The Physics of Superheroes: Spectacular Second Edition by James Kakalios Read Free Book Online Page B

each other (which are simply devices to measure a force, namely, your weight due to gravity). When they press against each other’s scale, no matter how hard Superman pushes on the left, if they remain stationary, then the Hulk’s scale on the right will read exactly the same force. Moreover, no matter how hard Superman is pushing, his scale will read zero pounds of force if the Hulk offers no resistance and just moves his scale out of the way and steps aside. 11 Forces always come in pairs, and you cannot push or pull on something unless it pushes or pulls back. When you stand on the sidewalk, your feet exert a force on the ground due to gravity pulling you toward the center of the Earth. People on the opposite side of the planet do not fall off because gravity pulls everyone in toward the center of the planet, regardless of where they are located. You do not accelerate while standing; the ground provides an equal and opposite force exactly equal to your weight. During the brief moment when Superman jumps, his legs exert a force greater than just his normal standing weight. Because forces come in pairs, his pushing down on the pavement causes the pavement to push back on him. Thus, he experiences an upward force lifting him up and away.
    And that’s it—all of Newton’s laws of motion can be summarized in two simple ideas: that any change in motion can only result from an external force ( F = ma ), and that forces always come in pairs. This will be all we need to describe all motions, from the simple to the complex, from a tossed ball to the orbits of the planets. In fact, we already have enough physics in hand to figure out the initial velocity Superman needs to leap a tall building.

IN A SINGLE BOUND
    Superman starts off with some large initial velocity (fig. 4). At the top of his leap, a height h = 660 feet above the ground, his final velocity must be zero, or else this wouldn’t be the highest point of his jump, and he would in fact keep rising. The reason Superman slows down is that an external force, namely gravity, acts on him. This force acts downward, toward the surface of the Earth, and opposes his rise. Hence, the acceleration is actually a deceleration, slowing him down, until at 660 feet, he comes to rest.
    Imagine ice-skating into a strong, stiff wind. Initially you push off from the ice and start moving quickly into the wind. But the wind provides a steady force opposing your motion. If you do not push off again, then this steady wind slows you down until you are no longer moving and you come to rest. But the wind is still pushing you, so you still have an acceleration and now start sliding backward the way you came, with the wind. By the time you reach your initial starting position, you are moving as fast as when you began, only now in the opposite direction. This constant wind in the horizontal direction affects an ice-skater the same way gravity acts on Superman as he jumps. The force of gravity is the same at the start, middle, and highest points of his leap. Since F = ma , his acceleration is the same at all times as well. In order to determine what starting speed Superman needs to jump 660 feet, we have to figure out how his velocity changes in the presence of a uniform, constant acceleration g in the downward direction.

    Fig. 4. Panel from Superman # 1 (June 1939) showing Superman in the process of leaping a…well, you know.
    As common sense would indicate, the higher one wishes to leap, the faster the liftoff velocity must be. How, exactly, are the starting speed and final height connected? Well, when you take a trip, the distance you travel is just the product of your average speed and the length of time of the trip. After driving for an hour at an average speed of 60 mph, you are 60 miles from your starting point. Because we don’t know how long Superman’s leap lasts, but only his final height of h = 660 feet, we perform some algebraic manipulation of the definition of acceleration as the