The Physics of Superheroes: Spectacular Second Edition by James Kakalios Page A

bungee jumping even more inexplicable. Nevertheless, comic-book fans have long argued over whether it was indeed the fall or the webbing that killed Gwen Stacy. This question was listed as one of the great comic-book controversies (alongside whether the Hulk is stronger than Superman, and who is faster: the Flash or Superman 17 ) in the January 2000 issue of Wizard magazine. We now turn to physics to definitively resolve the question of the true cause of the death of Gwen Stacy.
    The central question we pose is: How large is the force supplied by Spider-Man’s webbing when stopping the falling Gwen Stacy?

PHYSICS AND THE FINAL FATE OF GWEN STACY
    To determine the forces that acted upon Gwen Stacy, we first need to know how fast she was falling when the webbing stopped her. In our previous discussion of the velocity required for Superman to leap a tall building in a single bound, we calculated that the necessary initial velocity v was related to the final height h (where his speed is zero) by the expression v 2 = 2gh, where g is the acceleration due to gravity. The process of falling from a height h with initial velocity v = 0, speeding up due to the constant attractive force of gravity, is the mirror image of the leaping processes that got him to the height h in the first place.
    Consequently we can employ the expression v 2 = 2gh to calculate Gwen Stacy’s speed right before she is caught in Spider-Man’s webbing. Assuming that Spidey’s webbing catches her after she has fallen approximately 300 feet, Gwen’s velocity turns out to be nearly 95 mph. Again, air resistance will slow her down somewhat, but as indicated in fig. 6, she is falling in a fairly streamlined trajectory. As we are about to discuss, the danger for Gwen is not the speed but the sudden stopping she’ll face when she hits the river.
    In order to change Gwen Stacy’s motion from 95 mph to zero mph, an external force is required, supplied by Spider-Man’s webbing. The larger the force, the greater will be the change in Gwen’s velocity, or rather, her deceleration. To calculate how large a force is needed in order to bring Gwen to rest before she strikes the water, we once again turn to Newton’s second law, F = ma . Recall that the acceleration is the change in velocity divided by the time during which the speed changes. Multiplying both sides of the expression F = ma by the time over which the speed decreases, we can rewrite Newton’s second law as:
    (FORCE) × (TIME) = (MASS) × (CHANGE IN SPEED)
    The momentum of an object is defined as the product of its mass and its speed (the right-hand side of the above equation). The product of (Force) × (time) on the left-hand side of this equation is called the Impulse. This equation, therefore, tells us that in order to change the momentum of a moving object, an external force F must be applied for a given time. The larger the interval of time, the smaller the force needed to achieve the same change in momentum.
    This is the principle behind the air bags in your automobile. As your car travels down the highway at a speed of, say, 60 mph, you as the driver are obviously also moving at this same speed. When your car strikes an obstacle and stops, you continue to move forward at 60 mph, for an object in motion will remain in motion unless acted upon by an external force (that outside force is coming up in an instant). In the days before seat belts and air bags, the steering column typically supplied this external force. The time your head spent in contact with the steering wheel was brief, so consequently, the force needed to bring your head to rest was large. By rapidly inflating an air bag, which is designed to deform under pressure, the time your head remains in contact with the inflated air bag increases, compared with the steering wheel, so the force needed to bring your head to rest decreases. Distributing the force over the larger surface area of the air bag also helps to reduce injuries in a sudden