Playground physics

It’s spring, the time when a young girl’s (or boy’s) heart turns to thoughts of…swings, slides, and merry-go-rounds.

At least, that’s the case with the young girl I know best, my daughter Alice, who has been talking about playgrounds ever since the snow started melting.

I’m sure her desire to visit one is all part of the natural toddler’s urge to learn about physics, because your typical playground is full of the stuff.

Take the slide, for instance. This smooth inclined plane demonstrates the conversion of energy, the effects of gravity, plus friction and, for good measure, the second law of thermodynamics.

When you sit at the top of the slide, your body contains lots of potential energy, which is converted into kinetic energy when you push yourself onto the inclined portion of the slide. The energy comes from gravity, exerted by the Earth’s enormous mass. If there were no inclined plane, you’d accelerate at 9.8 metres per second per second. Because the inclined plane is between you and the ground, however, part of the force of gravity presses you onto the slide, leaving only a portion of it available to accelerate you toward the ground–so you slide less rapidly than you’d fall. The steeper the slide, the larger the component of the force of gravity that acts to pull you toward the ground, and the faster you descend.

Friction affects your speed, as well. Slides are made of very smooth material to minimize friction, so the biggest friction factor is usually what you’re wearing. Pants, especially slick ones, produce less friction than bare legs–which is why you’ll usually slide more slowly, or even get stuck, in shorts.

There’s another good reason to avoid shorts on slides. The second law of thermodynamics states that heat flows spontaneously from hot to cold–so a metal slide heated by the sun transfers its heat to you, while in winter, were you silly enough to slide in shorts, your legs would transfer heat to the slide. Neither sensation is pleasant.

Alice loves slides, but she loves swings even more. A swing is nothing but a pendulum, essentially a mass attached to a cord of some kind. Give the mass a push, and it oscillates.

A pendulum’s period, from highest point on one side to highest on the other, is determined solely by its length: neither the mass at the end of the pendulum nor how fast its moving changes the period. In other words, my almost-three daughter swinging slowly takes just as long to swing from one side to the other as a 12-year-old swinging as high as she can.

Swings also demonstrate the conversion of potential energy to kinetic, and vice versa. As a swinger nears the high point of the swing, more and more kinetic energy gets stored as potential energy. At the top of the swing, briefly all of the kinetic energy is stored as potential energy–and the swinger stops moving. Then gravity, which acted to slow the swinger as he or she neared the top of the swing, takes over and pulls the swinger back down toward the ground, and the potential energy is released as kinetic energy.

Pumping your legs adds energy produced by your body to the system to keep the swing moving. You lift your legs as you pass through the bottom of the swing’s arc, then drop them at the top of the arc. Each time you shift your centre of mass slightly, which creates a slight pushing force that makes the swing go higher.

Finally, consider the merry-go-round, which demonstrates rotational kinematics (in other words, it spins). You can stand easily at the centre of a merry-go-round, while at the outside edge you have to hang on for dear life. That’s because the outside edge of the merry-go-round has to travel further than the center in order to go once around the axis in the same amount of time, so it moves much faster.

Why do you have to hang on? Because Newton’s First Law of Motion says that an object moving in a straight line will continue to do so unless a net force acts upon it. In the case of a merry-go-round, that force comes from gravity (holding you to the merry-go-round), friction (between your feet and the merry-go-round) and possibly your own body (because you’re holding on). When that force becomes insufficient to keep us from obeying Newton’s First Law, we fly off the merry-go-round in a straight line.

So there you have it. The next time your tot goes to the playground, be sure to deliver a short physics lecture at each piece of equipment.

I’m sure your little one will find it most enlightening.

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