept. It's derived from an observation, the Law of Conservation of Energy, meaning that energy will always stay the same. Hence, all there is to know about energy is that, as a whole, it is constant.

Now let's take a closer look at the specific types of energy. The first is kinetic energy. This is the energy associated with movement, meaning the faster you move, the more kinetic energy you have. If you stand still, your kinetic energy is zero. The other type of energy to discuss today is gravitational potential energy. This is a harder concept to understand, but for today, it will suffice to have a rudimentary description. This type of energy can be interpreted as a measure of how much energy you've used to combat gravity. For instance, Imagine you hold a brick in your hands. If you lift it up by one foot, it's intuitive that you are going against gravity. Gravity pulls the brick down, but your arms overcome that force in order to push the brick up. During this process, energy leaves your muscles and is transferred into increasing the height of the brick. You can't tell that this brick has used that energy by any physical property in the brick (the brick has the same temperature and speed). Our method of defining the energy that the brick utilized is by its height. For any object to be at a great height, there once had to be some energy used to move it up there. This is what we define as gravitational potential energy, measured by an object's height (Figure 3). If the book falls down, that gravitational potential energy changes into kinetic energy as the brick picks up speed.

Figure 1

Figure 2

Figure 3

Now let's return to our scene with the swing and person. From our definition of energy, the system's total energy must always stay the same. This means that if we sum up the person's muscular energy, the swing/person's kinetic energy, and the swing/person's gravitational potential energy, it will stay constant throughout the entire process. Now let's walk through it all, beginning with a little push that the person gets from kicking the ground. Refer to Figure 4 to follow along. At point c, the person is moving at their maximum speed, with only kinetic energy. As they move higher to point d, some of the kinetic energy transfers to gravitational potential energy. Finally, at point e, all of the kinetic energy is translated to gravitational potential energy. When the swing switches directions of movement from up to down, there is a quick instant where the person isn't moving, meaning kinetic energy is 0. Since all of the energy goes to gravitational potential energy, this is the maximum height. On the way back down, this gravitational potential energy returns to kinetic energy and the cycle continues.

Now let's take a look at how the person's technique of swinging their legs is helpful (exemplified by Figure 5, notice the legs are extended at the top. It's easiest to observe at point e, the maximum height. We already know that this point has only gravitational potential energy, measured by height. When you tilt your legs up at the top, your body's average height is a little bit higher than it would have been if you sat normally. The tiny increase of this height, and hence gravitational potential energy, is now conserved in the system. The next time you come back to your maximum height, you would reach that new height without even kicking your legs. Now you may wonder where this extra tad of energy came from. It's from the chemical energy that was burned in the contraction of the person's leg muscles. Now let's look back at the process as a whole. The person begins with a small kick. Then, every time they reach the highest point, the tilt of their legs changes a bit of their body's energy into gravitational potential energy. With each swing back and forth, this energy accumulates as the person goes faster and reaches greater heights. Some food for thought exists in the situation itself. Without much time, a person could attempt to reach a maximum height by jumping off the swing. However, the extra possibility of time allows the person to harness their energy with a slow accumulation that gives the true maximum height. Without time, the person still had the capacity to exert that amount of energy, but slow and steady wins the race.

Figure 4

Figure 5